A dynamic Markov regime-switching GARCH model and its cumulative impulse response function

This paper concerns with a generalized regime-switching GARCH model to capture dynamic behavior of volatility in financial market. Four-state Markov chain regime-switching is adopted with white noise, stationary, integrated and explosive states. We consider time-dependent transition probabilities of the Markov chain and derive time-dependent probability of each state under the assumption of conditional normality on the noise of the GARCH model. Multi-step ahead volatility is formulated and cumulative impulse response function, which is a measure of persistence in volatility, is discussed. A Monte-Carlo experiment shows the dynamics of the volatilities and time-dependent probabilities as well as the behaviors of the cumulative impulse response functions.