Testing the Number of Regimes in Markov Regime Switching Models

01/21/2018

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by   Hiroyuki Kasahara, et al.

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Markov regime switching models have been used in numerous empirical studies in economics and finance. However, the asymptotic distribution of the likelihood ratio test statistic for testing the number of regimes in Markov regime switching models has been an unresolved problem. This paper derives the asymptotic distribution of the likelihood ratio test statistic for testing the null hypothesis of M_0 regimes against the alternative hypothesis of M_0 + 1 regimes for any M_0 ≥ 1 both under the null hypothesis and under local alternatives. We show that the contiguous alternatives converge to the null hypothesis at a rate of n^-1/8 in regime switching models with normal density. The asymptotic validity of the parametric bootstrap is also established.