In this paper, we focus on estimating the causal effect of an intervention over time on a dynamical system. To that end, we formally define causal interventions and their effects over time on discrete-time stochastic processes (DSPs). Then, we show under which conditions the equilibrium states of a DSP, both before and after a causal intervention, can be captured by a structural causal model (SCM). With such an equivalence at hand, we provide an explicit mapping from vector autoregressive models (VARs), broadly applied in econometrics, to linear, but potentially cyclic and/or affected by unmeasured confounders, SCMs. The resulting causal VAR framework allows us to perform causal inference over time from observational time series data. Our experiments on synthetic and real-world datasets show that the proposed framework achieves strong performance in terms of observational forecasting while enabling accurate estimation of the causal effect of interventions on dynamical systems. We demonstrate, through a case study, the potential practical questions that can be addressed using the proposed causal VAR framework.

本文研究了干预对动态系统因果效应的时间估计，填补了传统模型在时序数据处理中的不足。我们提出了一种新的因果VAR框架，能够从观察性时间序列数据中准确推断因果效应，实验结果表明该方法在预测和因果推断方面表现优异，具有重要的实用性和应用潜力。

一种实用的时间因果推理方法