Abstract Cross-correlation of a bivariate time series induces interdependencies between local patterns in the two series, which cooperatively exhibit in turn the structure of the cross-correlation. However, this structure is lost in the procedure of statistical average in time series analysis. In this paper a new concept called pattern interdependent network is proposed to display the structure of cross-correlation, in which the nodes are unique local patterns and the linkages are co-occurring frequencies of the unique local patterns in the series. The performance is illustrated by the bivariate series generated with the Gaussian process and the auto-regressive fractionally integrated moving average (ARFIMA) model. It is found that the cross-correlation and the scaling behaviors dominate the pattern of backbone structure (the set of the nodes and the set of linkages) and the symmetry of the network, respectively. The ARFIMA model can reproduce the structural behaviors of cross-correlations in U.S. stock markets. This concept provides us with a new method for detecting the structure of couplings between time series in various fields, such as clinical pathological signals.

中文翻译：

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多元时间序列中互相关的模式相互依赖网络

摘要 二元时间序列的互相关导致两个序列中局部模式之间的相互依赖性，这两个序列又协同表现出互相关的结构。然而，这种结构在时间序列分析中的统计平均过程中丢失了。在本文中，提出了一种称为模式相互依赖网络的新概念来显示互相关的结构，其中节点是唯一的局部模式，链接是序列中唯一局部模式的共现频率。使用高斯过程和自回归分数积分移动平均 (ARFIMA) 模型生成的双变量系列说明了性能。发现互相关和缩放行为分别支配着骨干结构的模式（节点集和链接集）和网络的对称性。ARFIMA 模型可以再现美国股票市场互相关的结构性行为。这个概念为我们提供了一种新的方法来检测各个领域的时间序列之间的耦合结构，例如临床病理信号。