Causal inference seeks to identify cause-and-effect interactions in coupled systems. A recently proposed method by Liang detects causal relations by quantifying the direction and magnitude of information flow between time series. The theoretical formulation of information flow for stochastic dynamical systems provides a general expression and a data-driven statistic for the rate of entropy transfer between different system units. To advance understanding of information flow rate in terms of intuitive concepts and physically meaningful parameters, we investigate statistical properties of the data-driven information flow rate between coupled stochastic processes. We derive relations between the expectation of the information flow rate statistic and properties of the auto- and cross-correlation functions. Thus, we elucidate the dependence of the information flow rate on the analytical properties and characteristic times of the correlation functions. Our analysis provides insight into the influence of the sampling step, the strength of cross-correlations, and the temporal delay of correlations on information flow rate. We support the theoretical results with numerical simulations of correlated Gaussian processes.

翻译：因果推断旨在识别耦合系统中的因果交互作用。Liang最近提出的一种方法通过量化时间序列间信息流的方向与大小来检测因果关系。针对随机动力系统的信息流理论公式给出了熵在不同系统单元间传递率的一般表达式及数据驱动的统计量。为从直观概念与物理意义参数角度深入理解信息流率，我们研究了耦合随机过程间数据驱动信息流率的统计特性。推导出信息流率统计量期望值与自相关及互相关函数性质之间的关系，从而阐明信息流率对相关函数解析特性与特征时间的依赖性。通过分析揭示了采样步长、互相关强度及相关时滞对信息流率的影响，并利用相关高斯过程的数值模拟验证了理论结果。