UnobservedComponents: time-varying regression coefficients

[mysterious-ben]

It is impossible to specify state disturbance variances for exogeneous regressors in UnobservedComponents (passed by exog parameter). Currently, coefficients of exogeneous parameters can only be computed using least squares (mle_regression=True) or recursive least squares (mle_regression=False).

It would be great to have an option for time-varying regression coefficients. To do this, we need to associate disturbance variables to exogeneous regressors:

It can be done by addining an additional flag (e.g., time_varying_regression) to UnobservedComponents constructor. If the flag is True, regression coefficients are added to the state vector; at the same time, the same number of state disturbances is added (state disturbances are stored in self.parameters_state_cov, if I'm not mistaken). The resulting Kalman filter will be very similar to the one constructed with mle_regression=False. This solution should only require a moderate effort.

Time-varying regression coefficients are briefly mentioned in the section 6.2.1. of Time Series Anaylysis by State Space Methods (J. Durbin, S. J. Koopman).

[ChadFulton]

This is a design question. We have support for time-varying regression in SARIMAX, but we can't support all variations of all state space models in each model class. The best long-term solution would be to allow composing multiple models together, but we don't have a framework for that yet.

[mysterious-ben]

I think it makes sense. I guess two points in favor of adding this option availabe to UnobservedComponents would be:

1. This option is already available in another model - SARIMAX
2. This case is fairly common (I can't prove the latter point but pretty much everytime I was using this model I wanted to add some regressors with time-varying coefficients)

In the meanwhile, are there any code examples that would help me to subclass UnobservedComponents to add regressors with time-varying coefficients?

[prathak]

I have the same doubt, how did you solve it?

[mysterious-ben]

I haven't: I wanted to do it a few times but just never found time. I think the only way would be to tweak the class UnobservedComponents, maybe using implementation of time-varying coefficients in SARIMAX as inspiration.