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H 2 Testing the existence of moments for GARCH-type processes

Auteurs : Zakoïan, Jean-Michel (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : It is generally admitted that financial time series have heavy tailed marginal distributions. When time series models are fitted on such data, the non-existence of appropriate moments may invalidate standard statistical tools used for inference. Moreover, the existence of moments can be crucial for risk management. This talk considers testing the existence of moments in the framework of standard and augmented GARCH models. In the case of standard GARCH, even-moment conditions involve moments of the independent innovation process. We propose tests for the existence of moments of the returns process that are based on the joint asymptotic distribution of the estimator of the volatility parameters and empirical moments of the residuals. To achieve efficiency gains we consider non Gaussian QML estimators founded on reparametrizations of the GARCH model, and we discuss optimality issues. We also consider augmented GARCH processes, for which moment conditions are less explicit. We establish the asymptotic distribution of the empirical moment Generating function (MGF) of the model, defined as the MGF of the random autoregressive coefficient in the volatility dynamics, from which a test is deduced. An alternative test is based on the estimation of the maximal exponent characterizing the existence of moments. Our results will be illustrated with Monte Carlo experiments and real financial data.

    Keywords : conditional variance models; tests of moments; efficiency comparisons

    Codes MSC :
    37M10 - Time series analysis
    62M10 - Time series, auto-correlation, regression, etc.
    62P20 - Applications of statistics to economics

    Ressources complémentaires :

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 09/10/2020
      Date de captation : 17/09/2020
      Collection : Research talks ; Probability and Statistics
      Durée : 00:38:20
      Domaine : Probability & Statistics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2020-09-17_Zakoian.mp4

    Informations sur la rencontre

    Nom de la rencontre : New Results on Time Series and their Statistical Applications / Séries chronologiques: nouveaux résultats et applications statistiques
    Organisateurs de la rencontre : Bardet, Jean-Marc ; Eckley, Idris ; Fokianos, Konstantinos ; Neumann, Michael H. ; Philippe, Anne
    Dates : 14/09/2020 - 19/09/2020
    Année de la rencontre : 2020
    URL Congrès : https://conferences.cirm-math.fr/2233.html

    Citation Data

    DOI : 10.24350/CIRM.V.19655303
    Cite this video as: Zakoïan, Jean-Michel (2020). Testing the existence of moments for GARCH-type processes. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19655303
    URI : http://dx.doi.org/10.24350/CIRM.V.19655303

    Voir aussi


    1. FRANCQ, Christian et ZAKOIAN, Jean-Michel. Testing the existence of moments for GARCH processes. Journal of Econometrics, 2020. - https://doi.org/10.1016/j.jeconom.2020.05.009