Predicting Hyper-Chaotic Time Series Using Adaptive Higher-Order Nonlinear Filter

A newly proposed method,i.e.the adaptive higher-order nonlinear finite impulse response(HONFIR)filter based on higher-order sparse Volterra series expansions,is introduced to predict hyper-chaotic time series.The effectiveness of using adaptive HONFIR filter for making one-step and multi-step predictions is tested based on very few data points by computer-generated hyper-chaotic time series including Mackey-Glass equation and 4-dimensional nonlinear dynamical system.A comparison is made with some neural networks for predicting the Mackey-Glass hyper-chaotic time series.Numerical simulation results show that the adaptive HONFIR filter proposed here is a very powerful tool for making prediction of hyper-chaotic time series.