Hidden Markov partition models

We describe an extension of the hidden Markov model in which the manifest process conditionally follows a partition model. The assumption of local independence for the manifest random variable is thus relaxed to arbitrary dependence. The proposed class generalizes different existing models for discrete and continuous time series, and allows for the finest trading off between bias and variance. The models are fit through an EM algorithm, with the usual recursions for hidden Markov models extended at no additional computational cost.