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 split-conformal calibration layer on a rolling window and, in its \textbf{TCP-RM} variant, augments the conformal threshold with a single online Robbins-Monro (RM) offset to steer coverage toward a target level in real time. We benchmark TCP against GARCH, Historical Simulation, a rolling tree-based Quantile Regression (QR) model, a classical linear quantile regression baseline (QR-Linear), and an adaptive conformal method (ACI) across equities (S\&P 500), cryptocurrency (Bitcoin), and commodities (Gold). Three results are consistent across assets. First, both QR and QR-Linear yield the sharpest intervals but are materially under-calibrated, and even ACI remains below the nominal 95\% target in our full-sample backtests. Second, TCP (and TCP-RM) achieves near-nominal coverage across assets, with intervals that are wider than Historical Simulation in this evaluation (e.g., S\&P 500: 5.21 vs.\ 5.06). Third, the RM update changes calibration and width only marginally at our default hyperparameters. Crisis-window visualizations around March 2020 show TCP/TCP-RM expanding and then contracting their interval bands promptly as volatility spikes and recedes, with \textbf{red dots} marking days where realized returns fall outside the reported 95\% interval (miscoverage). A sensitivity study confirms robustness to window size and step-size choices. Overall, TCP provides a practical, theoretically grounded solution to calibrated uncertainty quantification under distribution shift, bridging statistical inference and machine learning for risk forecasting.

翻译：我们提出了**时序保形预测（TCP）**，这是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窗口上的分割保形校准层相结合，并在其**TCP-RM**变体中，通过单个在线Robbins-Monro（RM）偏移量来增强保形阈值，以实时引导覆盖率趋近目标水平。我们在股票（标普500指数）、加密货币（比特币）和大宗商品（黄金）上，将TCP与GARCH、历史模拟法、基于滚动树的分位数回归（QR）模型、经典线性分位数回归基线（QR-Linear）以及一种自适应保形方法（ACI）进行了基准测试。三项结果在不同资产中表现一致。首先，QR和QR-Linear产生的区间最窄，但存在明显的校准不足，即使ACI在我们的全样本回测中也低于名义95%的目标水平。其次，TCP（以及TCP-RM）在不同资产上实现了接近名义水平的覆盖率，其区间在此次评估中比历史模拟法更宽（例如，标普500指数：5.21 vs. 5.06）。第三，在我们默认的超参数下，RM更新对校准和区间宽度的影响微乎其微。围绕2020年3月的危机窗口可视化显示，TCP/TCP-RM在波动率飙升和回落时迅速扩大并随后收缩其区间带，其中**红点**标记了实际收益率落在报告的95%区间之外（覆盖错误）的日期。敏感性研究证实了其对窗口大小和步长选择的稳健性。总体而言，TCP为分布漂移下的校准不确定性量化提供了一个实用且理论依据充分的解决方案，为风险预测架起了统计推断与机器学习之间的桥梁。