RareCP: Regime-Aware Retrieval for Efficient Conformal Prediction

Conformal prediction has become increasingly popular for uncertainty quantification, providing distribution-free coverage guarantees and extensions that remain applicable to sequential and time-series data. Yet, broad common protocol comparisons between conformal methods and the native uncertainty estimates of recent time series foundation models remain limited. We show that, for one-step prediction intervals, existing conformal approaches can be substantially less efficient than native intervals. To close this gap, we introduce RareCP, a weighted conformal prediction method with a retrieval architecture tailored to learning recurring residual regimes and adapting to the current forecasting context. We characterize conditions under which calibration consistently estimates the fitted model's population quantiles, isolating its remaining learning and approximation error. We additionally use adaptive conformal inference (ACI) for long-run empirical coverage control under distribution drift.