BUG/ENH: VARMAX Fix trend / exog. timing. Add polynomial trends.

[ChadFulton]

VARMAX models with trend or exog used a misleading timing convention that I think qualifies as type-bug-wrong. The timing convention it used was as according to the general state space transition equation:

\alpha_{t+1} = d_t + T_t \alpha_t + \eta_t

But for a VAR, \alpha_t = y_t, and so trend / exog for time t would be associated with the endog for t+1.

This fixes this problem and also adds a more extensive set of trends (allows a polynomial trend like in SARIMAX rather than just trend='c').

Also adds a bunch of unit tests for VARX models with and without trends against the R package "vars".

[josef-pkt]

This pull request introduces 1 alert and fixes 1 when merging 7501356 into 450f30d - view on LGTM.com

new alerts:

• 1 for Unused local variable

fixed alerts:

• 1 for Unused import

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Comment posted by LGTM.com

[coveralls]

Coverage increased (+0.004%) to 83.646% when pulling d6d1b3d on ChadFulton:varmax-exog into 450f30d on statsmodels:master.

[josef-pkt]

This pull request introduces 1 alert and fixes 1 when merging e16ef78 into 450f30d - view on LGTM.com

new alerts:

• 1 for Unused local variable

fixed alerts:

• 1 for Unused import

---

Comment posted by LGTM.com

[ChadFulton]

This PR also switches from raising an error on non-stationary or non-invertible starting params to giving a warning. This is the same as what #4739 did for SARIMAX.

Edit: this could also be pulled out of this PR since it's not related, if that was cleaner.

[ChadFulton]

This is coming up green. Since it's a bigger PR, I'll wait a bit (tomorrow or on the weekend) before merging (or longer if there are concerns), but it would be good to get the fix in.

[josef-pkt]

This pull request fixes 1 alert when merging d6d1b3d into 450f30d - view on LGTM.com

fixed alerts:

• 1 for Unused import

---

Comment posted by LGTM.com

[codecov-io]

Codecov Report

Merging #4766 into master will increase coverage by <.01%.
The diff coverage is 95.68%.

@@            Coverage Diff            @@
##           master   #4766      +/-   ##
=========================================
+ Coverage    81.1%   81.1%   +<.01%     
=========================================
  Files         580     581       +1     
  Lines       89615   89796     +181     
  Branches     9991   10028      +37     
=========================================
+ Hits        72678   72833     +155     
- Misses      14657   14683      +26     
  Partials     2280    2280

Impacted Files	Coverage Δ
statsmodels/tsa/statespace/tests/test_var.py	100% <100%> (ø)
statsmodels/tsa/statespace/tests/test_varmax.py	99.12% <100%> (-0.01%)	⬇️
statsmodels/tsa/statespace/tests/test_simulate.py	100% <100%> (ø)	⬆️
statsmodels/tsa/statespace/kalman_filter.py	84.16% <50%> (-3.59%)	⬇️
statsmodels/tsa/statespace/tools.py	73.74% <86.2%> (+0.84%)	⬆️
statsmodels/tsa/statespace/varmax.py	91.21% <93.05%> (+0.45%)	⬆️
statsmodels/base/data.py	90.29% <0%> (+0.48%)	⬆️

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