• AR model;
  • threshold AR model;
  • likelihood ratio test;
  • structural change;
  • marked empirical process
  • C12;
  • C22;
  • C51

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.