Dynamic Bayesian smooth transition autoregressive models

In this paper we propose the Gaussian Dynamic Bayesian Smooth Transition Autoregressive (DBSTAR) models for nonlinear autoregressive time series processes as alternative to both the classical Smooth Transition Autoregressive (STAR) models of Chan and Tong (1986) and the computational Bayesian STAR (CBSTAR) models of Lopes and Salazar (2005). The DBSTAR models are autoregressive formulations of dynamic linear models by West and Harrison (1997) based on polynomial approximations of transition functions of STAR models. Unlike the classical STAR and CBSTAR models, their estimate parameters vary in time, being suitable for modelling non-stationary processes. For being Bayesian, the DBSTAR models do not require extensive historical data for parameter estimation and allow expert intervention via prior distribution assessment of model parameters. For being sequential and analytical, the DBSTAR models avoid potential computational problems associated with the CBSTAR models and allow fast estimation of the dynamic parameters sequentially in time, being thus suitable for real time applications. The application of DBSTAR models to the Canadian Lynx data showed improved fitting performances when compared with both the classical and the CBSTAR models.