  We introduce multiple hidden Markov models (MHMMs) where an observed
multivariate categorical time series depends on an unobservable multivariate
Mar- kov chain. MHMMs provide an elegant framework for specifying various
independence relationships between multiple discrete time processes. These
independencies are interpreted as Markov properties of a mixed graph and a
chain graph associated to the latent and observable components of the MHMM,
respectively. These Markov properties are also translated into zero
restrictions on the parameters of marginal models for the transition
probabilities and the distributions of the observable variables given the
latent states.
