INTEGRATED MARKOV-SWITCHING GARCH PROCESS
研究了集成马尔可夫切换GARCH过程的平稳性，证明其可能存在无限方差的平稳解，并给出了有限方差平稳解的存在条件。
This paper investigates stationarity of the so-called integrated Markov-switching generalized autoregressive conditionally heteroskedastic (GARCH) process, which is an important subclass of the Markov-switching GARCH process introduced by Francq, Roussignol, and Zakoïan (2001, Journal of Time Series Analysis 22,197–220) and a Markov-switching version of the integrated GARCH (IGARCH) process. We show that, like the classical IGARCH process, a stationary solution with infinite variance for the integrated Markov-switching GARCH process may exist. To this purpose, an alternative condition for the existence of a strictly stationary solution of the Markov-switching GARCH process is presented, and some results obtained in Hennion (1997, Annals of Probability 25, 1545–1587) are employed. In addition, we also discuss conditions for the existence of a strictly stationary solution of the Markov-switching GARCH process with finite variance, which is a modification of Theorem 2 in Francq et al. (2001).