A Bayesian Thershold Nonlinearity Test for TAR Models

Under the hypothesis of normal distribution, the change-point problems have four cases according to mean and variance changing. In this paper, we look upon the threshold nonlinearity test of TAR models as a change-point problem, which has a change-mean and constant-variance. We adopt reversible-jump Markov chain Monte Carlo (RJMCMC) methods to calculate the posterior probabilities of two competitive models, namely AR and TAR models. Posterior evidence favoring the TAR model indicates threshold nonlinearity. Simulation experiments demonstrate that our method works very well in distinguishing AR and TAR models.