Conformal Coverage of Time Series: Validity and Inference
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.
Related
- Dynamic Dual-Feedback Conformal Inference for Time Series Forecasting
- Adaptive Conformal Inference Under Delayed Feedback: Coverage Guarantees and a Delay-to-Memory Diagnostic
- Honest Inference for Synthetic Controls with Imperfect Fit: Time-Split Validity and the Choice of Anchor
- Auditing Conformal Prediction for Language Models Under Inference-Time Model Shift
- Conformal Prediction for Time Series with Deep Sequence Models
BibTeX
@misc{zhai2026conformal,
title = {{Conformal Coverage of Time Series: Validity and Inference}},
author = {Percy S. Zhai and Maggie Cheng and Wei Biao Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33868},
eprint = {2609.33868},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33868},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Conformal Coverage of Time Series: Validity and Inference
AU - Percy S. Zhai
AU - Maggie Cheng
AU - Wei Biao Wu
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33868
UR - https://arxiv.org/abs/2609.33868
AB - 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.
ER -