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Portmanteau Tests for Semiparametric Nonlinear Conditionally Heteroscedastic Time Series 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)

  • Thomas Verdebout

    (ULB - Université libre de Bruxelles = Free University of Brussels, ECARES - European Center for Advanced Research in Economics and Statistics - ULB - Université libre de Bruxelles = Free University of Brussels)

  • Jean-Michel Zakoian

    (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

A class of multivariate time series models is considered, with general parametric specifications for the conditional mean and variance. In this general framework, the usual Box–Pierce portmanteau test statistic, based on the sum of the squares of the first residual autocorrelations, cannot be accurately approximated by a parameter-free distribution. A first solution is to estimate from the data the complicated asymptotic distribution of the Box–Pierce statistic. The solution proposed by Li [23] consists of changing the test statistic by using a quadratic form of the residual autocorrelations which follows asymptotically a chi-square distribution. Katayama [21] proposed a distribution-free statistic based on a projection of the autocorrelation vector. The first aim of this paper is to show that the three methods, initially introduced for specific time series models, can be applied in our general framework. The second aim is to compare the three approaches. The comparison is made on (i) the mathematical assumptions required by the different methods and (ii) the computations of the Bahadur slopes (in some cases via Monte Carlo simulations).
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Christian Francq & Thomas Verdebout & Jean-Michel Zakoian, 2023. "Portmanteau Tests for Semiparametric Nonlinear Conditionally Heteroscedastic Time Series Models," Post-Print hal-05417181, HAL.
    • Handle: RePEc:hal:journl:hal-05417181
    DOI: 10.1007/978-981-99-0803-5_5
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