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

Christian Francq, Lajos Horvath and Jean-Michel Zakoian

Econometric Theory, 2010, vol. 26, issue 4, 965-993

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.

Date: 2010
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Working Paper: Sup-Tests for Linearity in a General Nonlinear AR(1) Model (2009)
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