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Sup-Tests For Linearity In A General Nonlinear Ar(1) Model

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] - GENES - 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 - GENES - 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)

  • Lajos Horvath

    (Mathematics department - University of Utah)

  • Jean-Michel Zakoïan

    (LFA - Laboratoire de Finance Assurance - Centre de Recherche en Économie et Statistique (CREST) - GENES - Groupe des Écoles Nationales d'Économie et Statistique, EQUIPPE - Economie Quantitative, Intégration, Politiques Publiques et Econométrie - Université de Lille, Sciences et Technologies - Université de Lille, Sciences Humaines et Sociales - PRES Université Lille Nord de France - Université de Lille, Droit et Santé)

Abstract

We consider linearity testing in a general class of nonlinear time series models of order one, involving a nonnegative nuisance parameter that (a) is not identified under the null hypothesis and (b) gives the linear model when equal to zero. This paper studies the asymptotic distribution of the likelihood ratio test and asymptotically equivalent supremum tests. The asymptotic distribution is described as a functional of chi-square processes and is obtained without imposing a positive lower bound for the nuisance parameter. The finite-sample properties of the sup-tests are studied by simulations.

Suggested Citation

  • Christian Francq & Lajos Horvath & Jean-Michel Zakoïan, 2009. "Sup-Tests For Linearity In A General Nonlinear Ar(1) Model," Post-Print hal-05417894, HAL.
    • Handle: RePEc:hal:journl:hal-05417894
    DOI: 10.1017/S0266466609990430
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