Incorporate covariates

[timoadam]

Incorporate covariates into the state process(es) to determine which factors affect the probabilities of switching to bearish and bullish markets, respectively (just an idea, perhaps something for later versions of the package!).

[ErikBertolino]

Oof, that is the harder one, because that means one has to work with the transition probability matrix.

Another approach (which is not the same question of course, but far easier) to add covariates would be to add covariates to better estimate mu and sigma within each regime. It is (probably) the case that it is numerically easier and there are more data points within the regime, since regime-switching is rare.

If there is a "smoothing assumption" (i.e, mu and sigma are continuously varying), then as mu and sigma are moving, then that can indicate a regime switch.