Assessing Time-Series Causal Discovery without Ground Truth

Assessing the relevance of a causal graph inferred from observational data remains limited when no reference graph is available, since standard structural and interventional metrics require ground-truth causal relations. We extend the Causal Relevance Index to lagged causal discovery by aggregating edge-specific p-value bounds over a fixed set of candidate lagged relations. The graph-level properties of the resulting index are shown to follow from a marginal condition on the conditional independence tests: for every absent edge, a super-uniform p-value obtained for at least one tested separating set provides a sufficient condition. This result requires no assumptions on the joint dependence structure among the edge-specific quantities. Conditions under which temporal dependence preserves this super-uniformity property are further derived, together with an empirical null normalization based on iterative amplitude-adjusted Fourier transform surrogates to account for finite-sample and test-specific effects. The resulting criteria are evaluated on nonlinear synthetic time series spanning several graph structures, sample sizes, causal discovery algorithms, and conditional independence tests, as well as on measurements from the Causal Chambers wind-tunnel system. Across these experiments, CRI follows the same trend as true-positive recovery without access to ground truth, while providing a continuous measure of the adequacy of the inferred graph to the conditional dependence structure supported by the data, as quantified by the edge-specific p-value bounds.