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.

翻译：共形预测方法在数据可交换且训练过程中对称处理时，具有强大的理论和经验预测推断性能。然而，这些假设在许多场景中并不实用，例如时间序列中时间依赖性违反了可交换性，且更倾向于通过非对称处理数据来利用依赖性的预测器。近期研究表明，分裂共形预测对此类问题具有鲁棒性，但样本分裂可能降低精度，这促使人们在时间序列场景中研究不依赖数据分裂的方法。本文证明，即使在具有轻度时间依赖性的典型时间序列模型中，原始留一刀切法也可能遭受任意覆盖损失。为此，我们提出一种针对此类场景的改进方法，称为留一窗口法，并证明在模型拟合过程满足轻度稳定性条件时，该方法能够实现有效覆盖。我们的证明基于量化数据偏离循环可交换性的程度，并引入新系数进行测量。时间序列实验表明，当原始刀切法失效时，我们的方法通常能实现有效覆盖，同时产生的预测区间远窄于分裂共形预测。