# Leave a Window Out: Modifying the Jackknife for Predictive Inference in Time Series

arXiv: https://arxiv.org/abs/2605.30292 · HTML: https://mlsanity.com/paper/2605.30292/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 57 references that are in the map.
- First posted on arXiv 28 May 2026.

## Builds on (most cited first, 30 of 31)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Financial Time Series Forecasting with Deep Learning : A Systematic Literature Review: 2005-2019](https://mlsanity.com/paper/1911.13288/) (2019)
- [Tackling Climate Change with Machine Learning](https://mlsanity.com/paper/1906.05433/) (2019)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [Distribution-free uncertainty quantification for classification under label shift](https://mlsanity.com/paper/2103.03323/) (2021)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [Nested conformal prediction and quantile out-of-bag ensemble methods](https://mlsanity.com/paper/1910.10562/) (2019)
- [Conformal PID Control for Time Series Prediction](https://mlsanity.com/paper/2307.16895/) (2023)
- [Sequential Predictive Conformal Inference for Time Series](https://mlsanity.com/paper/2212.03463/) (2022)
- [Exact and Robust Conformal Inference Methods for Predictive Machine Learning With Dependent Data](https://mlsanity.com/paper/1802.06300/) (2018)
- [Predictive Inference Is Free with the Jackknife+-after-Bootstrap](https://mlsanity.com/paper/2002.09025/) (2020)
- [Conformal prediction for multi-dimensional time series by ellipsoidal sets](https://mlsanity.com/paper/2403.03850/) (2024)
- [Conformal Validity Guarantees Exist for Any Data Distribution (and How to Find Them)](https://mlsanity.com/paper/2405.06627/) (2024)
- [Split Localized Conformal Prediction](https://mlsanity.com/paper/2206.13092/) (2022)
- [Multi Split Conformal Prediction](https://mlsanity.com/paper/2103.00627/) (2021)
- [Stable Conformal Prediction Sets](https://mlsanity.com/paper/2112.10224/) (2021)
- [Bagging Provides Assumption-free Stability](https://mlsanity.com/paper/2301.12600/) (2023)
- [Kernel-based Optimally Weighted Conformal Time-Series Prediction](https://mlsanity.com/paper/2405.16828/) (2024)
- [Predictive inference for time series: why is split conformal effective despite temporal dependence?](https://mlsanity.com/paper/2510.02471/) (2025)
- [Extending Conformal Prediction to Hidden Markov Models with Exact Validity via de Finetti's Theorem for Markov Chains](https://mlsanity.com/paper/2210.02271/) (2022)
- [Spatial Conformal Inference through Localized Quantile Regression](https://mlsanity.com/paper/2412.01098/) (2024)
- [Just Wing It: Near-Optimal Estimation of Missing Mass in a Markovian Sequence](https://mlsanity.com/paper/2404.05819/) (2024)
- [Conformal Predictions under Markovian Data](https://mlsanity.com/paper/2407.15277/) (2024)

## Built on by (most cited first, 4 of 4)

- [Sequential statistical inference for Large Language Models: Representation, validity, and monitoring](https://mlsanity.com/paper/2606.07624/) (2026)
- [Next-token functional estimation](https://mlsanity.com/paper/2609.19529/) (2026)
- [Rolling Conformal Prediction in Sequential Model Training](https://mlsanity.com/paper/2609.26951/) (2026)
- [Valid and Efficient Split Conformal Regression for Time Series](https://mlsanity.com/paper/2609.33866/) (2026)

## Abstract (arXiv)

Conformal prediction methods enjoy strong theoretical and empirical predictive inference performance, provided the data is exchangeable and is treated symmetrically during training. However, these assumptions are impractical in many settings, such as time series, where temporal dependence violates exchangeability and it is preferable to use predictors that leverage dependence by treating data asymmetrically. Recent work shows that split conformal prediction is robust to these issues, but sample splitting can reduce accuracy, motivating the study of methods that do not rely on data splitting in the time series setting. In this work, we show that the vanilla leave-one-out jackknife can suffer arbitrary loss of coverage even in canonical time series models with mild temporal dependence. As a remedy, we propose a modification tailored to such settings, which we term the leave-a-window-out (LWO) method, and show that it can achieve valid coverage provided that the model-fitting procedure satisfies mild stability properties. Our proofs are based on quantifying the degree to which the data departs from cyclic exchangeability, which we introduce new coefficients to measure. Experiments on time series demonstrate that our method often enjoys valid coverage when the vanilla jackknife fails to cover, while producing much narrower intervals than split conformal prediction.