Modified Likelihood Ratio Test for Regime Switching

This paper proposes a modified quasi-likelihood test of Markov regime switching models. Despite its popularity in economics and finance, there are few papers that develop tests for regime switching models. Recently, Cho and White (2007) derive the asymptotic distribution of the quasi-likelihood ratio (QLR) statistic of Markov regime switching models with a scalar parameter. The asymptotic distribution of the QLR s statistic is, however, a function of a supremum of a Gaussian process that depends on the model structure as well as the parameter space. Further, taking the supremum over the parameter space is often difficult and needs elaborate simulations to obtain precise critical values. We propose a modified quasi-likelihood ratio that substantially simplifies inference of Markov regime switching models. Our approach adds a penalty term to the quasi-likelihood function that controls the inference problem that occurs when the parameter is on the boundary. With an appropriate choice of the penalty term, the asymptotic distribution of the modified QLR statistic is a simple function of a standard normal random variable. Consequently, the critical values can be easily obtained, and the inference is no more complicated than in the standard case. Our simulation shows that the modified QLR test has good size and power, and its size and power are similar to those of the QLR test.