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On The Stationarity Of Markov-Switching Garch Processes

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  • Abramson, Ari
  • Cohen, Israel
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    Abstract

    Generalized autoregressive conditional heteroskedasticity (GARCH) models with Markov-switching regimes are often used for volatility analysis of financial time series. Such models imply less persistence in the conditional variance than the standard GARCH model and potentially provide a significant improvement in volatility forecast. Nevertheless, conditions for asymptotic wide-sense stationarity have been derived only for some degenerated models. In this paper, we introduce a comprehensive approach for stationarity analysis of Markov-switching GARCH models, which manipulates a backward recursion of the model s second-order moment. A recursive formulation of the state-dependent conditional variances is developed, and the corresponding conditions for stationarity are obtained. In particular, we derive necessary and sufficient conditions for the asymptotic wide-sense stationarity of two different variants of Markov-switching GARCH processes and obtain expressions for their asymptotic variances in the general case of m-state Markov chains and (p,q)-order GARCH processes.The authors thank Professor Rami Atar for helpful discussions. The authors thank the co-editor Bruce Hansen and the three anonymous referees for their helpful comments and suggestions and in particular the referee who proposed a generalization of the proof in Appendix B. This research was supported by the Israel Science Foundation (grant 1085 05).

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    Bibliographic Info

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

    Volume (Year): 23 (2007)
    Issue (Month): 03 (June)
    Pages: 485-500

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    Handle: RePEc:cup:etheor:v:23:y:2007:i:03:p:485-500_07

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    Cited by:
    1. Luc Bauwens & Arie Preminger & Jeroen V. K. Rombouts, 2010. "Theory and inference for a Markov switching GARCH model," Econometrics Journal, Royal Economic Society, vol. 13(2), pages 218-244, 07.
    2. Monica Billio & Roberto Casarin & Anthony Osuntuyi, 2012. "Efficient Gibbs Sampling for Markov Switching GARCH Models," Working Papers 2012:35, Department of Economics, University of Venice "Ca' Foscari".
    3. Szabolcs Blazsek & Anna Downarowicz, 2008. "Regime switching models of hedge fund returns," Faculty Working Papers 12/08, School of Economics and Business Administration, University of Navarra.

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