Fitting of Threshold Models for Time Series

One of the most important parametric nonlinear time series models is the (self exciting) threshold autoregressive model. The TAR model was introduced by Tong/Lim (1980). There are some extensions to this class of models, namely smooth transition threshold autoregressive model. Other nonlinear models like functional auroregressive models can be thought of as generalizations. It is rather often stated that nonlinear models are necessary but there are not such many applications. In fact there exists a gap between the theoretical development of nonlinear time series models and their application. One reason for this gap may be the lack of applicable software and some investigations of the numerical side of these models. The present paper tries to do a step to fill this gap. For this we describe a procedure to implement the fitting process efficiently. Also we report on some difficulties with estimating STAR models and give some advice to overcome the problems. For FAR models it seems to be of help to smooth the observed parametric relationship. Nevertheless, the usefulness of FAR models to recover more complicated functional coefficients from the data is doubted. All programming was done in GAUSS. The progams are available at request from the author