Time series perturbation by genetic programming

Abstract

This paper presents a new algorithm that combines perturbation theory and genetic programming for modeling and forecasting real-world chaotic time series. Both perturbation theory and time series modeling have to build symbolic models for very complex system dynamics. Perturbation theory does not work without a well-defined system equation. Difficulties in modeling time series lie in the fact that we cannot have or assume any system equation. The new algorithm shows how genetic programming can be combined with perturbation theory for time series modeling. Detailed discussions on successful applications to chaotic time series from practically important fields of science and engineering are given. Computational resources were negligible as compared with earlier similar regression studies based on genetic programming. A desktop PC provides sufficient computing power to make the new algorithm very useful for real-world chaotic time series. Especially, it worked very well for deterministic or stationary time series, while stochastic or nonstationary time series needed extended effort, as it should be.