Forecasting with computer-evolved model specifications: a genetic programming application

Abstract

This paper uses genetic programming (GP) to evolve model specifications of time series data. GP is a computerized random search optimization algorithm that assembles equations until it identifies the fittest one. The technique is applied here to artificially simulated data first then to real-world sunspot numbers. One-step-ahead forecasts produced by the fittest of computer-evolved models are evaluated and compared with alternatives. The results suggest that GP may produce reasonable forecasts if their user selects appropriate input variables and comprehends the process investigated. Further, the technique appears promising in forecasting noisy complex series perhaps better than other existing methods. It is suitable for decision makers who set high priority on obtaining accurate forecasts rather than on probing into and approximating the underlying data generating process. Scope and purpose This paper contains a brief introduction and an evaluation of the use of genetic programming (GP) in forecasting time series. GP is a computerized random search optimization technique based upon Darwin's theory of evolution. The algorithm is first applied to model and forecast artificially simulated linear and nonlinear time series. Results are used to evaluate the effectiveness of GP as a forecasting technique. It is then applied to model and forecast sunspot numbers—the most frequently analyzed and forecasted series. An autoregressive and a threshold nonlinear dynamical systems to capture the dynamics of the irregular sunspot numbers’ cycle were tested using GP. The latter delivered estimated equations yielding the lowest mean square error ever reported for the series. This paper demonstrates that GP's forecasting capabilities depend on the structure and complexity of the process to model. Skills and intuition of GP's user are its limitation.