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Multiple hidden Markov models for categorical time series

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  • Colombi, R.
  • Giordano, S.

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.

Suggested Citation

  • Colombi, R. & Giordano, S., 2015. "Multiple hidden Markov models for categorical time series," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 19-30.
    • Handle: RePEc:eee:jmvana:v:140:y:2015:i:c:p:19-30
    DOI: 10.1016/j.jmva.2015.04.002
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    References listed on IDEAS

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    1. Thomas Richardson, 2003. "Markov Properties for Acyclic Directed Mixed Graphs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 145-157, March.
    2. Colombi, R. & Giordano, S., 2012. "Graphical models for multivariate Markov chains," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 90-103.
    3. Gilles Celeux & Jean-Baptiste Durand, 2008. "Selecting hidden Markov model state number with cross-validated likelihood," Computational Statistics, Springer, vol. 23(4), pages 541-564, October.
    4. Roberto Colombi & Sabrina Giordano, 2011. "Testing lumpability for marginal discrete hidden Markov models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(3), pages 293-311, September.
    5. Colombi, Roberto & Giordano, Sabrina & Cazzaro, Manuela, 2014. "hmmm: An R Package for Hierarchical Multinomial Marginal Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 59(i11).
    6. Florens, J.P. & Mouchart, M. & Rolin, J.M., 1993. "Noncausality and Marginalization of Markov Processes," Econometric Theory, Cambridge University Press, vol. 9(2), pages 241-262, April.
    7. Chris Sherlock & Tatiana Xifara & Sandra Telfer & Mike Begon, 2013. "A coupled hidden Markov model for disease interactions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(4), pages 609-627, August.
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