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.