基于多变量相重构的混沌时间序列预测

提出了一种基于多变量相重构的混沌时间序列预测方法.该预测方法从非线性动力学系统中获取与待预测时间序列相关的信息组成多变量时间序列,首先进行多变量相空间重构,然后利用局域多元线性回归模型在相空间中进行预测,最后从预测出的高维相点中分离出时间序列的预测值.由于考虑了动力学系统中多个变量之间相互耦合的关系,从而增加了重构相空间的系统信息量,使得相空间的相点轨迹更加逼近原系统的动力学行为.与采用单变量进行预测的方法相比,基于多变量相重构的预测方法无论是单步预测还是多步预测,都能有效地提高预测精度,且具有嵌入维数的选择对预测精度影响较小的优点.通过对Lorenz混沌信号进行预测,实验结果验证了方法的有效性.

Prediction for chaotic time series based on phase reconstruction of multivariate time series

A nonlinear prediction method based on phase reconstruction of multivariate time series was proposed.Together with the candidate time series for prediction,the correlated information of the same nonlinear dynamical system was selected to construct a multivariate time series.In the phase reconstruction space of the multivariate time series,a local multi-variant linear regression model was used to forecast the evolution data of phase point,through which the future data of the candidate time series were predicted.Since the coupled relationship among different variants of the dynamical system were taken into consideration,the reconstructed phase space had more dynamical information and phase point trajectory more approximated the original dynamical behavior.Compared with the univariate method,for either one-step or multi-step prediction,the new method has better prediction preciseness with less sensitivity to the selection of embedding dimension.The validity of the new prediction method was verified by the results of prediction experiments on the Lorenz system.