| Abstract: | This article investigates some structural properties of theMarkov-switching GARCH process introduced by Haas, Mittnik,and Paolella. First, a sufficient and necessary condition forthe existence of the weakly stationary solution of the processis presented. The solution is weakly stationary, and the causalexpansion of the Markov-switching GARCH process is also established.Second, the general conditions for the existence of any integer-ordermoment of the square of the process are derived. The techniqueused in this article for the weak stationarity and the high-ordermoments of the process is different from that used by Haas,Mittnik, and Paolella and avoids the assumption that the processstarted in the infinite past with finite variance. Third, asufficient and necessary condition for the strict stationarityof the Markov-switching GARCH process with possibly infinitevariance is given. Finally, the strict stationarity of the so-calledintegrated Markov-switching GARCH process is also discussed. |
