Jointly Determining the State Dimension and Lag Order for Markov-Switching Vector Autoregressive Models

This paper studies the problem of joint identification of the state dimension and lag order for a class of Markov-switching vector autoregressive (MS-VAR) models, in which all parameters are presumed to be regime-dependent. To this end, three complexity-penalized criteria AIC^{MS}, HQC^{MS} and SIC^{MS} are considered, and a new criterion AIC_c^{MS} is derived by minimizing the Kullback-Leibler (KL) divergence. The efficacy of the procedure is evaluated by means of Monte Carlo experiments. We illustrate the usefulness of the joint model selection procedure with empirical applications to the modeling of business cycles in the U.S. and Australia.