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

Asymptotic Properties of the Maximum Likelihood Estimator in Regime Switching Econometric Models