Doubly Robust Adaptive Conformal Inference for Causal Effects Under Temporal Dependence

Quantifying uncertainty for individual treatment effects (CATEs) is challenging when data are temporally dependent, as standard conformal prediction methods rely on exchangeability. The authors address this by developing DR-ACI, which constructs prediction intervals for doubly robust pseudo-outcomes. To handle temporal dependence, they employ temporal block cross-fitting with guard bands—a technique that ensures training and calibration sets are sufficiently separated to preserve the validity of the doubly robust estimator's product-bias rate. The method then uses online adaptive conformal inference (ACI) to maintain long-run coverage guarantees.

The paper establishes a three-term coverage decomposition for DR-ACI: a mixing gap, a nuisance-bias tax, and an adaptation rate. The authors prove that, under beta-mixing, this decomposition provides a valid coverage guarantee for the pseudo-outcome. A key technical contribution is proving that temporal block cross-fitting with guard bands preserves the doubly robust product-bias rate, with an explicit coupling remainder that decays with the guard band size. In simulations calibrated to high-frequency financial data, the variance-standardized version of the method (VS-DR-ACI) reduces interval width by 63% compared to split conformal while maintaining valid coverage. Furthermore, VS-DR-ACI remains robust under combined temporal dependence and covariate drift, where other methods suffer significant coverage loss or interval inflation.

This work provides a rigorous framework for uncertainty quantification in causal inference for time-series data, which is common in finance, epidemiology, and macroeconomics. By enabling valid, adaptive prediction intervals for latent treatment effects, the method allows researchers to move beyond average treatment effects and identify heterogeneous impacts with statistical confidence. The application to Nasdaq’s Dynamic M-ELO rollout demonstrates the method's practical utility in identifying which securities benefit most from market microstructure reforms.