基于混沌时间序列的非线性动态系统神经网络建模与预测

基于混沌时间序列的非线性动态系统神经网络建模与预测 Modeling and Forecasting of the Nonlinear Dynamic System Neural Network Based on the Chaotic Time Series 郁俊莉 YU Jun-li 1 first-author 北京大学政府管理学院,北京,100871 北京大学政府管理学院,北京,100871 School of Government, Peking University School of Government, Peking University 在分析神经网络非线性建模原理的基础上,以典型的非线性差分方程为研究对象,提出了一类基于神经网络的非线性动态系统建模方法.针对传统BP算法的局限性,提出了一种非线性动态系统神经网络改善梯度估计精度的新算法.并以上证综合指数时间序列为研究对象,运用本文提出的建模方法和算法,进行了我国资本市场混沌时间序列预测研究的实例分析,得到的单步预测上证综合指数误差很小（-100 1 00）;多步预测在最初的10步之内预测效果较为理想,而在此之后的预测值则严重偏离真实值.这与混沌时间序列特性相吻合,同时也证明了所用算法的有效性. It is inevitable to deal with the nonlinear problems to know the natural world correctly. This is also true the nonlinear properties make the world have become complicated and changeable. This paper establishes a modeling method for predicting a type of chaotic time series, discusses the principle of the multi layers feedback neural network in modeling the nonlinear system, gives a neural network model for the nonlinear system; puts forward a new BP algorithm; researches on the prediction of chaotic time series of the capital market combined with the time series of the Shanghai Stock Market, verifies the affectivity of results of analysis. 混沌时间序列 非线性动态系统 神经网络 BP算法 chaotic time series nonlinear dynamic system neural network BP algorithm F224 中国博士后自然科学基金资助项目（2003033080） 2005-03-01 2021-04-01 3