Bayesian Inference of Autoregressive and Functional-Coefficient Moving Average Models

Based on free-knot splines techniques, we develop a fully Bayesian method to make inference about the autoregressive and functional-coefficient moving-average models, including estimation and prediction. We approximate different functional-coefficients by polynomial splines with different orders to adapt to different smoothness. To make the estimation and prediction robust, we assign heavy-tailed student-t priors on the coefficients of both the splines and the autoregressive terms. The posterior predictive distribution is derived from a Bayesian model average over all of the possible models. The proposed method is demonstrated by both simulated and real data examples.