The Prediction Research Of Chaotic Time Series On Wavelet Neural Network

In the real world, a large number of chaotic time series are frequently observed from complex non-linear systems, such as runoff series from hydrological systems, stock price series from financial system, load series from electricity power system, and so on. Because of the universality and particularity of chaotic time series, the prediction research is tremendous meaningful.Based on the profound research on related theories and methods of chaotic time series prediction, this article introduces hybrid wavelet neural network to the prediction of chaotic time series, and proposes a forecast framework to predict noisy chaotic time series as well. In a conclusion, this article discusses the following contents.1. Based on the application and research of traditional wavelet neural network, a varietal wavelet neural network which integrates linear regression model is discussed, the hybrid model can capture the linear and nonlinear characteristics of a given time series; the back-propagation (BP) learning algorithm of the hybrid model is also provided, to make further efforts, a algorithm combined the virtues of both BP and genetic algorithm (GA) is proposed to overcome the drawbacks of BP algorithm.2. To apply the hybrid model to the prediction of noisy chaotic time series, a forecast framework which consists of wavelet de-noise, phase space reconstruction and hybrid wavelet neural network modeling is designed. Wavelet de-noise is introduced to lower the impact of noise signal and to improve the quality of data. Phase space reconstruction is used to deeply mine the useful information hidden in time series and to determine the input/output of hybrid time series. The hybrid model characterizes the nonlinear structure of chaotic time series.3. All simulation instances involved in this article are implemented in MATLAB, such as phase space reconstruction and wavelet de-noise of Mackey-Glass time series, moreover, the prediction of Mackey-Glass with/without noise is discussed, and the simulation results validate the excellence performance of hybrid model and forecast framework.