In this work, we present a novel conformal prediction method for time-series, which we call Kernel-based Optimally Weighted Conformal Prediction Intervals (KOWCPI). Specifically, KOWCPI adapts the classic Reweighted Nadaraya-Watson (RNW) estimator for quantile regression on dependent data and learns optimal data-adaptive weights. Theoretically, we tackle the challenge of establishing a conditional coverage guarantee for non-exchangeable data under strong mixing conditions on the non-conformity scores. We demonstrate the superior performance of KOWCPI on real and synthetic time-series data against state-of-the-art methods, where KOWCPI achieves narrower confidence intervals without losing coverage.

翻译：本文提出了一种新颖的时间序列共形预测方法，称为基于核函数的最优加权共形预测区间（KOWCPI）。具体而言，KOWCPI将经典的重加权Nadaraya-Watson（RNW）估计量应用于相依数据的分位数回归，并学习最优的数据自适应权重。在理论上，我们解决了在非共形分数满足强混合条件下，为非可交换数据建立条件覆盖保证的挑战。通过在真实与合成时间序列数据上与前沿方法进行对比，我们证明了KOWCPI的优越性能——在保持覆盖范围的同时，能够获得更窄的置信区间。