Best Subset Selection for Double-Threshold-Variable Autoregressive Moving-Average Models: The Bayesian Approach

In this paper, we propose an effective Bayesian subset selection method for the double-threshold-variable autoregressive moving-average (DT-ARMA) models. The usual complexity of estimation is increased mainly by capturing the correlation between two threshold variables and including moving-average terms in the model. By adopting the stochastic search variable selection method, combined with the Gibbs sampler and Metropolis-Hastings algorithm, we can simultaneously estimate the unknown parameters and select the best subset model from a large number of possible models. The simulation experiments illustrate that the proposed approach performs well. In applications, two real data sets are analyzed by the proposed method, and the fitted DT-ARMA model is better than the double-threshold autoregressive (DT-AR) model from the view of parsimony.