A Semiparametric Smooth Transition ARX Model for Nonlinear Time Series

Abstract

In this paper, I propose an extension to the class of semiparametric time series models by incorporating a weight function to allow for smooth transitions between a linear autoregressive and a nonparametric component. The weight function and nonparametric component may depend on auxiliary variables. The inclusion of the weight function broadens the flexibility of the semiparametric model and allows for testing against smooth transition parametric models and against linearity. If no auxiliary variables are used the model is a special case of the functional coefficient autoregressive model, while if auxiliary variables are used the model's solution is a distributed lag in nonlinear functions. The nonparametric component is approximated using a Fourier series expansion and the model is estimated using the MINPIN approach proposed in Andrews (1994). An empirical illustration is provided using the U.S. quarterly unemployment rate data, previously analyzed in Montgomery et al. (1998).