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SUP-TESTS FOR LINEARITY IN A GENERAL NONLINEAR AR(1) MODEL

Published online by Cambridge University Press:  04 November 2009

Christian Francq ,
Lajos Horvath  and
Jean-Michel Zakoïan
Christian Francq
Affiliation:
Université Lille III, GREMARS-EQUIPPE
Lajos Horvath
Affiliation:
University of Utah
Jean-Michel Zakoïan*
Affiliation:
Université Lille III, GREMARS-EQUIPPE and CREST
*
*Address correspondence to Jean-Michel Zakoïan, CREST, 15 boulevard Gabriel Péri, 92245 Malakoff Cedex, France; e-mail: zakoian@ensae.fr.
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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.

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Type
ARTICLES
Information
Econometric Theory , Volume 26 , Issue 4 , August 2010 , pp. 965 - 993
Copyright
Copyright © Cambridge University Press 2009

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