Conformal prediction provides distribution-free prediction intervals under exchangeability, but many modern data streams are neither independent nor stable. They exhibit recurring regimes, changing seasonal frequencies, abrupt shifts, and gradual drift. We propose drift-aware spectral conformal prediction (DASC), a streaming uncertainty quantification framework for structured non-exchangeable data subject to distributional drift. DASC forms conformal prediction intervals using calibration residuals weighted by local spectral similarity, while a transport-based drift score monitors whether the current test distribution has moved away from past calibration regimes. When drift is mild, DASC borrows calibration residuals from structurally similar historical windows; when drift is severe, it contracts or reweights the calibration pool and updates the target miscoverage level online. The method also reports an effective sample size diagnostic that warns when a weighted conformal quantile is statistically fragile. We establish an approximate coverage bound that decomposes coverage loss into drift, residual mismatch, and weighted effective sample size. In synthetic experiments and five stress-test regimes, DASC maintains near-nominal coverage after drift where rolling, recency-weighted, and spectral-only conformal methods can under-cover. In real electricity and weather streams, DASC reduces average interval width by approximately 28% and 42%, respectively, relative to the best calibrated non-DASC baseline, while preserving calibrated or conservative coverage. A financial volatility example shows a more nuanced regime in which spectral-only calibration is competitive, but DASC retains near-nominal coverage and adds drift diagnostics.

翻译：共形预测在可交换性假设下提供无分布假设的预测区间，但现代数据流既非独立也非平稳，呈现出周期性模式、季节性频率变化、突变和渐进漂移等特征。本文提出漂移感知频谱共形预测（DASC），这是一种面向受分布漂移影响的结构化非可交换流数据的不确定性量化框架。DASC通过局部频谱相似性加权的校准残差构建共形预测区间，同时采用基于传输理论的漂移分数监测当前测试分布是否偏离历史校准区域。当漂移较小时，DASC从结构相似的历史窗口中借用校准残差；当漂移严重时，则收缩或重新加权校准池并在线调整目标误覆盖水平。该方法还报告有效样本量诊断指标，用于预警加权共形分位数存在统计脆弱性。本文建立了覆盖损失的近似边界，将覆盖损失分解为漂移、残差失配和加权有效样本量三个分量。在合成实验和五个压力测试场景中，当滚动窗口、近邻加权和纯频谱共形方法出现欠覆盖时，DASC在漂移后仍能维持近名义覆盖水平。针对真实电力负荷和气象数据流，与最佳校准的非DASC基线相比，DASC分别将平均区间宽度缩减约28%和42%，同时保持校准或保守的覆盖性能。金融波动率实例展示了更复杂的场景：纯频谱校准在此具有竞争力，但DASC仍能维持近名义覆盖水平并增加漂移诊断功能。