Implement an iterative algorithm for MLE in the AR model with correlated Gaussian noise about ssm HOT 3 CLOSED

hi @slinderman !
Any progress on the above, would be awesome addition to this great library.
Best,
Andrew

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Hi @andrewczgithub, I think the current implementation should work just fine, but there are some small changes that could further improve the estimation. @ahwillia has been thinking about this too. The next step is to write up a short derivation of the M-step for autoregressive models with correlated noise. We need to do this anyway for the LDS models, since there we want to maximize the expected log probability under the posterior distribution on continuous latent states.

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Update: Spoke with @ahwillia and we convinced ourselves that for the M-step of linear regressions (including linear autoregressive models), the MLE mean estimate does not depend on the covariance, so our two-step procedure should be valid.

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