# Conformal Coverage of Time Series: Validity and Inference

arXiv: https://arxiv.org/abs/2609.33868 · HTML: https://mlsanity.com/paper/2609.33868/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 33 references that are in the map.
- First posted on arXiv 27 Sep 2026.

## Builds on (most cited first, 8 of 8)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Exact and Robust Conformal Inference Methods for Predictive Machine Learning With Dependent Data](https://mlsanity.com/paper/1802.06300/) (2018)
- [Predictive inference for time series: why is split conformal effective despite temporal dependence?](https://mlsanity.com/paper/2510.02471/) (2025)
- [Simultaneous Inference for Covariance and Precision Matrices of Long-Range Dependent Time Series](https://mlsanity.com/paper/2604.16219/) (2026)
- [Rolling-Origin Conformal Prediction under Local Stationarity and Weak Dependence](https://mlsanity.com/paper/2605.08422/) (2026)
- [Conformal Prediction via Transported Beta Laws](https://mlsanity.com/paper/2605.19024/) (2026)

## Abstract (arXiv)

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.