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So far, all standard HMM implementations I've seen assume some variation of a Gaussian Mixture (GMM) as their emission model. It can of course only have a single mixture component which reduces it to a standard multivariate normal distribution.

In other words, conditional on the hidden state, a particular GMM model produces the observations.

Is it possible to replace this GMM with an autoregressive model, for example, a Vector Autoregression (VAR) in the multivariate case? And if yes, how would the parameters of this model be updated within the Baum-Welch forward/backward parameter estimation framework?