Likelihood ratio tests for the structural change of an AR(p) model to a Threshold AR(p) model

Abstract

This article considers the likelihood ratio (LR) test for the structural change of an AR model to a threshold AR model. Under the null hypothesis, it is shown that the LR test converges weakly to the maxima of a two‐parameter vector Gaussian process. Using the approach in Chan and Tong (1990)and Chan (1991), we obtain a parameter‐free limiting distribution when the errors are normal. This distribution is novel and its percentage points are tabulated via a Monte Carlo method. Simulation studies are carried out to assess the performance of the LR test in the finite sample and a real example is given.