Local higher-order Volterra filter multi-step prediction model of chaotic time series

In general, the prediction modeling of chaotic time series is conducted by Volterra filters through constructing nonlinear fitting functions according to the methodology of pattern training. Since the proposed approach is consistent with the nonlinear characteristics of chaotic systems, the corresponding model turns to be more effective than conventional models. However, something abnormal is likely to occur, such as inadequate trainingor, over training, and the training data set size is not easy to choose, because the existing Volterra filters are trained point by point along the chaotic orbit. Based on the similarity of the evolving tendency of neighbor orbits in phase space, the chaotic time series multi-step-prediction model (MSP-HONFIR) employing the adaptive higher-order nonlinear Volterra filter (HONFIR) is constructed in this paper. A new method of choosing neighbor orbits in phase space is presented by considering the Euclidean distance and the evolving tendency. In addition, the criterion for the choice of the training data set size is discussed. Numerical experiments demonstrate that the performances of multi-step-prediction are improved compared to the original HONFIR method.