Evolving nonlinear time-series models using evolutionary programming

Abstract

Different variants of evolutionary programming (EP) have been proposed recently to determine the order and parameters of time series models. Unlike conventional algorithms, the model order and coefficients are evolved simultaneously in evolutionary algorithms. In this paper, the performance of the different types of evolutionary algorithms was tested on standard problems. In particular, the algorithms considered in this paper were evolutionary programming, fast evolutionary programming and modified simulated evolutionary optimization, EP was used to evolve both the order and coefficients of the reduced parameter bilinear model and recurrent bilinear perceptron. These models were used for one-step prediction of four well investigated time series, namely the sunspot series, the Mackey-Glass series, the laser data series and the astrophysical data series. The performance of the algorithms was compared on the basis of the order of the model evolved and normalized mean square error. Fast evolutionary programming with recurrent bilinear perceptrons produced the best models with fewer parameters and lower normalized mean square error.