  Markov regime switching models have been widely used in numerous empirical
applications in economics and finance. However, the asymptotic distribution of
the maximum likelihood estimator (MLE) has not been proven for some empirically
popular Markov regime switching models. In particular, the asymptotic
distribution of the MLE has been unknown for models in which some elements of
the transition probability matrix have the value of zero, as is commonly
assumed in empirical applications with models with more than two regimes. This
also includes models in which the regime-specific density depends on both the
current and the lagged regimes such as the seminal model of Hamilton (1989) and
switching ARCH model of Hamilton and Susmel (1994). This paper shows the
asymptotic normality of the MLE and consistency of the asymptotic covariance
matrix estimate of these models.
