Dynamic behavior of volatility in a nonstationary generalized regime-switching GARCH model

In this paper we consider a generalized regime-switching GARCH model with a wide class of dependent innovations, and establish asymptotic normality of the logarithm of volatility in the nonstationary generalized regime-switching GARCH model. This extends existing results for volatilities in nonstationary GARCH model with mixing sequences of innovations. A Monte-Carlo experiment is conducted to validate the main theory for the dynamics of the nonstationary volatilities.