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Causal Discovery

Granger Causality (granger_pairwise)

Ref: Granger (1969) Econometrica 37(3)

Tests whether past values of X help predict Y beyond Y's own past. Uses VAR-based AIC lag selection, stationarity gating (ADF), and BH-FDR correction.

Assumptions: Bivariate testing. Stationarity (auto-differencing applied). Linear relationships. Minimum N=20.

Works well when: Two time series with a clear lag relationship. Quick pairwise exploration.

Fails when:

  • Transitive chains (X→Y→Z): Granger will find X→Z even when the direct effect is mediated by Y. This is not a bug — it's a bivariate limitation. Use PCMCI+ to condition on Y.
  • Nonlinear relationships: p-values are not meaningful for strongly nonlinear systems.
  • Short series: N < 50 makes AIC lag selection unstable.

FDR note: All pairs are BH-corrected. evidence_strength="moderate" means adjusted p < 0.05. Check confounder_candidates for Z that drives both X and Y.

from dqt.causality.granger import granger_pairwise
report = granger_pairwise(df, max_lag=4)
for edge in report.significant_edges:
    print(f"{edge.cause} → {edge.effect}  "
          f"(lag={edge.selected_lag}, strength={edge.evidence_strength})")
    if edge.confounder_candidates:
        print(f"  ⚠ possible confounders: {edge.confounder_candidates}")

PCMCI+ (pcmci_pairwise)

Ref: Runge et al. (2019) Science Advances

Multivariate causal discovery that conditions each bivariate test on all other variables — solves Granger's transitive-chain problem.

Assumptions: Stationarity (auto-differencing applied). Linear (ParCorr) or nonlinear (GPDC) conditional independence. Minimum N=50.

Works well when: Panel of 3+ time series where you want to distinguish direct from indirect effects. Better precision than Granger on chains and forks.

Fails when: N < 100 (multivariate conditioning is expensive). Requires dqt[causal] extra.

Hyperparameter sensitivity: Run with tau_max=3 and tau_max=5 — if results differ materially, flag edges as "fragile."

from dqt.causality.pcmci import pcmci_pairwise
report = pcmci_pairwise(df, tau_max=3, cond_ind_test="parcorr")
for edge in report.significant_edges:
    print(f"{edge.cause} → {edge.effect}  lag={edge.lag}")