Detection and characterization of changes of the correlation structure in multivariate time series.
Detection and characterization of changes of the correlation structure in multivariate time series.
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DOI：
10.1103/physreve.71.046116
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发表时间：
2005-04
期刊：
影响因子：
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通讯作者：
M. Müller;G. Baier;A. Galka;U. Stephani;H. Muhle
中科院分区：
文献类型：
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作者：
M. Müller;G. Baier;A. Galka;U. Stephani;H. Muhle
我们提出了一种基于等时相关矩阵的方法，作为多变量数据集相形相关性的灵敏检测器。该方法的关键在于时间序列间同步度的变化会引起相关矩阵谱两端特征态之间的水平排斥。因此，关于多元数据集的相关结构的详细信息被印入特征值的动态和相应的特征向量的结构中。通过对N(f)-环面、自回归模型和耦合混沌系统的应用证明了该技术的性能。该方法的高灵敏度、相对较小的计算量和良好的时间分辨率使其适合于分析复杂的、空间扩展的、非平稳的系统。
We propose a method based on the equal-time correlation matrix as a sensitive detector for phase-shape correlations in multivariate data sets. The key point of the method is that changes of the degree of synchronization between time series provoke level repulsions between eigenstates at both edges of the spectrum of the correlation matrix. Consequently, detailed information about the correlation structure of the multivariate data set is imprinted into the dynamics of the eigenvalues and into the structure of the corresponding eigenvectors. The performance of the technique is demonstrated by application to N(f)-tori, autoregressive models, and coupled chaotic systems. The high sensitivity, the comparatively small computational effort, and the excellent time resolution of the method recommend it for application to the analysis of complex, spatially extended, nonstationary systems.