Jointly determining the state dimension and lag order for Markov-switching vector autoregressive models

This article studies the problem of joint selection of the state dimension and lag order for a class of Markov-switching vector autoregressive models, in which all parameters are presumed to be regime-dependent. To this end, three complexity-penalized criteria are considered, and a new criterion is derived by minimizing the Kullback-Leibler 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 USA and Australia.