Fitting piecewise linear threshold autoregressive models by means of genetic algorithms

A nonlinear version of the threshold autoregressive model for time series is introduced. A peculiar requirement on parameters, except possibly for the constant term, is the continuity, that seems a natural and useful assumption. This model is a special case of the general state-dependent models, where the moving-average term is dropped and a particular form for the dependence on the state is speci3ed. Such model meets also the functional autoregressive model formulation, but the “least demanding” functional form is assumed. Further restrictive assumptions are not needed. Both identi3cation and estimation problems will be taken into account. The proposed approach brings together the genetic algorithm, in its simplest binary form, and some basic features from spline theory. It results in a powerful 8exible tool which is shown to be able to approximate a wide class of nonlinear time series models. This method is found to compare favorably with existing procedures in modeling some well-known real-time series, which often are taken as a benchmark for testing and comparing modeling procedures. c © 2003 Elsevier B.V. All rights reserved.