Reaching the Tail: Calibration Diversity Drives Conformal Coverage under Data Scarcity

Recent advances in uncertainty quantification for time series forecasting show that conformal prediction can provide reliable prediction intervals, yet standard conformal methods are often inefficient under temporal dependence, drift, and heterogeneous error behavior. Existing methods typically either update miscoverage rates over time or learn unconstrained calibration weights, without explicitly separating two central sources of nonstationarity: smoothly drifting error distributions and co-existing distinct error regimes. We introduce RareCP, a regime-aware retrieval method for adaptive conformal time series prediction. RareCP learns local calibration representations through a mixture of cosine-attention experts that each capture distinct error regimes, while a compact hypernetwork adapts the kernel parameters to track temporal drift. Given a new forecasting context, RareCP retrieves the top-k most relevant calibration examples, assigns similarity weights, and forms a weighted conformal quantile over their signed residuals, yielding asymmetric prediction intervals. The adaptive kernel is trained using a smooth interval score objective, with a parameter-space anchor to a lightweight teacher kernel to preserve stable local representations. On the GIFT-Eval benchmark, RareCP improves interval efficiency over recent conformal baselines and foundation model uncertainty estimates while maintaining empirical coverage. Ablations confirm that regime-specific experts, drift-adaptive kernels, sparse retrieval, and teacher anchoring each contribute to the final performance.

Conformal prediction provides distribution-free prediction intervals but relies on exchangeability, an assumption often violated in economic forecasting because of covariate shift, concept drift, local heterogeneity and latent regimes. We propose Dynamic Regime-Aware Conformal Prediction (DRACP), which combines density-ratio, localized kernel and probabilistic regime-aware weighting with a self-tuning online significance controller in a unified weighted conformal calibration framework. We distinguish three theoretical results: finite-sample validity under oracle importance weights, a coverage-gap bound for estimated weights with rates in effective sample size, and deterministic or regret guarantees for the online controller. We evaluate DRACP against six baselines on 48 real forecasting series covering euro-area and EU-27 HICP inflation, US macroeconomic and energy indicators, and daily financial series. Recent online methods (FACI, strongly-adaptive online conformal prediction and conformal PID) were verified against the authors' implementations. DRACP is not the most efficient method: strongly-adaptive online conformal prediction achieves the best interval score and intervals about 20% narrower. Instead, DRACP provides the most reliable calibration, achieving coverage closest to the nominal 0.90 (0.890), never falling below 0.80 on any series, maintaining the best coverage at all forecast horizons, and performing best during the 2021-2023 inflation surge. The strongly-adaptive method undercovers on 20 of 48 series versus 10 for DRACP. DRACP therefore offers a principled trade-off between calibration and efficiency, favoring reliable coverage when prediction intervals must satisfy coverage standards. An ablation study shows that the online controller and conditional-scale normalization provide most of the performance gain, whereas the weighting components make a smaller contribution.

Modern conformal forecasting systems often maintain several adaptive pipelines that differ in base forecasters, conformity scores, calibration windows, and update rules. Comparing them is difficult because coverage is a hard constraint, whereas efficiency should be optimized only among feasible pipelines. We formulate this problem as sequential inference for a stochastic constrained argmin. At each time, the target is the set of minimum-cost pipelines satisfying multiple prefix-average conditional miscoverage constraints. We introduce Coverage-Constrained Sequential Model Confidence Sets (CC-SMCS), which separate certifiably feasible, possibly feasible, and possibly constrained-optimal pipelines. Using simultaneous martingale confidence sequences, CC-SMCS projects a rectangular confidence region onto the constrained argmin and admits an exact closed-form rule. With probability at least $1-δ$, it contains every constrained-optimal pipeline simultaneously over all times. This finite-sample guarantee requires no stationarity or mixing assumptions and remains valid under data-dependent stopping. We also establish an impossibility result for safe certification at the coverage boundary and extend the construction to delayed multi-horizon feedback and outcome-dependent efficiency objectives.