非线性时序的混沌特性分析与预测

Analysis and Prediction of Fund Index of Nonlinear Time Series

非线性时间序列相空间重构过程中的参数选择问题以及有效的预测方法一直是该领域研究的热点和难点,基于虚假最近邻域概念,同时确定最佳的嵌入维数m与时间延迟τ,对实际非线性时间序列进行相空间重构,求解出时间序列最在Lyapunov指数LE,验证了其中混沌特性,其可预报尺度为[1/LE].并应用基于[1/LE]个输入神经元与Kenya提出的m∶2m∶m∶1这两种人工神经网络结构对非线性时间序列进行训练和预测,预测结果的平均误差分别为4%和2%左右,后一种神经网络结构能提供更好的预测结果.

Determining the parameters in the reconstruction of phase space and effective predict method is key points in this field.Based on the conception of false nearest neighbor,which determines the best embedding dimension m and time delay τ simultaneously,the nonlinear time series is reconstructed.The max Lyapunov exponent LE validates the chaotic property in the time series.The predictable scale is [1/LE] days.And the two architectures of artificial neural net work,based on [1/LE] input neurons and m∶2m∶m∶l,are applied in the prediction of the time series.The average errors are 4% and 2% respectively.the latter can offers better result.