Abstract:
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Markov switching models have wide applications in economics, finance, and other fields. Most studies focusing on identifying the number of regimes in a Markov switching model have been limited to testing the null hypothesis of only one regime (i.e., a linear model with no switching) against an alternative hypothesis with two regimes. Even in such simple cases, this type of problem raises issues of nonstandard asymptotic distributions, identification failure, and nuisance parameters. In this paper, we propose Monte Carlo test methods [Dufour (2006)] which deal transparently with these distributional issues, even allowing for finite-sample inference. The procedure is applied to likelihood ratio statistics. The tests circumvent the issues plaguing conventional hypothesis testing. This also allows one to deal with non-stationary processes, models with non-Gaussian errors and multivariate settings, which have received little attention in the literature. An important contribution of this paper is the Maximized Monte Carlo Likelihood Ratio Test (MMC-LRT), which is an identifications-robust valid test procedure both in finite samples and asymptotically. Further, the methods proposed are applicable to more general settings where a null hypothesis with M0 regimes is tested against an alternative with M0 + m regimes where both M0 = 1 and m = 1. This allows one to compare different Markov switching models and Hidden Markov Models. Simulation results suggest the proposed tests are able to control the level of the test and have good power.
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