ENH: function to compute smoothed state weights (observations and prior mean) for state space models

[ChadFulton]

• tests added / passed.
• code/documentation is well formatted.
• properly formatted commit message.

In state space models, the estimates of the state vector (and a number of other quantities) can be written as a weighted vector sum of the observations (see Durbin and Koopman, 2012, section 4.8) and the prior mean ("initial state"). This PR adds a function to compute the weights for the smoothed state vector, which can be useful in a variety of ways (e.g. decomposing estimates of the unobserved components, or computing leverage statistics, etc.).

Two other notes:

• While the main function here is in Cython for performance, the original commit contains an implementation in Python. This is removed in the second commit to avoid zombie code, while the Git history will still have the Python implementation.
• Although I think these weights are typically the most useful, this function could be easily expanded to compute e.g. weights for the predicted or filtered state vector.

[pep8speaks]

Hello @ChadFulton! Thanks for updating this PR. We checked the lines you've touched for PEP 8 issues, and found:

There are currently no PEP 8 issues detected in this Pull Request. Cheers! 🍻

Comment last updated at 2022-01-13 02:54:22 UTC