引用本文:席剑辉, 韩敏.主成分分析与神经网络的结合在多变量序列预测中的应用[J].控制理论与应用,2007,24(5):719~724.[点击复制]
XI Jian-hui, HAN Min.Prediction of multivariate time series based on principal component analysis and neural networks[J].Control Theory and Technology,2007,24(5):719~724.[点击复制]
主成分分析与神经网络的结合在多变量序列预测中的应用
Prediction of multivariate time series based on principal component analysis and neural networks
摘要点击 2565  全文点击 2018  投稿时间：2005-05-08  修订日期：2006-10-27
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DOI编号  
  2007,24(5):719-724
中文关键词  多元变量时间序列  神经网络  预测  主成分分析
英文关键词  multivariate time series  neural network  prediction  principal component analysis
基金项目  国家自然科学基金资助项目(60374064).
作者单位
席剑辉, 韩敏 沈阳航空工业学院自动控制系, 辽宁沈阳110034
大连理工大学电子与信息工程学院, 辽宁大连116023 
中文摘要
      目前预测方法的研究主要集中在单变量时间序列上, 本文建立起一种针对多元变量非线性时间序列建模和预测的方法框架. 首先, 同时考虑序列状态间的线性相关性和非线性相关性, 建立初始延迟窗以包含充分的预测信息; 然后, 利用主成分分析(PCA)方法寻找不同变量在数据空间中的最大方差方向, 扩展PCA应用于提取多个变量的综合信息, 重构多元变量输入状态相空间; 最后, 利用神经网络逼近不同变量之间以及当前状态和将来状态之间的函数映射关系, 实现多元变量预测. 对Rossler混沌方程和大连降雨、气温序列的预测仿真说明了本文方法的有效性, 为多元变量时间序列分析提供了一条新的途径.
英文摘要
      Most of previously published prediction methods are concentrated on the modeling of univariate time series. The main purpose of this paper is to study a new methodology to model and predict multivariate nonlinear time series. Firstly, both the linear correlations and the nonlinear correlations are detected to initialize an embedding delay window, which could contain enough information for prediction. Then, the principal components analysis (PCA) method is expanded to extract the joint information of multiple variables in a complex system since PCA could find the uncorrelated directions of maximum variance in the data space of different variables. The multivariate phase space is reconstructed. Furthermore, neural network makes predictions on the basis of approximating both the functional relation between different variables and the map between current state and future state. Finally, two simulation examples, one is from the typical Rossler equation and the other is from the practically observed values of rainfall and temperature of Dalian, are used to explain the validity of the proposed method. It provides a new way to analyze the multivariate time series.