Data-based causality analysis tries to detect the true structural relations between measurements of complex multivariate systems. The detected relations should correspond to the true structure of the underlying data generation process. Even though there are many methodologies developed to extract causal relations from data, existence of instantaneous correlation between some variables in the data set, requires special care in order to correctly do the analysis. It is required to detect the instantaneous relations between variables as a prerequisite for subsequent causality analysis. Not only is detection of instantaneous relations important, but it is also necessary to discover the direction of information flow in the instantaneous relations. This piece of information plays a vital role in selection of correct modeling structure to achieve a reliable result about causal relations between variables. Using prior knowledge about the process or blind mathematical transformations are usual solutions for this problem in the literature. However, there is a lack of reliable mathematical methodologies to address this issue completely based on data analysis. This brief proposes a method to detect the direction of instantaneous causal relations between variables and supports it through simulation and case studies. The proposed algorithm uses a third variable as an instrument to detect the direction of information flow between any two instantaneously correlated variables. The instrument variable is required to meet some conditions for the algorithm to work; however, the application of the algorithm does not require any prior information about the process.

中文翻译：

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在变量之间的瞬时关系中检测信息流的方向

基于数据的因果关系分析试图检测复杂多元系统的度量之间的真实结构关系。检测到的关系应对应于基础数据生成过程的真实结构。即使开发了许多从数据中提取因果关系的方法，但是为了正确进行分析，也需要特别注意数据集中某些变量之间存在瞬时相关性。需要检测变量之间的瞬时关系，作为后续因果关系分析的前提。检测瞬时关系不仅很重要，而且有必要在瞬时关系中发现信息流的方向。这条信息在选择正确的建模结构以实现有关变量之间因果关系的可靠结果方面起着至关重要的作用。使用有关过程的先验知识或盲目数学变换是文献中针对此问题的常见解决方案。但是，缺乏可靠的数学方法来完全基于数据分析来解决此问题。本摘要提出了一种检测变量之间的瞬时因果关系方向的方法，并通过仿真和案例研究对其进行了支持。所提出的算法使用第三变量作为一种工具来检测任意两个瞬时相关变量之间的信息流方向。需要仪器变量来满足算法运行的某些条件；然而，