混沌时间序列局域线性预测方-法

在许多场合下，时间序列中的明显随机性可能是由于非线性确定性系统中混沌行为的缘故．混沌系统对初值的极端敏感性使之不可能对其时间序列进行长期预测，然而，利用混沌的确定性可以进行短期预期．混沌时间序列预测首先要重构相空间，接着再利用非线性函数逼近方法构造一个动力学系统模型．探讨了预测模型问题，并用数值分析的方法对Ｆａｒｍｅｒ＆Ｓｉｄｏｒｏｗｉｃｈ，Ｌｉｎｓａｙ和Ｎａｖｏｎｅ＆Ｃｅｃｃａｔｏ提出的三种典型混沌时间序列局域线性预测方法进行了研究．实验结果表明，这三种方法的性能是相同的．本文的结果将平息人们对这三种方法优劣的争论，有利于在实际中选择合适的预测模型．

Local Linear Prediction Method of Chaotic Time Series

In some cases, apparent randomness in time series may be due to chaotic behavior of a nonlinear but deterministic system, and sensitivity of the chaotic system to initial conditions impedes long term predictions of time series. However, it is possible to make short term predictions by exploiting the determi nism. This is done by first reconstructing a state space and then using nonlinear function approximation methods to create a dynamical model. The model for time series prediction was considered. In particular, three typical methods developed by Farmer and Sidorowich, Linsay and Navone and Ceccatto were investigated using numerical method. The expermental results show that they have the same prediction performance.