Forecasting Probability Densities by Using Hidden Markov Models with Mixed States (Data Set D)

We note similarities of the state-space reconstruction ( uembedology”) practiced in numerical work on chaos, state-space methods of stochastic systems theory, and the hidden Markov models (HMMs) used in speech research. We review Baum’s EM algorithm in general and the specific forwardbackward algorithm that optimizes a class of HMM that has a mixed state space consisting of continuous and discrete parts. We then describe forecasts based on models fit to Data Set D.