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Stationarity of a Markov-Switching GARCH Model

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  • Ji-Chun Liu

Abstract

This article investigates some structural properties of the Markov-switching GARCH process introduced by Haas, Mittnik, and Paolella. First, a sufficient and necessary condition for the existence of the weakly stationary solution of the process is presented. The solution is weakly stationary, and the causal expansion of the Markov-switching GARCH process is also established. Second, the general conditions for the existence of any integer-order moment of the square of the process are derived. The technique used in this article for the weak stationarity and the high-order moments of the process is different from that used by Haas, Mittnik, and Paolella and avoids the assumption that the process started in the infinite past with finite variance. Third, a sufficient and necessary condition for the strict stationarity of the Markov-switching GARCH process with possibly infinite variance is given. Finally, the strict stationarity of the so-called integrated Markov-switching GARCH process is also discussed. Copyright 2006, Oxford University Press.

Suggested Citation

  • Ji-Chun Liu, 2006. "Stationarity of a Markov-Switching GARCH Model," Journal of Financial Econometrics, Oxford University Press, vol. 4(4), pages 573-593.
    • Handle: RePEc:oup:jfinec:v:4:y:2006:i:4:p:573-593
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbl004
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    Citations

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    Cited by:

    1. Haas Markus, 2010. "Skew-Normal Mixture and Markov-Switching GARCH Processes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(4), pages 1-56, September.
    2. Kuang-Liang Chang & Charles Ka Yui Leung, 2022. "How did the asset markets change after the Global Financial Crisis?," Chapters, in: Charles K.Y. Leung (ed.), Handbook of Real Estate and Macroeconomics, chapter 12, pages 312-336, Edward Elgar Publishing.
    3. Haas, Markus & Mittnik, Stefan, 2008. "Multivariate regimeswitching GARCH with an application to international stock markets," CFS Working Paper Series 2008/08, Center for Financial Studies (CFS).
    4. Abdelhakim Aknouche & Christian Francq, 2022. "Stationarity and ergodicity of Markov switching positive conditional mean models," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 436-459, May.
    5. Philippe Charlot & Vêlayoudom Marimoutou, 2008. "Hierarchical hidden Markov structure for dynamic correlations: the hierarchical RSDC model," Working Papers halshs-00285866, HAL.
    6. Teräsvirta, Timo, 2006. "An introduction to univariate GARCH models," SSE/EFI Working Paper Series in Economics and Finance 646, Stockholm School of Economics.
    7. Kwon, Dream & Lee, Oesook, 2024. "The functional central limit theorem for Markov-switching GARCH model," Economics Letters, Elsevier, vol. 238(C).
    8. Mawuli Segnon & Stelios Bekiros, 2020. "Forecasting volatility in bitcoin market," Annals of Finance, Springer, vol. 16(3), pages 435-462, September.
    9. Maddalena Cavicchioli, 2021. "Statistical inference for mixture GARCH models with financial application," Computational Statistics, Springer, vol. 36(4), pages 2615-2642, December.
    10. Carol Alexander & Emese Lazar, 2009. "Modelling Regime‐Specific Stock Price Volatility," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(6), pages 761-797, December.
    11. Haas, Markus & Liu, Ji-Chun, 2015. "Theory for a Multivariate Markov--switching GARCH Model with an Application to Stock Markets," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112855, Verein für Socialpolitik / German Economic Association.
    12. Mawuli Segnon & Stelios Bekiros, 2019. "Forecasting Volatility in Cryptocurrency Markets," CQE Working Papers 7919, Center for Quantitative Economics (CQE), University of Muenster.

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