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On a dynamic mixture GARCH model


  • Xixin Cheng

    (Department of Statistics and Actuarial Science, University of Hong Kong)

  • Philip L. H. Yu

    (Department of Statistics and Actuarial Science, University of Hong Kong)

  • W. K. Li

    (Department of Statistics and Actuarial Science, University of Hong Kong)


This paper proposes a new mixture GARCH model with a dynamic mixture proportion. The mixture Gaussian distribution of the error can vary from time to time. The Bayesian Information Criterion and the EM algorithm are used to estimate the number of parameters as well as the model parameters and their standard errors. The new model is applied to the S&P500 Index and Hang Seng Index and compared with GARCH models with Gaussian error and Student's t error. The result shows that the IGARCH effect in these index returns could be the result of the mixture of one stationary volatility component with another non-stationary volatility component. The VaR based on the new model performs better than traditional GARCH-based VaRs, especially in unstable stock markets. Copyright © 2008 John Wiley & Sons, Ltd.

Suggested Citation

  • Xixin Cheng & Philip L. H. Yu & W. K. Li, 2009. "On a dynamic mixture GARCH model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(3), pages 247-265.
  • Handle: RePEc:jof:jforec:v:28:y:2009:i:3:p:247-265 DOI: 10.1002/for.1093

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    References listed on IDEAS

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    2. Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(4), pages 493-530.
    3. Thomas Mikosch & Cătălin Stărică, 2004. "Nonstationarities in Financial Time Series, the Long-Range Dependence, and the IGARCH Effects," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 378-390, February.
    4. Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-1153, December.
    5. Sercu, Piet & Uppal, Raman & Van Hulle, Cynthia, 1995. " The Exchange Rate in the Presence of Transaction Costs: Implications for Tests of Purchasing Power Parity," Journal of Finance, American Finance Association, vol. 50(4), pages 1309-1319, September.
    6. Li, C W & Li, W K, 1996. "On a Double-Threshold Autoregressive Heteroscedastic Time Series Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(3), pages 253-274, May-June.
    7. Michael, Panos & Nobay, A Robert & Peel, David A, 1997. "Transactions Costs and Nonlinear Adjustment in Real Exchange Rates: An Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 105(4), pages 862-879, August.
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    12. Berka, Martin, 2005. "General Equilibrium Model of Arbitrage Trade and Real Exchange Rate Persistence," MPRA Paper 234, University Library of Munich, Germany.
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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. Haas, Markus & Krause, Jochen & Paolella, Marc S. & Steude, Sven C., 2013. "Time-varying mixture GARCH models and asymmetric volatility," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 602-623.
    3. Klein, Tony & Walther, Thomas, 2016. "Oil price volatility forecast with mixture memory GARCH," Energy Economics, Elsevier, vol. 58(C), pages 46-58.

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