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QML estimation of a class of multivariate GARCH models without moment conditions on the observed process

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  • Francq, Christian
  • Zakoian, Jean-Michel

Abstract

We establish the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator of the parameters of a class of multivariate GARCH processes. The conditions are mild and coincide with the minimal ones in the univariate case. In particular, contrary to the current literature on the estimation of multivariate GARCH models, no moment assumption is made on the observed process. Instead, we require strict stationarity, for which a necessary and sufficient condition is established.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 20779.

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Date of creation: Feb 2010
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Handle: RePEc:pra:mprapa:20779

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Keywords: Asymptotic Normality; Conditional Heteroskedasticity; Consistency; Constant Conditional Correlation; Multivariate GARCH; Quasi Maximum Likelihood Estimation; Strict Stationarity Condition;

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  1. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
  2. Annastiina Silvennoinen & Timo Teräsvirta, 2008. "Multivariate GARCH models," CREATES Research Papers 2008-06, School of Economics and Management, University of Aarhus.
  3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 31(3), pages 307-327, April.
  4. Hafner, Christian M. & Preminger, Arie, 2009. "Asymptotic Theory For A Factor Garch Model," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 25(02), pages 336-363, April.
  5. He, Changli & Ter svirta, Timo, 2004. "An Extended Constant Conditional Correlation Garch Model And Its Fourth-Moment Structure," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 20(05), pages 904-926, October.
  6. Robert F. Engle & Kevin Sheppard, 2001. "Theoretical and Empirical properties of Dynamic Conditional Correlation Multivariate GARCH," NBER Working Papers 8554, National Bureau of Economic Research, Inc.
  7. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 19(02), pages 280-310, April.
  8. Nakatani, Tomoaki & Teräsvirta, Timo, 2007. "Testing for Volatility Interactions in the Constant Conditional Correlation GARCH Model," Working Paper Series in Economics and Finance, Stockholm School of Economics 649, Stockholm School of Economics, revised 24 Jan 2007.
  9. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 84(1), pages 61-84, January.
  10. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 14(01), pages 70-86, February.
  11. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 987-1007, July.
  12. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(3), pages 339-50, July.
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Cited by:
  1. Massimiliano Caporin & Michael McAleer, 2012. "Robust Ranking of Multivariate GARCH Models by Problem Dimension," Working Papers in Economics, University of Canterbury, Department of Economics and Finance 12/06, University of Canterbury, Department of Economics and Finance.
  2. Rasmus S. Pedersen & Anders Rahbek, 2014. "Multivariate variance targeting in the BEKK–GARCH model," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 17(1), pages 24-55, 02.

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