Autocovariance structure of Markov regime switching models and model selection

Research Report SRR97-005

Autocovariance structure of Markov regime switching models and model selection

Jing Zhang and Robert A Stine

Abstract: We show through elementary means that the covariance functions of second-order stationary vector Markov regime switching time series models have vector ARM A(p,q) representations, where the upper bounds for p and q are elementary functions of the number of regimes. This applies in general to vector Markov regime switching processes with both mean-variance and autoregressive switching. This result yields an easily computed method for setting a lower bound on the number of underlying Markov regimes from an estimated autocovariance function.

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