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A note on the mixture transition distribution and hidden Markov models

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  • Francesco Bartolucci
  • Alessio Farcomeni

Abstract

We discuss an interpretation of the mixture transition distribution (MTD) for discrete-valued time series which is based on a sequence of independent latent variables which are occasion-specific. We show that, by assuming that this latent process follows a first order Markov Chain, MTD can be generalized in a sensible way. A class of models results which also includes the hidden Markov model (HMM). For these models we outline an EM algorithm for the maximum likelihood estimation which exploits recursions developed within the HMM literature. As an illustration, we provide an example based on the analysis of stock market data referred to different American countries. Copyright Copyright 2010 Blackwell Publishing Ltd

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  • Francesco Bartolucci & Alessio Farcomeni, 2010. "A note on the mixture transition distribution and hidden Markov models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 132-138, March.
  • Handle: RePEc:bla:jtsera:v:31:y:2010:i:2:p:132-138
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    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9892.2009.00650.x
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    References listed on IDEAS

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    1. 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.
    2. Francesco Bartolucci, 2002. "A recursive algorithm for Markov random fields," Biometrika, Biometrika Trust, vol. 89(3), pages 724-730, August.
    3. Francesco Bartolucci, 2006. "Likelihood inference for a class of latent Markov models under linear hypotheses on the transition probabilities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 155-178.
    4. Bartolucci, Francesco & Farcomeni, Alessio, 2009. "A Multivariate Extension of the Dynamic Logit Model for Longitudinal Data Based on a Latent Markov Heterogeneity Structure," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 816-831.
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    Cited by:

    1. Bolano, Danilo & Berchtold, André, 2016. "General framework and model building in the class of Hidden Mixture Transition Distribution models," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 131-145.
    2. F. Bartolucci & A. Farcomeni & F. Pennoni, 2014. "Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 433-465, September.
    3. repec:eee:empfin:v:43:y:2017:i:c:p:1-32 is not listed on IDEAS
    4. Farcomeni, Alessio, 2011. "Hidden Markov partition models," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1766-1770.
    5. Alessio Farcomeni & Luca Greco, 2015. "S-estimation of hidden Markov models," Computational Statistics, Springer, vol. 30(1), pages 57-80, March.

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