We study a specific type of SCM, called a Dynamic Structural Causal Model (DSCM), whose endogenous variables represent functions of time, which is possibly cyclic and allows for latent confounding. As a motivating use-case, we show that certain systems of Stochastic Differential Equations (SDEs) can be appropriately represented with DSCMs. An immediate consequence of this construction is a graphical Markov property for systems of SDEs. We define a time-splitting operation, allowing us to analyse the concept of local independence (a notion of continuous-time Granger (non-)causality). We also define a subsampling operation, which returns a discrete-time DSCM, and which can be used for mathematical analysis of subsampled time-series. We give suggestions how DSCMs can be used for identification of the causal effect of time-dependent interventions, and how existing constraint-based causal discovery algorithms can be applied to time-series data.

翻译：我们研究一种特定类型的结构因果模型（SCM），称为动态结构因果模型（DSCM），其内生变量表示时间的函数，该模型允许循环性和潜在混杂。作为一个激励性的应用案例，我们证明了某些随机微分方程（SDE）系统可以用DSCM恰当地表示。这种构建的一个直接结果是SDE系统的图马尔可夫性质。我们定义了一种时间分割操作，使我们能够分析局部独立性（一种连续时间格兰杰（非）因果性的概念）。我们还定义了一种子采样操作，该操作返回一个离散时间DSCM，并可用于子采样时间序列的数学分析。我们提出了DSCM如何用于识别时间依赖性干预的因果效应，以及如何将现有的基于约束的因果发现算法应用于时间序列数据。