时间序列预测的置信区间一直是个难题，做时序建模的团队可以试试LWO——它比分割法更高效，也比原始Jackknife更可靠，值得在ARIMA或LSTM上跑一跑。
传统共形预测方法依赖数据可交换性和无记忆预测器，这在时间序列中不现实。近期研究表明分割共形预测对时间序列的依赖性和记忆性预测器具有鲁棒性，但分割会降低精度。本文发现原始留一法Jackknife在时间序列中可能严重损失覆盖率，因此提出“留窗口法”（LWO），通过修改Jackknife使其在温和稳定性条件下实现有效覆盖率。实验显示LWO在原始Jackknife失效时仍能保持有效覆盖率，且预测区间比分割共形预测更窄。
Leave a Window Out: Modifying the Jackknife for Predictive Inference in Time Series
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.