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Researchers introduce Doubly Robust Adaptive Conformal Inference (DR-ACI), a new method to build prediction intervals for causal effects when data are temporally dependent. The method targets a constructed, observable quantity called a doubly robust pseudo-outcome. Calibrating on that observable gives distribution-free guarantees even when observations are not independent, which is common in finance and epidemiology.
The team combines three ideas. First, they use a doubly robust pseudo-outcome that mixes two standard building blocks: a model for the treatment probability (the propensity score) and a model for the outcome under each treatment. This pseudo-outcome has the useful property that its bias behaves like the product of the two nuisance-model errors, so it can be accurate if at least one nuisance model is well estimated. Second, they adapt conformal prediction, a way to make intervals that do not rely on correct model assumptions, to the time-series setting. Third, they introduce temporal block cross-fitting with guardbands: the time series is split into contiguous blocks, neighboring observations around a calibration block are left out of training, and models are trained on the remaining data. This reduces dependence between training and calibration.
At a technical level, the paper proves two properties that make conformal calibration feasible under weak dependence. One is a switch-coefficient control for the doubly robust conformity scores, which controls how dependence affects calibration. The other is a preserved double-machine-learning product-bias bound, with an explicit extra coupling term that shrinks as the guardband grows. The authors decompose the coverage gap into three parts: a mixing gap that depends on the time dependence, a nuisance-bias tax from estimating the propensity and outcome models, and an adaptation rate that behaves like T−1/2 where T is the series length. Under certain fast-mixing conditions, their rate matches what one would get with independent (exchangeable) data.
Why this matters: conformal methods give finite-sample, distribution-free interval guarantees for observable quantities. DR-ACI extends those guarantees to a causal setting with time dependence, so practitioners can obtain observation-by-observation uncertainty quantification for estimated treatment effects in dependent data. In simulations the variance-standardized version of DR-ACI (VS-DR-ACI) produced intervals 63% narrower than split conformal at valid coverage. In experiments that mixed dependence and a simulated drift, VS-DR-ACI kept near-valid coverage (about 89.9%) while conventional double-machine-learning confidence intervals lost about 35 percentage points after the drift started. The authors also apply the method to Nasdaq market microstructure data to produce stock-level intervals for hidden-order execution quality.
Important caveats: the conformal calibration targets the observable pseudo-outcome, not the latent conditional average treatment effect (CATE) itself. The paper proves asymptotic containment for the latent CATE only under extra consistency assumptions on the point estimator. It does not claim finite-sample (1−α) coverage for the latent CATE. The theoretical guarantees rely on strict stationarity and β-mixing (a formal notion of weak dependence). These assumptions exclude structural breaks, regime changes, and covariate drift; the paper’s regime-change experiments are noted as empirical robustness checks rather than covered by the main theorems. The authors also note that their mixing bounds are conservative in practice and that tightening those bounds is future work.
Code to reproduce simulations is available on GitHub. The paper’s main technical contributions include the temporal block cross-fitting analysis and the three-term coverage decomposition that makes the method’s trade-offs transparent.