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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. 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.
  2. Annastiina Silvennoinen & Timo Teräsvirta, 2008. "Multivariate GARCH models," CREATES Research Papers 2008-06, School of Economics and Management, University of Aarhus.
  3. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen, 2003. "Multivariate GARCH models: a survey," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. 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.
  5. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  6. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(02), pages 280-310, April.
  7. HAFNER, Christian M. & PREMINGER, Arie, 2006. "Asymptotic theory for a factor GARCH model," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2006071, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. He, Changli & Ter svirta, Timo, 2004. "An Extended Constant Conditional Correlation Garch Model And Its Fourth-Moment Structure," Econometric Theory, Cambridge University Press, vol. 20(05), pages 904-926, October.
  9. Tomoaki Nakatani & Timo Terasvirta, 2009. "Testing for volatility interactions in the Constant Conditional Correlation GARCH model," Econometrics Journal, Royal Economic Society, vol. 12(1), pages 147-163, 03.
  10. 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.
  11. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 70-86, February.
  12. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
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Cited by:
  1. Caporin, M. & McAleer, M.J., 2012. "Robust Ranking of Multivariate GARCH Models by Problem Dimension," Econometric Institute Research Papers EI2012-13, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  2. Rasmus Søndergaard Pedersen & Anders Rahbek, 2012. "Multivariate Variance Targeting in the BEKK-GARCH Model," CREATES Research Papers 2012-53, School of Economics and Management, University of Aarhus.

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