Temporal Conformal Prediction (TCP): A Distribution-Free Statistical and Machine Learning Framework for Adaptive Risk Forecasting

We propose 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 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, and a rolling Quantile Regression (QR) baseline across equities (S&P 500), cryptocurrency (Bitcoin), and commodities (Gold). Three results are consistent across assets. First, rolling QR yields the sharpest intervals but is materially under-calibrated (e.g., S&P 500: 83.2% vs. 95% target). 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 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.