Evolving reduced parameter bilinear models for time series prediction using fast evolutionary programming

We propose fast evolutionary programming (FEP) for optimizing the parameters of a reduced parameter bilinear model (RPBL) used for predicting nonlinear and chaotic time series. The RPBL model is capable of effectively representing nonlinearity and multiperiodicity with the additional advantage of using fewer parameters than a conventional bilinear model. FEP has been shown to have reasonable optimization performance and can be coupled with the ability to determine model structure. Unlike conventional methods where the model order is chosen first and the parameters of the model are determined subsequently, both the model order and the parameters are evolved simultaneously in light of the minimum description length (MDL) criterion. The effectiveness of FEP is first tested on the Bohachevsky and Rosenbrock functions and then used for prediction of the sunspot series, laser generated data, Mackey-Glass series, and astrophysical data. Experimental results show that FEP, in comparison with conventional evolutionary programming, evolves RPBL models with lower normalized mean squared error (NMSE) and also lower model order.