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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 the 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 the Mackey-Glass equation and four-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.