Causal Discovery for Non-stationary Time Series Data by Harnessing Latent Variables

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Abstract
Recovering causal structures from non-stationary time series data is a challenging task across numerous domains. Conventional methods often assume that the non-stationarity of data is indexed by a specific time, domain, or regime, rendering them inadequate for complex scenarios driven by unobserved external factors. To address these limitations, we adopt a latent-variable perspective, viewing non-stationarity as arising from unobserved external factors whose changing states induce temporal variations in causal mechanisms. This perspective motivates a unified framework that exploits global causal structure to guide local causal discovery, rather than treating temporal segmentation and causal structure learning as independent tasks. Specifically, we propose a two-stage algorithm. First, we leverage LPCMCI as a global structural heuristic to identify observed variables potentially affected by latent confounding. Second, we monitor the statistical stability of the identified variables to partition the time series into approximately stationary intervals, within which PCMCI+ is applied to recover local causal structures. By integrating global structural analysis with stability-guided segmentation, our framework narrows the search space and facilitates the recovery of temporal variations in causal relationships, including changes in causal strengths and graph structure. Experiments on synthetic benchmarks and real-world datasets demonstrate the effectiveness of the proposed approach in recovering non-stationary causal structures.

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