Genetic algorithms for building double threshold generalized autoregressive conditional heteroscedastic models of time series

A procedure based on genetic algorithms (GAs) is proposed for building double-threshold generalized autoregressive conditional heteroscedastic (DTGARCH) models. Multi-regime, conditional heteroscedastic and their combinations were shown to be useful models in financial applications as well as in many other fields, so that it is of interest investigating appropriate methods for designing identification and estimation procedures. GAs may be considered optimization tools that mimic the evolution of a living population towards fitness to the natural environment. The key feature of GAs is manipulation of a population of individuals each of which represents a feasible solution of the optimization problem. Only a subset of the solution space is processed as GAs may confine the search into the “more promising” regions of this space. Usefulness of GAs is apparent when the search is to be performed in large discrete spaces where the desirable objective function properties such as continuity, differentiability or convexity are not satisfied. For a DTGARCH model to be fully specified a set of structural parameters is needed along with a set of real coefficients. The most efficient choice may be using GAs for searching for structural parameters and, once these latter have been provided, applying a numerical optimization algorithm to compute the model’s coefficients. The effectiveness of the proposed procedure is demonstrated by applications to real data concerned with stock exchange indexes (the Hong Kong Hang Seng index in various years) and exchange-rate series (French franc/dollar and Japanese yen/dollar).