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Analysis And Modeling Of Multivariate Chaotic Time Series Basedon Neural Network

机译：基于神经网络的多元混沌时间序列分析与建模

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摘要

A new nonlinear multivariate technique is proposed for modeling and predicting chaotic time series with a view to improve estimates and predictions. With analysis of the relations among different state spaces by the proposed method, which introduces the reverse-predictability and time spans to discover the underlying relationship, the connections among multivariate time series are discussed before prediction. Then we predict the time series by multivariate prediction. Though multivariate time series can bring more information about the complex system, which can enhance the accuracy of prediction, they also bring a too large number of input variables which may result in overfitting and poor generalization abilities. To overcome the shortcomings, principal component analysis (PCA) based on singular value decomposition (SVD) is used to extract main features of multivariate time series and reducing the dimension of the model inputs. Then based on Takens' delay time theory, the multivariate time series are reconstructed. Subsequently, a four-layer feedforward neural network is trained as the multivariate predictive model. Three simulation examples, that are coupled Henon equation and two set of real world time series, are used to demonstrate the validity of the proposed method.
机译：提出了一种新的非线性多元技术，用于建模和预测混沌时间序列，以改善估计和预测。通过所提出的方法对不同状态空间之间的关系进行分析，引入反向可预测性和时间跨度以发现潜在的关系，在预测之前讨论了多元时间序列之间的联系。然后，我们通过多元预测来预测时间序列。尽管多元时间序列可以带来有关复杂系统的更多信息，可以提高预测的准确性，但是它们也带来了过多的输入变量，这可能导致拟合过度和泛化能力差。为了克服该缺点，基于奇异值分解（SVD）的主成分分析（PCA）用于提取多元时间序列的主要特征并减小模型输入的维数。然后根据Takens的延迟时间理论，重构了多元时间序列。随后，将四层前馈神经网络训练为多元预测模型。结合Henon方程和两组真实世界时间序列的三个仿真实例，证明了该方法的有效性。

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