论文部分内容阅读
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.
A method of predicting chaotic time series based on multivariable phase reconstruction is proposed.The method obtains the information related to the predicted time series from the nonlinear dynamic system to form a multivariate time series. Firstly, multivariable phase space reconstruction , And then use the local multivariate linear regression model in the phase space prediction, and finally from the predicted high-dimensional phase points in the time series of predictive value is separated.Because of the consideration of the dynamic system of the relationship between the mutual coupling of variables , Which increases the amount of system information in the reconstructed phase space and makes the phase point trajectory of the phase space more approximate to the dynamic behavior of the original system.Compared with the method of univariate prediction, Whether the single-step prediction or the multi-step prediction can effectively improve the prediction accuracy and has the advantage that the choice of embedding dimension has little effect on the prediction accuracy.According to the Lorenz chaotic signal prediction, the experimental results verify the effectiveness of the method.