基于多维泰勒网的自适应混沌时间序列多步预测
Adaptive multi-step prediction of chaotic time series based on multi-dimensional Taylor network

提出了一种新的混沌时间序列预测方法――多维泰勒网方法.该方法不以相空间重构方法中嵌入维数和时间延迟这两个关键参数的选取为前提,无需系统的先验知识和机理,仅根据已知的时间序列样本,通过多维泰勒网模型获得n元一阶多项式差分方程组,进而得到能反映非线性系统动力学特性的多维泰勒网动态模型.在此基础上提出了基于多维泰勒网的自适应多步预测方法,通过数据窗口的滑动自适应建模,实现对混沌时间序列的多步预测. 将该方法应用于Lorenz混沌时间序列的一步和多步预测,均方误差分别达到2.56×10-5和2.76×10-3.仿真结果表明,该方法可以对混沌时间进行有效预测,且具有较高的预测精度.
A new chaotic time series prediction method, the method based on multi-dimensional Taylor network, is proposed. In this method it is unnecessary to choose the embedding dimension and delay time which are referred to as two key parameters in the process of phase-space reconstruction. Without prior knowledge and mechanism of the system, the first order n-variables polynomial difference equations can be obtained by the multi-dimensional Taylor network according to the known samples of the time series. Thus, the multi-dimensional Taylor network dynamics model is obtained, which can describe the dynamic characteristics of the nonlinear system. On this basis, an adaptive multi-step prediction method based on the multi-dimensional Taylor network is presented. The adaptive model realizes the multi-step prediction of chaotic time series by sliding the data window. Then the method is applied to single step and multi-step prediction of the Lorenz chaotic time series and the mean square errors are 2.56×10-5and 2.76×10-3, respectively. The simulation results indicate that the new method is valid in chaotic time series prediction with better predictive accuracy