Online Conformal Prediction for Non-Exchangeable Panel Data
This work addresses the challenge of quantifying predictive uncertainty in panel data settings with temporal dependence and unit heterogeneity, which is important for practitioners in science and engineering who need reliable prediction intervals.
The paper proposes an online conformal prediction framework for non-exchangeable panel data that uses contemporaneous calibration units and two adaptive mechanisms—similarity weights and an adaptive miscoverage level—to achieve stepwise and long-run coverage guarantees. Empirically, the method improves coverage on worst-covered target units via adaptive interval-width allocation rather than uniform inflation.
Panel data, in which multiple units are repeatedly observed over time, arise throughout science and engineering. Quantifying predictive uncertainty in such settings is challenging because conformal prediction, while distribution-free and model-agnostic, classically relies on exchangeability assumptions that fail under temporal dependence and unit heterogeneity. We propose a simple online conformal framework for non-exchangeable panel data. The method exploits a key feature of online panel prediction: when a forecast is required for one unit, contemporaneous outcomes from related units may already be observed and can serve as a calibration panel. At each round, prediction sets are formed using currently observed calibration units together with two adaptive quantities: history-based similarity weights that emphasize calibration units resembling the target, and an adaptive miscoverage level that is updated whenever target feedback is revealed. This two-state design yields a stepwise coverage bound and a long-run coverage guarantee. Empirically, across synthetic and real panel data sets, the method improves coverage on the worst-covered target units through adaptive interval-width allocation rather than uniform inflation. The two states are complementary: similarity weights protect coverage when target feedback is sparse, while the adaptive level further improves coverage as feedback accumulates.