Bias-Corrected Adaptive Conformal Inference for Multi-Horizon Time Series Forecasting

TL;DR

This paper introduces Bias-Corrected Adaptive Conformal Inference (BC-ACI), a method that improves prediction interval calibration in time series forecasting by online bias correction, especially under distribution shifts.

Contribution

The paper proposes BC-ACI, an extension of ACI that incorporates bias correction via an online EWM estimate, addressing persistent bias and improving interval accuracy.

Findings

BC-ACI reduces Winkler interval scores by 13-17% under distribution shifts.

BC-ACI maintains performance on stationary data, with a ratio of 1.002x.

Finite-sample analysis shows graceful coverage degradation with bias estimation error.

Abstract

Adaptive Conformal Inference (ACI) provides distribution-free prediction intervals with asymptotic coverage guarantees for time series under distribution shift. However, ACI only adapts the quantile threshold -- it cannot shift the interval center. When a base forecaster develops persistent bias after a regime change, ACI compensates by widening intervals symmetrically, producing unnecessarily conservative bands. We propose Bias-Corrected ACI (BC-ACI), which augments standard ACI with an online exponentially weighted moving average (EWM) estimate of forecast bias. BC-ACI corrects nonconformity scores before quantile computation and re-centers prediction intervals, addressing the root cause of miscalibration rather than its symptom. An adaptive dead-zone threshold suppresses corrections when estimated bias is indistinguishable from noise, ensuring no degradation on well-calibrated data. In controlled experiments across 688 runs spanning two base models, four synthetic regimes, and three real datasets, BC-ACI reduces Winkler interval scores by 13--17% under mean and compound distribution shifts (Wilcoxon p < 0.001) while maintaining equivalent performance on stationary data (ratio 1.002x). We provide finite-sample analysis showing that coverage guarantees degrade gracefully with bias estimation error.