Stationarity-Aware Causal Discovery in Time Series via Minimal Separating Sets

Discovering causal relationships from observational time series is a fundamental problem with broad applications in climate science, healthcare, and finance. Causal graphs with time-lagged structure capture the effects of underlying mechanisms over time. Under the causal stationarity assumption, these causal mechanisms remain consistent across time. Existing constraint-based methods leverage stationarity for conditional independence testing and reduce the problem to learning the parents of variables at the final time point, which can then be used to reconstruct the stationary graph. However, their separating set search strategy mimics the PC algorithm and does not take advantage of the stationary structure. We observe that the stationary graph structure and autoregressive edges impose many meaningful constraints on the separating sets between variables at different time lags. After characterizing the behavior of such separating sets, we propose a novel causal discovery algorithm that exploits this structure of minimal separating sets. Extensive evaluations on synthetic and real-world datasets demonstrate the robustness and accuracy of our method.