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Adaptiveness of the empirical distribution of residuals in semi-parametric conditional location scale models

Author

Listed:
  • Christian Francq

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, IP Paris - Institut Polytechnique de Paris)

  • Jean-Michel Zakoïan

    (CREST - Centre de Recherche en Economie et Statistique [Bruz] - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique, IP Paris - Institut Polytechnique de Paris)

Abstract

This paper addresses the problem of deriving the asymptotic distribution of the empirical distribution function F n of the residuals in a general class of time series models, including conditional mean and conditional heteroscedaticity, whose independent and identically distributed errors have unknown distribution F. We show that, for a large class of time series models (including the standard ARMA-GARCH), the asymptotic distribution of √ n{ F n (·) − F (·)} is impacted by the estimation but does not depend on the model parameters. It is thus neither asymptotically estimation free, as is the case for purely linear models, nor asymptotically model dependent, as is the case for some nonlinear models. The asymptotic stochastic equicontinuity is also established. We consider an application to the estimation of the conditional Value-at-Risk.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Christian Francq & Jean-Michel Zakoïan, 2022. "Adaptiveness of the empirical distribution of residuals in semi-parametric conditional location scale models," Post-Print hal-05417235, HAL.
    • Handle: RePEc:hal:journl:hal-05417235
    DOI: 10.3150/21-BEJ1357
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