TNN # CE479 - REV. A Flexible Coefficient Smooth Transition Time Series Model

In this paper, we consider a flexible smooth transition autoregressive (STAR) model with multiple regimes and multiple transition variables. This formulation can be interpreted as a time varying linear model where the coefficients are the outputs of a single hidden layer feedforward neural network. This proposal has the major advantage of nesting several nonlinear models, such as, the Self-Exciting Threshold AutoRegressive (SETAR), the AutoRegressive Neural Network (AR-NN), and the Logistic STAR models. Furthermore, if the neural network is interpreted as a nonparametric universal approximation to any Borelmeasurable function, our formulation is directly comparable to the Functional Coefficient AutoRegressive (FAR) and the Single-Index Coefficient Regression models. A model building procedure is developed based on statistical inference arguments. A Monte-Carlo experiment showed that the procedure works in small samples, and its performance improves, as it should, in medium size samples. Several real examples are also addressed.