Local Adaptive Nonlinear Filter Prediction Model with a Parameter for Chaotic Time Series

Abstract

In order to improve the predictive performance for chaotic time series， we propose a novel local adaptive nonlinear filter prediction model. We use a function with a parameter to build an adaptive nonlinear filter in this model, and we train this model with an adaptive algorithm, deduced by the minimum square-root-error criterion and the steepest gradient descent rule. We evaluate the proposed model using four well-known chaotic systems, namely Logistic map, Henon map, Lorenz system and Rosslor system. All the results show a remarkable increase in predictive performance, comparing with the local adaptive nonlinear filter prediction model.