Likelihood Ratio Test and Information Criteria for Markov Switching Var Models: An Application to the Italian Macroeconomy

In this work we consider multivariate autoregressions subject to Markovian changes in regime. Estimation methods and filtering techniques for such processes are well established in the literature as well as the asymptotic distribution of the maximum likelihood estimators. Assuming the conditions under which the standard asymptotic distribution theory holds, the likelihood ratio (LR) has the null distribution. We give explicit formulae for LR tests of various hypotheses of interest in the context of Markov switching VAR models. The proposed LR statistic has a rather simple form as it reduces to the use of the estimated unrestricted and restricted variance-covariance matrices. Moreover, we derive simple expressions for some information criteria to address the question of linearity versus nonlinearity. An application to Italian macroeconomic data gives new insights on the number of regimes and the dynamics characterizing the economy.