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Vine-GARCH process: Stationarity and Asymptotic Properties

Author

Listed:
  • Benjamin Poignard

    (Ensae-Crest, University Paris-Dauphine)

  • Jean-David Fermanian

    (Ensae-Crest)

Abstract

We provide conditions for the existence and the uniqueness of strictly stationary solutions of the Vine-GARCH process. The proof is based on Tweedie's (1988) criteria, after rewriting the Vine-GARCH process as a nonlinear Markov chain. Furthermore, we provide asymptotic results of the estimators obtained by the quasimaximum likelihood method. We prove the weak consistency and asymptotic normality of the quasi-maximum likelihood estimator obtained in a two-step procedure.

Suggested Citation

  • Benjamin Poignard & Jean-David Fermanian, 2016. "Vine-GARCH process: Stationarity and Asymptotic Properties," Working Papers 2016-03, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2016-03
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    References listed on IDEAS

    as
    1. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(2), pages 280-310, April.
    2. Lewandowski, Daniel & Kurowicka, Dorota & Joe, Harry, 2009. "Generating random correlation matrices based on vines and extended onion method," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1989-2001, October.
    3. Boussama, Farid & Fuchs, Florian & Stelzer, Robert, 2011. "Stationarity and geometric ergodicity of BEKK multivariate GARCH models," Stochastic Processes and their Applications, Elsevier, vol. 121(10), pages 2331-2360, October.
    4. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
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