Conformal prediction gives prediction intervals with finite-sample coverage when the data are exchangeable. Many time-indexed datasets are not exchangeable. They have seasons, recurring regimes, changing frequencies, or other forms of structured dependence. This paper studies a simple way to use that structure. We propose spectral adaptive conformal prediction, a method that forms weighted conformal quantiles using local spectral similarity and then updates the target miscoverage level online. The spectral weights choose calibration residuals that look relevant to the current test point. The adaptive update corrects the long-run miss rate when uncertainty changes over time. We give an approximate coverage result for the fixed spectral weighted quantile and a deterministic long-run calibration result for the adaptive update. Simulations with recurring regimes and slowly changing frequencies, together with three U.S. real-data examples, show that the hybrid method can improve on fixed spectral weighting, while also showing that spectral weighting must be monitored through effective sample size diagnostics.

翻译：保形预测在数据可交换时能提供有限样本覆盖的预测区间。许多时间索引数据集并不满足可交换性，它们包含季节性、周期性模式、变化的频率或其他形式的结构化依赖关系。本文研究利用这种结构的简单方法。我们提出谱自适应保形预测，该方法利用局部谱相似性构建加权保形分位数，并在线更新目标错误覆盖率。谱权重选取与当前测试点相关的校准残差。自适应更新在不确定性随时间变化时校正长期错误率。我们给出了固定谱加权分位数的近似覆盖结果，以及自适应更新的确定性长期校准结果。针对周期性模式和慢变频率的仿真实验，结合三个美国真实数据案例，表明该混合方法能改进固定谱加权的性能，同时揭示需通过有效样本量诊断来监控谱加权过程。