基于支持向量回归模型的混沌系统多步预测

Multi-step prediction of chaotic systems based on support vector regression model

混沌时间序列具有不可预测性和类随机性等特性,会导致混沌时间序列的多步预测及其困难。文章探讨了基于支持向量回归模型的混沌时间序列递归多步预测理论及应用。首先,介绍了支持向量回归模型和混沌时间序列递归多步预测理论;然后,将该理论分别应用于Logistic Map和太阳黑子混沌时间序列,并进行实证分析。结果表明,受累积误差的影响,预测步数越多,均方误差和归一化均方误差均越大,而R 2越小。Logistic Map递归可预测步数大概是14步,太阳黑子递归可预测步数大概是6步;最后,对后续的研究工作提出了几点思考意见。

Chaotic time series have chaotic characteristics of unpredictability and pseudo-randomness,which leads to the difficulty of multi-step prediction.This paper discusses the recursive multi-step prediction theory of chaotic time series based on support vector regression model and its application.Firstly,the support vector regression model and the recursive multi-step prediction theory of chaotic time series are introduced.Then,the theory is applied to logistic map and sunspot chaotic time series for empirical analysis.The results show that the greater the number of prediction steps,the greater the mean square error and the normalized mean square error,and the smaller the R 2.The logistic map recursion has a predictable number of steps of about 14 and the sunspot recursion has a predictable number of steps of about 6.Finally,some suggestions are put forward for the follow-up research work.