Time-Varying Smooth Transition Autoregressive Models

Nonlinearity, and regime-switching behavior in particular, and structural change have often been perceived as competing alternatives to linearity. In this paper we propose a model, based on the principle of smooth transition, that allows for regime-switching behavior in conjunction with time-varying parameters. This Time-Varying Smooth Transition Autoregressive [TV-STAR] model can be used both for describing simultaneous nonlinearity and structural change and for distinguishing between these features. Two modeling strategies for empirical specification of TV-STAR models are developed and tested by Monte Carlo simulation. The simulations show that neither of the two strategies dominates the other. The relative merits of each of the specification procedures are illustrated with empirical applications. The specific-to-general-to-specific procedure is best suited for obtaining a quick impression of the importance of nonlinearity and/or structural change for a particular time series. This is illustrated by an application to a large number of US macroeconomic time series. The specific-to-general procedure is most useful in careful specification of a model with nonlinear and/or time-varying properties. This is demonstrated by a worked example involving the US help-wanted advertising index.