Neural Volterra filter for chaotic time series prediction

A new second-order neural Volterra filter (SONVF) with conjugate gradient (CG) algorithm is proposed to predict chaotic time series based on phase space delay-coordinate reconstruction of chaotic dynamics system in this paper, where the neuron activation functions are introduced to constraint Volterra series terms for improving the nonlinear approximation of second-order Volterra filter (SOVF). The SONVF with CG algorithm improves the accuracy of prediction without increasing the computation complexity. Meanwhile, the difficulty of neuron number determination does not exist here. Experimental results show that the proposed filter can predict chaotic time series effectively, and one-step and multi-step prediction performances are obviously superior to those of SOVF, which demonstrate that the proposed SONVF is feasible and effective.