Sparseness, consistency and model selection for Markov regime-switching Gaussian autoregressive models

Abstract

We study Markov regime-switching Gaussian autoregressive models which are aimed at capturing temporal heterogeneity exhibited by time series data. In the construction of a Markov regime-switching model, several specifications must be made relating to both the state and observation models; in particular, the complexity of these models must be specified when fitting to a dataset. We propose new regularization methods based on conditional likelihood for simultaneous autoregressive-order and parameter estimation with the number of regimes fixed, and use a regularized Bayesian information criterion for selection of the number of regimes. Unlike the existing information-theoretic approaches, the new methods avoid an exhaustive search of the model space for model selection and thereby are computationally more efficient. We establish large sample properties of the proposed methods for estimation, model selection, and forecasting. We also evaluate finite sample performance of the methods via simulations, and illustrate their applications by analyzing two real datasets.