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

2026-05-28

AI Summary

Traditional leave-one-out Jackknife prediction intervals fail for time series due to the lack of exchangeability, leading to inadequate coverage. This work proposes a “leave-a-window-out” (LWO) approach that introduces a measure of “circular exchangeability deviation” to construct valid prediction intervals while preserving model stability. By avoiding data splitting, LWO circumvents the associated loss in predictive accuracy and leverages both stability analysis and circular exchangeability theory to substantially improve coverage fidelity. Empirical results demonstrate that LWO achieves nominal coverage levels across classical time series models and yields narrower prediction intervals than split conformal methods, significantly outperforming conventional Jackknife procedures.

Abstract

Conformal prediction methods enjoy strong theoretical and empirical predictive inference performance, provided the data is exchangeable, and predictors are trained in a memoryless fashion. However, these assumptions and constraints are impractical in many real-data settings, such as time series (where temporal dependence violates exchangeability, and where memoryless predictors will inevitably have poor predictive accuracy). Recent work shows that the split conformal prediction method is robust to these issues of memory-based predictors and deviations from exchangeability that are common features of time-series data. However, since using sample splitting can lead to lower accuracy, this motivates asking whether other predictive inference methods (that do not rely on data splitting) could also be reliably used in the time series setting. In this work, we show that the vanilla leave-one-out jackknife can suffer an arbitrary loss of coverage even in canonical time series models with mild temporal dependence. As a remedy, we propose a careful modification tailored to such settings, which we term the \emph{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 \emph{cyclic exchangeability}, and we introduce new coefficients to measure the extent of this departure. Experiments on time series data demonstrate that our LWO method often enjoys valid coverage when the vanilla jackknife fails to cover, while producing much narrower intervals than split conformal prediction.

Problem

• time series
• predictive inference
• jackknife
• exchangeability
• coverage

Innovation

• leave-a-window-out
• time series
• predictive inference
• cyclic exchangeability
• jackknife