Time series prediction underpins a broad range of downstream tasks across many scientific domains. Recent advances and increasing adoption of black-box machine learning models for time series prediction highlight the critical need for uncertainty quantification. While conformal prediction has gained attention as a reliable uncertainty quantification method, conformal prediction for time series faces two key challenges: (1) \textbf{leveraging correlations in observations and non-conformity scores to overcome the exchangeability assumption}, and (2) \textbf{constructing prediction sets for multi-dimensional outcomes}. To address these challenges, we propose a novel conformal prediction method for time series using flow with classifier-free guidance. We provide coverage guarantees by establishing exact non-asymptotic marginal coverage and a finite-sample bound on conditional coverage for the proposed method. Evaluations on real-world time series datasets demonstrate that our method constructs significantly smaller prediction sets than existing conformal prediction methods, maintaining target coverage.

翻译：时间序列预测支撑着众多科学领域中广泛的下游任务。黑盒机器学习模型在时间序列预测中的最新进展与日益普及，凸显了对不确定性量化的关键需求。尽管共形预测作为一种可靠的不确定性量化方法已受到关注，但针对时间序列的共形预测面临两大挑战：(1) **利用观测值与非一致性分数中的相关性来克服可交换性假设**，以及(2) **为多维结果构建预测集**。为应对这些挑战，我们提出了一种新颖的基于流与无分类器引导的时间序列共形预测方法。通过建立所提方法的精确非渐近边际覆盖保证以及条件覆盖的有限样本上界，我们提供了覆盖保证。在真实世界时间序列数据集上的评估表明，与现有共形预测方法相比，我们的方法构建的预测集显著更小，同时维持目标覆盖率。