Online Conformal Prediction for Non-Exchangeable Panel Data

TL;DR

This paper introduces an online conformal prediction method tailored for non-exchangeable panel data, providing adaptive, distribution-free uncertainty quantification with coverage guarantees.

Contribution

It proposes a simple, adaptive online conformal framework that handles temporal dependence and heterogeneity in panel data, improving coverage for worst-covered units.

Findings

Method yields stepwise and long-run coverage guarantees.

Empirically improves coverage on worst-covered units.

Adaptive interval-widths outperform uniform inflation.

Abstract

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.