Detecting the Direction of Information Flow in Instantaneous Relations Between Variables

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.