VAR update

[ckrapu]

This PR modifies the AR distribution to accommodate cross-series coefficients as desired in a vector autoregressive model. More information can be found at https://discourse.pymc.io/t/how-to-implement-vector-autoregression-with-interdependencies/4287/2 and #4665. This is marked as a WIP as I would like some advice on how to handle the constant argument for the AR distribution.

• what are the (breaking) changes that this PR makes?
  Depending on the dimensions of rho, the logp function will either use an elementwise operation or a matrix multiplication for the independent and dependent time series cases, respectively. However, models which assume 2 or more dimensions indexing independent time series will no longer behave the same. In this case, the recommended approach is to reshape these two dimensions into a single one so that a rho tensor with shape [lags, d, d] can be interpreted as using multiple d x d cross-series coefficients.

• important background, or details about the implementation
  There is a constant argument for the AR distribution which I am unable to decipher and have not been able to address the case in which constant is used.

• are the changes—especially new features—covered by tests and docstrings?
  No new tests or doc modifications have been added yet.

• linting/style checks have been run

• consider adding/updating relevant example notebooks

• right before it's ready to merge, mention the PR in the RELEASE-NOTES.md

[mjhajharia]

from what i understand, only example notebooks and implementation details are left right?

[mjhajharia]

are there existing notebooks that need to be updated or do we need to create new ones? @ckrapu i can take this up if you can tell me how far stuff is done and what would you have liked to do further :)

[ckrapu]

@almostmeenal The reason I paused on this PR was because I couldn't quite figure out exactly what the self.contant option was implementing. I essentially put in what looked to me like the broadcasted equivalent of it, but I'd like to figure it out some more.

[ckrapu]

Also, you are definitely welcome to take over this PR. For my part, I am going to try to dig up the reason for that formulation and I'll leave the answer here if I find it.

[mjhajharia]

mentioning #5291, so we remember this PR once the new AR dist is made

[ricardoV94]

Closing this as it went stale. Feel free to open a new PR on top of the newer V4 code ;)