Sup-Tests for Linearity in a General Nonlinear AR(1) Model

Christian Francq, Lajos Horvath and Jean-Michel Zakoian

No 2009-16, Working Papers from Center for Research in Economics and Statistics

Abstract: We consider linearity testing in a general class of nonlinear time series model of order 1, involvinga nonnegative nuisance parameter which (i) is not identified under the null hypothesis and (ii)gives the linear model when equal to zero. This paper studies the asymptotic distribution of theLikelihood Ratio test and asymptotically equivalent supremum tests. The asymptotic distributionis described as a functional of chi-square processes and is obtained without imposing a positivelower bound for the nuisance parameter. The finite sample properties of the sup-tests are studiedby simulations.

Pages: 33
Date: 2009
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Journal Article: SUP-TESTS FOR LINEARITY IN A GENERAL NONLINEAR AR(1) MODEL (2010)
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