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Testing for Common GARCH Factors


  • Prosper Dovonon
  • Éric Renault


This paper proposes a test for common conditionally heteroskedastic (CH) features in asset returns. Following Engle and Kozicki (1993), the common CH features property is expressed in terms of testable overidentifying moment restrictions. However, as we show, these moment conditions have a degenerate Jacobian matrix at the true parameter value and therefore the standard asymptotic results of Hansen (1982) do not apply. We show in this context that the Hansen's (1982) J-test statistic is asymptotically distributed as the minimum of the limit of a certain empirical process with a markedly nonstandard distribution. If two assets are considered, this asymptotic distribution is a half-half mixture of x_(H-1)^2and x_H^2, where H is the number of moment conditions, as opposed to a x_(H-1)^2. With more than two assets, this distribution lies between the x_(H-p)^2 and x_H^2 (p, the number of parameters). These results show that ignoring the lack of first order identification of the moment condition model leads to oversized tests with possibly increasing over-rejection rate with the number of assets. A Monte Carlo study illustrates these findings. Cet article propose un test pour la détection de caractéristiques communes d'hétéroscédasticité conditionnelle (HC) dans des rendements d'actifs financiers. Conformément à Engle et Kozicki (1993), l'existence de caractéristiques communes HC est exprimée en termes de conditions de moment sur-identifiantes testables. Cependant, nous montrons que ces conditions de moment ne sont pas localement linéairement indépendantes; la matrice Jacobienne est nulle à la vraie valeur des paramètres et, par conséquent, la théorie asymptotique de Hansen (1982) ne s'applique pas. Nous montrons dans ce contexte que la statistique de J-test de Hansen (1982) est distribuée asymptotiquement comme le minimum de la limite d'un processus empirique avec une distribution non standard. Quand on considère deux actifs, cette distribution asymptotique est un mélange à parts égales de x_(H-1)^2 et x_H^2, où H est le nombre de conditions de moment, par opposition à x_(H-1)^2. Avec plus de deux actifs, cette distribution est comprise entre x_(H-p)^2 et x_H^2 (p, le nombre de paramètres). Ces résultats montrent que l'ignorance du défaut d'identification au premier ordre dans ce modèle de conditions de moments conduit à des tests qui rejettent trop souvent l'hypothèse nulle, le degré de sur-rejet étant croissant avec le nombre d'actifs. Une étude de Monte-Carlo illustre ces résultats.

Suggested Citation

  • Prosper Dovonon & Éric Renault, 2012. "Testing for Common GARCH Factors," CIRANO Working Papers 2012s-34, CIRANO.
  • Handle: RePEc:cir:cirwor:2012s-34

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    References listed on IDEAS

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    Cited by:

    1. Alastair R. Hall, 2013. "Generalized Method of Moments," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 14, pages 313-333 Edward Elgar Publishing.
    2. Prosper Dovonon & Sílvia Gonçalves, 2014. "Bootstrapping the GMM overidentification test Under first-order underidentification," CIRANO Working Papers 2014s-25, CIRANO.

    More about this item


    Common features; GARCH factors; Nonstandard asymptotics; GMM; GMM overidentification test; identification; first order identification;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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