Nonlinear prediction of time series

There is considerable interest in the use of nonlinear techniques to perform prediction of naturally occurring time series, e.g. medical signals and signals from seismic returns. The motivation in considering these techniques lies in the fact that may of the underlying generation mechanisms are nonlinear. There has been growing interest in the use of neural network architectures for such applications. This has been coupled with the research carried out in the field of nonlinear dynamical systems, especially so-called chaotic systems. This paper reports an investigation of the prediction of a chaotic time series arising from a well-known differential equation. A series approach is applied to the estimation of such a series as well as the more regular and well-understood periodic case. First of all, the radial basis function technique is applied, using a approach based on the Wiener theory. A brief comparison is made with the same sort of approach applied to the Volterra series predictor (Nisbet et al., 1991)