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

Hiroyuki Kasahara, Katsumi Shimotsu

Published 2017-05-30Version 1

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 the regime-specific density depends on both the current and the lagged regimes, which include the seminal model of Hamilton (1989)and the switching ARCH model of Hamilton and Susmel (1994). This paper shows the asymptotic normality of the MLE and the consistency of the asymptotic covariance matrix estimate of these models.