  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 $M_0 \geq 1$ 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.
