改进时间序列预测的置信区间，让误差更准更窄。
Bias-Corrected Adaptive Conformal Inference for Multi-Horizon Time Series Forecasting
- 用动态偏差估计修正预测区间中心，而非仅扩大范围。
- 在688次实验中，平均降低13%~17%的置信区间评分。
- 适合需要精准置信区间的金融、气象等实际场景。
自适应共形推断（ACI）在分布漂移下可提供无分布假设的预测区间，但仅调整分位数阈值，无法移动区间中心。当基线预测器在制度变化后产生持续偏差时，ACI只能对称地扩大区间，导致过度保守。本文提出偏差校正的自适应共形推断（BC-ACI），引入在线指数加权移动平均（EWM）估计预测偏差，在分位数计算前修正非符合性得分，实现区间重中心化，从根源上解决校准失准问题。通过自适应死区阈值抑制噪声误判下的修正，确保在良好校准数据上性能不降。在2个基线模型、4种合成制度、3个真实数据集上共688次实验中，BC-ACI在均值与复合分布漂移下使Winkler区间评分降低13%~17%（威尔科克斯检验p < 0.001），而在平稳数据上表现几乎不变（比值1.002倍）。有限样本分析表明，覆盖率随偏差估计误差平滑退化。
原文摘要 · Abstract (English)
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.
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