  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.
