发表机构
School of Economics and Management, Beihang University; Beijing Shuji Intelligent Technology Co., Ltd.; Center for Forecasting Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（北京航空航天大学经济管理学院; 北京数智科技有限公司; 中国科学院数学与系统科学研究院预测科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
PID-Expert通过在线聚合多个PID校准器，在保持覆盖率的同时生成更窄的预测区间，提高了时间序列共形预测的效率。
AI 中文摘要
对于给定的点预测器，比例-积分-微分（PID）校准配置可以实现相似的整体覆盖率，但产生不同的区间宽度。我们引入了PID-Expert，一种用于提高时间序列共形预测区间效率的在线聚合方法。PID-Expert结合了来自固定PID校准器库的阈值，每个校准器在其自身的覆盖率反馈下演化。聚合权重取决于归一化区间宽度和误覆盖率，而共享乘数使用报告的区间反馈来调整误覆盖惩罚。我们在实现的乘数序列下建立了加权专家损失的局部遗憾界，并分别建立了时间平均聚合误覆盖率的路径上界，在稳定性条件下以期望和几乎必然的方式控制。在四个模拟设置和两个真实数据应用中，PID-Expert产生的平均区间比预设的Conformal PID基准更窄，同时保持整体经验覆盖率接近名义水平。与专家选择和等权平均相比，聚合通常在预测设置中提供更平衡的覆盖率-宽度权衡。滚动分析进一步揭示了局部覆盖率-效率权衡，特别是在突然的分布变化之后。总体而言，PID-Expert减少了对单一PID配置的依赖，同时提高了区间效率。
英文摘要
For a given point forecaster, proportional-integral-derivative (PID) calibration configurations can attain similar overall coverage yet produce different interval widths. We introduce PID-Expert, an online aggregation method for improving the efficiency of conformal prediction intervals for time series. PID-Expert combines thresholds from a fixed library of PID calibrators, each evolving under its own coverage feedback. Aggregation weights depend on normalized interval width and miscoverage, while a shared multiplier adapts the miscoverage penalty using feedback from the reported interval. We establish local regret bounds for weighted expert losses under the realized multiplier sequence and, separately, a pathwise upper bound on time-averaged aggregate miscoverage, with control in expectation and almost surely under a stability condition. Across four simulation settings and two real-data applications, PID-Expert produces narrower mean intervals than a prespecified Conformal PID benchmark while keeping overall empirical coverage close to the nominal level. Compared with expert selection and equal averaging, aggregation generally provides a more balanced coverage--width trade-off across forecasting settings. Rolling analyses further reveal local coverage--efficiency trade-offs, particularly following abrupt distributional shifts. Overall, PID-Expert reduces reliance on a single PID configuration while improving interval efficiency.
