Yet, I cannot help but wonder How did Hamilton estimate the Transition Probability Matrix? Is it through MLE, or did he use the Tauchen method which is basically a frequentist approach? In any case, it would be nice to be able to replicate it in Python or Julia.

Secondly, It would be really nice to have some Python or Julia code that deal with Hidden Markov Models and their uses in Economics.

Thanks a lot for your feedback, it’s much appreciated.

Regarding the stochastic matrix estimated by Hamilton, he estimated it as part of a regime switching estimation, using maximum likelihood. I’ll have a think about whether it’s worth setting things up so readers can replicate his results.

Great idea about hidden Markov models. Any particular study or paper you would like to see treated?

Piggy backing on this thread with a side question:

Are Hidden Markov Models the same as Markov Regime Switching models? From their descriptions I wouldn’t think so but in Python’s statsmodels library it clearly uses both terms interchangeably. Any clarification would be greatly appreciated!

I guess they’re pretty similar. However, if I think of a Markov regime switching model, I usually suppose that the observable state y is a function of both the unobservable Markov process and lagged values of y. That is, I think of a time series process in y such that the coefficients are perturbed by a Markov chain.

On the other hand, most HMMs I’ve seen have y as a function of the unobservable Markov state only.

However, usage changes across time and fields. Other readers might differ.