CausalSR: Scale-Resolved Causal Discovery from Time Series with Heterogeneous Responses

Causal discovery from time series has become increasingly important across a wide range of application domains. In practice, multivariate time series often exhibit heterogeneous responses across short, medium, and long time scales, causing causal effects at different temporal scales to overlap in the observed signals and making scale-specific causal relations difficult to separate, orient, and recover reliably. To address this issue, we propose CausalSR, a scale-resolved causal discovery framework that reorganizes multivariate time series in the time-frequency domain and learns causal structures at their corresponding temporal scales, instead of directly operating on the original time-domain observations. Specifically, the framework separates scale-specific temporal components, estimates interaction strength and directional evidence within each scale, suppresses indirect relations through regularized conditional-association screening, and jointly refines the resulting graphs using reconstruction consistency and acyclicity constraints, thereby enabling the recovery of more reliable scale-resolved structural information from complex time series for downstream temporal analysis. Theoretically, we prove that coherence-weighted phase aggregation preserves directional temporal ordering and enables scale-specific directed edge inference, thereby providing theoretical support for scale-resolved causal discovery. Experiments on synthetic benchmarks and real-world temporal datasets demonstrate the effectiveness of our method.