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

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.