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On the statistical properties of multiplicative GARCH models

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  • Conrad, Christian
  • Kleen, Onno

Abstract

We examine the statistical properties of multiplicative GARCH models. First, we show that in multiplicative models, returns have higher kurtosis and squared returns have a more persistent autocorrelation function than in the nested GARCH model. Second, we extend the results of Andersen and Bollerslev (1998) on the upper bound of the R2 in a Mincer-Zarnowitz regression to the case of a multiplicative GARCH model, using squared returns as a proxy for the true but unobservable conditional variance. Our theoretical results imply that multiplicative GARCH models provide an explanation for stylized facts that cannot be captured by classical GARCH modeling.

Suggested Citation

  • Conrad, Christian & Kleen, Onno, 2016. "On the statistical properties of multiplicative GARCH models," Working Papers 0613, University of Heidelberg, Department of Economics.
    • Handle: RePEc:awi:wpaper:0613
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    References listed on IDEAS

    as
    1. Heejoon Han, 2015. "Asymptotic Properties of GARCH-X Processes," Journal of Financial Econometrics, Oxford University Press, vol. 13(1), pages 188-221.
    2. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
    3. Robert F. Engle & Eric Ghysels & Bumjean Sohn, 2013. "Stock Market Volatility and Macroeconomic Fundamentals," The Review of Economics and Statistics, MIT Press, vol. 95(3), pages 776-797, July.
    4. Conrad, Christian & Schienle, Melanie, 2015. "Misspecification Testing in GARCH-MIDAS Models," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112919, Verein für Socialpolitik / German Economic Association.
    5. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    6. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    7. Hillebrand, Eric, 2005. "Neglecting parameter changes in GARCH models," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 121-138.
    8. Karanasos, Menelaos, 1999. "The second moment and the autocovariance function of the squared errors of the GARCH model," Journal of Econometrics, Elsevier, vol. 90(1), pages 63-76, May.
    9. Conrad, Christian & Schienle, Melanie, 2015. "Misspecification Testing in GARCH-MIDAS Models," Working Papers 0597, University of Heidelberg, Department of Economics.
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    More about this item

    Keywords

    Forecast evaluation; GARCH-MIDAS; Mincer-Zarnowitz regression; volatility persistence; volatility component model; long-term volatility.;
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