Elsevier

Journal of Multivariate Analysis

Volume 140, September 2015, Pages 19-30
Journal of Multivariate Analysis

Multiple hidden Markov models for categorical time series

https://doi.org/10.1016/j.jmva.2015.04.002Get rights and content
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Abstract

We introduce multiple hidden Markov models (MHMMs) where a multivariate categorical time series depends on a latent multivariate Markov 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 respectively to the latent and observation components of the MHMM. These Markov properties are also translated into zero restrictions on the parameters of marginal models for the transition probabilities and the distributions of observable variables given the latent states.

AMS subject classifications

68R10
60J10
62H99

Keywords

Conditional independence
Granger noncausality
Graphical models
Marginal models
Markov properties
Multivariate Markov chains

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