提出TCP框架，实现非平稳时间序列的自适应风险预测。
Temporal Conformal Prediction (TCP): A Distribution-Free Statistical and Machine Learning Framework for Adaptive Risk Forecasting
- 结合分位数预测与滚动分割校准，构建分布无关的预测区间。
- 在美股、比特币和黄金上达到近名义覆盖率，区间略宽于历史模拟法。
- 在线更新机制可实时调节覆盖度，适合金融风险场景应用。
我们提出一种名为时序置信预测（Temporal Conformal Prediction, TCP）的分布无关框架，用于非平稳时间序列中构造校准良好的预测区间。TCP将现代分位数预测器与滚动分割置信校准层结合；其变体TCP-RM引入在线Robbins-Monro偏移量，实现实时覆盖调节。我们在标普500、比特币和黄金上对比了GARCH、历史模拟法、分位数回归（QR）、线性QR及自适应置信推断（ACI）。结果一致：第一，QR基线区间最窄但严重欠校准，即使ACI也未达95%目标；第二，TCP实现接近名义覆盖率，区间略宽于历史模拟法（如标普500：5.21 vs. 5.06）；第三，RM更新在默认超参数下对校准影响微小。危机窗口可视化（2020年3月）显示TCP能随波动率突增迅速扩缩区间。敏感性分析表明其对超参数鲁棒。总体而言，TCP弥合了统计推断与机器学习的鸿沟，为分布漂移下的校准风险预测提供实用方案。
原文摘要 · Abstract (English)
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.
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