We propose \textbf{Temporal Conformal Prediction (TCP)}, a distribution-free framework for constructing well-calibrated prediction intervals in nonstationary time series. TCP couples a modern quantile forecaster with a rolling split-conformal calibration layer; its \textbf{TCP-RM} variant adds an online Robbins-Monro offset to steer coverage in real time. We benchmark TCP against GARCH, Historical Simulation, Quantile Regression (QR), linear QR, and Adaptive Conformal Inference (ACI) across S\&P 500, Bitcoin, and Gold. Three results are consistent. First, QR baselines yield the sharpest intervals but are materially under-calibrated; even ACI remains below the 95\% target. Second, TCP achieves near-nominal coverage, yielding intervals slightly wider than Historical Simulation (e.g., S\&P 500: 5.21 vs.\ 5.06). Third, the RM update changes calibration only marginally at default hyperparameters. Crisis-window visualizations (March 2020) show TCP promptly expanding and contracting intervals as volatility spikes. A sensitivity study confirms robustness to hyperparameters. Overall, TCP bridges statistical inference and machine learning, providing a practical solution for calibrated risk forecasting under distribution shift.

翻译：本文提出**时间一致性预测（TCP）**，一种用于在非平稳时间序列中构建校准良好的预测区间的无分布框架。TCP将现代分位数预测器与滚动分割一致性校准层相结合；其**TCP-RM**变体通过在线Robbins-Monro偏移量实时调整覆盖范围。我们在标普500指数、比特币和黄金数据上，将TCP与GARCH、历史模拟法、分位数回归（QR）、线性分位数回归以及自适应一致性推断（ACI）进行基准比较。得到三个一致的结论：首先，QR基线方法产生的区间最窄，但存在显著校准不足，即使ACI方法也低于95%的目标覆盖水平；其次，TCP实现接近名义覆盖水平，其区间宽度略大于历史模拟法（例如标普500指数：5.21对比5.06）；第三，在默认超参数下，RM更新对校准的调整幅度有限。危机窗口可视化（2020年3月）显示TCP能够随波动率激增及时扩展和收缩预测区间。敏感性研究证实了该方法对超参数的鲁棒性。总体而言，TCP架起了统计推断与机器学习之间的桥梁，为分布漂移下的校准风险预测提供了实用解决方案。