Conformal Coverage of Time Series: Validity and Inference

2026-09-27

AI Summary

This study addresses the lack of statistical inference theory for coverage rates in time series split conformal prediction and the unclear impact of temporal dependence. To bridge this gap, it leverages functional dependence measures, Bahadur representations, and block variance estimation techniques to establish non-asymptotic error bounds and a central limit theorem (CLT) for coverage. This work presents the first CLT for coverage under temporal dependence, enabling valid inference without requiring mixing conditions. Furthermore, it reveals that long-memory processes exhibit non-Gaussian limiting distributions, thereby elucidating the mechanism through which temporal dependence influences coverage uncertainty.

Abstract

Conformal prediction provides marginal coverage guarantees, yet practitioners may wonder if the observed coverage is truly abnormal or consistent with sampling variation. Inference for realized coverage has received comparatively little attention, especially for time series. We study split conformal prediction with adjacent calibration and test sets of temporally dependent data. Using the functional dependence measure, we derive non-asymptotic bounds on marginal coverage error without mixing assumptions, which can be difficult to verify and may fail even for simple short-memory models. We establish a Bahadur representation to derive, to our knowledge, the first central limit theorem for realized coverage of split conformal prediction under temporal dependence. A consistent block-based estimator of the standard error yields an asymptotically justified test. We further study long-memory time series, which remain understudied in conformal prediction. For Gaussian linear processes, we show how very strong temporal dependence can lead to a non-Gaussian limiting law of realized coverage and establish block-sampling inference with an estimated normalization. The resulting theory explains how temporal dependence changes coverage uncertainty.

Problem

• conformal prediction
• time series
• realized coverage
• temporal dependence
• statistical inference

Innovation

• conformal prediction
• time series
• functional dependence measure
• Bahadur representation
• long-memory