Discussion Papers 2017

CIRJE-F-1049	"Asymptotic Properties of the Maximum Likelihood Estimator in Regime Switching Econometric Models"
Author Name	Kasahara, Hiroyuki and Katsumi Shimotsu
Date	May 2017
Full Paper	PDF file
Remarks	Subsequently published in Journal of Econometrics, 208(2), February 2019, 442-467.

Abstract
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.
Keywords: asymptotic distribution; autoregressive conditional heteroscedasticity; maximum likelihood estimator; Markov regime switching

Abstract

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.

Keywords: asymptotic distribution; autoregressive conditional heteroscedasticity; maximum likelihood estimator; Markov regime switching