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Asymptotic Theory for Multivariate GARCH Processes

Author

Listed:
  • F. Comte

    (University of Paris)

  • Offer Lieberman

    (Technion-Israel Institute of Technology)

Abstract

We provide in this paper asymptotic theory for the multivariate GARCH (p,q) process. Strong consistency of the quasi-maximum likelihood estimator (MLE) is established by appealing to conditions given in Jeantheau [19] in conjunction with a result given by Boussama [9] concerning the existence of a stationary and ergodic solution to the multivariate GARCH (p,q) process. We prove asymptotic normality of the quasi-MLE when the initial state is either stationary or fixed.

Suggested Citation

  • F. Comte & Offer Lieberman, 2001. "Asymptotic Theory for Multivariate GARCH Processes," Cowles Foundation Discussion Papers 1349, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1349
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d13/d1349.pdf
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    Citations

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    Cited by:

    1. Massimiliano Caporin & Michael McAleer, 2009. "Do We Really Need Both BEKK and DCC? A Tale of Two Covariance Models," CARF F-Series CARF-F-156, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Roy van der Weide, 2002. "GO-GARCH: a multivariate generalized orthogonal GARCH model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 549-564.

    More about this item

    Keywords

    Asymptotic normality; BEKK; consistency; GARCH; Martingale CLT;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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