ENH: Improvements to new ARIMA-type estimators

[ChadFulton]

Collection of follow-ups to #5827. These can/should be broken out into individual PRs. Many are relatively straightforward and would make a good first PR.

General

• Documentation (none was added in original PR).
• Release notes.
• Example notebook.
• Double-check how sm.tsa.arima.ARIMA works with fix_params (it should fail except when the fit method is statespace).
• Estimators that do not support seasonal models per se should support models where the only seasonal part is seasonal differencing.

GLS

• Add support for fixed parameters
• Improve "Returns" documentation for other_results.
• Add documentation for why we have e.g. include_constant but not other trend specifications (e.g. that it is to maintain consistency with estimation methods with assumptions that require demeaned series).
• Fix the following test and put it back into the GLS test suite:

@pytest.mark.low_precision('Test against Example 6.6.3 in Brockwell and Davis'
                           ' (2016)')
# @pytest.mark.xfail(reason="Source appears to find suboptimal parameters")
def test_brockwell_davis_example_663():
    # TODO: the parameters described by BD appear to be suboptimal (based on
    # llf computed from state space form), so that this test fails. Should try
    # to confirm with ITSM2000 (i.e. see if we can get it to find better
    # parameters closer to what we find, or compare llf, or something).
    # TODO: quite a slow test, and xfail anyway due to finding better
    # parameters...
    # Get the data, perform seasonal differencing
    endog = sbl.diff(12).iloc[12:]

    exog = pd.Series((sbl.index > '1983-01-01').astype(int),
                     index=sbl.index).diff(12).iloc[12:]

    res, _ = gls(endog, exog, order=(0, 0, 12), max_iter=3)

    assert_allclose(res.exog_params, -328.45, atol=1e-2)
    assert_allclose(res.ma_params,
                    [.219, .098, .031, .064, .069, .111, .081,
                     .057, .092, -0.28, .183, -.672], atol=1e-3)
    assert_allclose(res.sigma2, 12581, atol=1)

Hannan Rissanen

• Better warnings / errors when series are short relative to lag length
• Add support for fixed parameters
• Seems like we could add support for seasonal parameters in this model.
• Tests for the case with the bias-corrected estimator.

Innovations MLE

• Add support for fixed parameters

Innovations algorithm

• Add support for ARMA models; see Brockwell and Davis (2016) p.154 and Example 5.1.6. This estimator should be feasible given the Cython versions of the general innovations algorithm that introduced in PERF: Cythonize innovations algo and filter #5947.

[rajathpatel23]

@ChadFulton I would like to work on this enhancement, would like to request some help in guiding to start working on this enhancement.

Thank you

[ChadFulton]

@rajathpatel23 that would be great, thanks!

There are a number of things here that I think should be pretty self-contained, including:

• Example notebooks: it would be great to add a notebook showing how to use the new models.
  • There are tons of options here that would be great. One would be to replicate some of the "Examples" sections from Brockwell and Davis' book.
• Tests: we could use more unit tests in general, and there are two specific issues I called out above:
  • GLS test: the test I put in the issue, above, fails because we find better parameters than are reported in Brockwell and Davis' book. Some more investigation on this case would be useful, especially comparing against their ITSM2000 program (can be found at http://extras.springer.com/2002/978-0-387-21657-7/ITSM2000, only runs on Windows).
  • We don't have any tests for the HR estimator with the bias correction, and this is because I couldn't find any packages that implemented it. However, I notice that Gomez and Maravall (e.g. in their chapter "Automatic Modeling Methods for Univariate Series") also have implemented this bias correction in TRAMO/SEATS, and so I was thinking that it is probably available in X13-ARIMA/SEATS, and we might be able to test against that package somehow.
  • In general, it would be great to add more unit tests for any of the methods against ITSM2000 or X13-ARIMA/SEATS
• Support for fixed parameters: GLS, innovations MLE, and Hannan Rissanen should each be able to support fixed parameters. If you wanted to try this, I would suggest picking just one to start with.

If you have a particular interest, I can go into more details.

[emilmirzayev]

Hi Chad,

How one can add examle Notebooks?
Which directory I should put them?

Thanks,

[bashtage]

Three steps to add a notebook:

1. Add your notebook to examples/notebooks
2. Add a block to the json file that contains the metadata for notebooks.
3. Add a nice screenshot for your notebook that makes it look interesting in docs/_static/images

I like the format that @ChadFulton uses with the title. I used it here: https://github.com/statsmodels/statsmodels/blob/master/docs/source/_static/images/rolling_ls.png

[bashtage]

NB: The json file determines where the example notebook appears in the docs, so please add in the correct section.