📝 SummarXiv

Abstract

We propose Temporal Conformal Prediction (TCP), a distribution-free framework for constructing well-calibrated prediction intervals in nonstationary time series. TCP combines a quantile forecaster with split-conformal calibration on a rolling window and, in its TCP-RM variant, augments the conformal threshold with a 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&P500), cryptocurrency (Bitcoin), and commodities (Gold). Three consistent findings emerge. First, rolling QR produces the sharpest intervals but is materially under-calibrated (e.g., S&P500: 86.3% vs. 95% target). Second, TCP and TCP-RM achieve near-nominal coverage while delivering substantially narrower intervals than Historical Simulation (e.g., S&P500: 29% reduction in width). Third, the RM update improves calibration with negligible width cost. Crisis-window visualizations around March 2020 show TCP/TCP-RM expanding and contracting intervals promptly as volatility spikes and recedes, with red dots marking days of miscoverage. A sensitivity study confirms robustness to window size and step-size choices. Overall, TCP provides a practical, theoretically grounded solution for calibrated uncertainty quantification under distribution shift, bridging statistical inference and machine learning for risk forecasting.