Nonlinear nonstationary model building by genetic algorithms

Abstract

Many time series exhibits both nonlinearity and nonstationarity. Though both features have been often taken into account separately, few attempts have been proposed for modeling them simultaneously. We consider threshold models and present a general model allowing for several different regimes both in time and in levels, where regime transitions may happen according to self-exciting, or smoothly varying, or piecewise linear threshold modeling. Since fitting such a model involves the choice of a large number of structural parameters, we propose a procedure based on genetic algorithms, evaluating models by means of a generalized identification criterion. The proposed model building strategy is applied to a financial index.