A simple hidden Markov model for Bayesian modeling with time dependent data

Consider a set of real valued observations collected over time. We propose a simple hidden Markow model for these realizations in which the the predicted distribution of the next future observation given the past is easily computed. The hidden or unobservable set of parameters is assumed to have a Markov structure of a special type. The model is quite flexible and can be used to incorporate different types of prior information in straightforward and sensible ways.