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INTEGRATED MARKOV-SWITCHING GARCH PROCESS

Published online by Cambridge University Press:  01 October 2009

Ji-Chun Liu
Ji-Chun Liu*
Affiliation:
Xiamen University
*
*Address correspondence to Ji-Chun Liu, School of Mathematical Science, Xiamen University, Xiamen, 361005, PR China; e-mail: liujichun65@126.com.
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Abstract

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).

Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 5 , October 2009 , pp. 1277 - 1288
Copyright
Copyright © Cambridge University Press 2009

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