Conformal prediction has been a popular distribution-free framework for uncertainty quantification. In this paper, 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 time-series against state-of-the-art methods, where KOWCPI achieves narrower confidence intervals without losing coverage.

翻译：共形预测已成为一种流行的无分布不确定性量化框架。本文提出了一种针对时间序列的新型共形预测方法，称为基于核的最优加权共形预测区间（KOWCPI）。具体而言，KOWCPI采用经典的重加权Nadaraya-Watson（RNW）估计器对相依数据进行分位数回归，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。我们在真实时间序列数据上展示了KOWCPI相对于现有先进方法的优越性能，其中KOWCPI在保持覆盖范围的同时实现了更窄的置信区间。