Testing for structural change of AR model to threshold AR model

The purpose of this article is to develop the likelihood ratio test for the structural change of an AR model to a threshold AR model. It is shown that the log-likelihood ratio test converges to the maxima of a two-parameter Gaussian process in distribution. This limiting distribution is novel and we tabulate the critical values. Some simulations are carried out to examine the finite-sample performance of this test statistic. This article also includes a weak convergence of a two-parameter marked empirical process, which is of independent interest.