When dealing with time series data, causal inference methods often employ structural vector autoregressive (SVAR) processes to model time-evolving random systems. In this work, we rephrase recursive SVAR processes with possible latent component processes as a linear Structural Causal Model (SCM) of stochastic processes on a simple causal graph, the \emph{process graph}, that models every process as a single node. Using this reformulation, we generalise Wright's well-known path-rule for linear Gaussian SCMs to the newly introduced process SCMs and we express the auto-covariance sequence of an SVAR process by means of a generalised trek-rule. Employing the Fourier-Transformation, we derive compact expressions for causal effects in the frequency domain that allow us to efficiently visualise the causal interactions in a multivariate SVAR process. Finally, we observe that the process graph can be used to formulate graphical criteria for identifying causal effects and to derive algebraic relations with which these frequency domain causal effects can be recovered from the observed spectral density.

翻译：在处理时间序列数据时，因果推断方法常采用结构向量自回归过程来建模随时间演化的随机系统。本文中，我们将具有潜在分量过程的递归SVAR过程重新表述为定义在简单因果图——即过程图——上的随机过程线性结构因果模型，该模型将每个过程视为单一节点。利用这一重构，我们将Wright著名的线性高斯SCM路径规则推广到新引入的过程SCM，并通过广义迹规则表达了SVAR过程的自协方差序列。借助傅里叶变换，我们推导了频域中因果效应的简洁表达式，从而能有效可视化多元SVAR过程中的因果交互作用。最后，我们指出过程图可用于构建识别因果效应的图准则，并推导出从观测谱密度中恢复这些频域因果效应的代数关系。