Testing a linear ARMA Model against threshold-ARMA models: a Bayesian approach

We introduce a Bayesian approach to test linear autoregressive moving-average (ARMA) models against threshold autoregressive moving-average (TARMA) models. Firstly, the marginal posterior densities of all parameters, including the threshold and delay, of a TARMA model are obtained by using Gibbs sampler with Metropolis-Hastings algorithm. Secondly, reversible-jump Markov chain Monte Carlo (RJMCMC) method is adopted to calculate the posterior probabilities for ARMA and TARMA models: Posterior evidence in favor of TARMA models indicates threshold nonlinearity. Finally, based on RJMCMC scheme and Akaike information criterion (AIC) or Bayesian information criterion (BIC), the procedure for modeling TARMA models is exploited. Simulation experiments and a real data example show that our method works well for distinguishing a ARMA from a TARMA model and for building TARMA models.