A Note on the Mixture Transition Distribution and Hidden Markov Models

We discuss an interpretation of the Mixture Transition Distribution (MTD) for discrete-valued time series which is based on a sequence of independent latent variables which are occasion-specific. We show that, by assuming that this latent process follows a first order Markov Chain, MTD can be generalized in a sensible way. A class of models results which also includes the Hidden Markov Model (HMM). For these models we out-line an EM algorithm for the maximum likelihood estimation which exploits recursions developed within the HMM literature. Some key words: Backward-forward Recursions; Discrete-valued time series; EM-algorithm; State-space models