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Bayesian analysis of multivariate Gaussian hidden Markov models with an unknown number of regimes

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  • Luigi Spezia

Abstract

Multivariate Gaussian hidden Markov models with an unknown number of regimes are introduced here in the Bayesian setting and new efficient reversible jump Markov chain Monte Carlo algorithms for estimating both the dimension and the unknown parameters of the model are presented. Hidden Markov models are an extension of mixture models that can be applied to time series so as to classify the observations in a small number of groups, to understand when change points occur in the dynamics of the series and to model data heterogeneity through the switching among subseries with different means and covariance matrices. These aims can be achieved by assuming that the observed phenomenon is driven by a latent, or hidden, Markov chain. The methodology is illustrated through two different examples of multivariate time series.

Suggested Citation

  • Luigi Spezia, 2010. "Bayesian analysis of multivariate Gaussian hidden Markov models with an unknown number of regimes," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(1), pages 1-11, January.
    • Handle: RePEc:bla:jtsera:v:31:y:2010:i:1:p:1-11
    DOI: 10.1111/j.1467-9892.2009.00635.x
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    References listed on IDEAS

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    1. Richard J. Boys & Daniel A. Henderson, 2004. "A Bayesian Approach to DNA Sequence Segmentation," Biometrics, The International Biometric Society, vol. 60(3), pages 573-581, September.
    2. Chang-Jin Kim & Charles R. Nelson, 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262112388, April.
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    Cited by:

    1. 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.
    2. Luigi Spezia, 2019. "Modelling covariance matrices by the trigonometric separation strategy with application to hidden Markov models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 399-422, June.
    3. Huber, Florian & Zörner, Thomas O., 2019. "Threshold cointegration in international exchange rates:A Bayesian approach," International Journal of Forecasting, Elsevier, vol. 35(2), pages 458-473.

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