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Integrated Markov-Switching Garch Process

  • Liu, Ji-Chun
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    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).

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    Article provided by Cambridge University Press in its journal Econometric Theory.

    Volume (Year): 25 (2009)
    Issue (Month): 05 (October)
    Pages: 1277-1288

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    Handle: RePEc:cup:etheor:v:25:y:2009:i:05:p:1277-1288_09
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