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

We propose Temporal Conformal Prediction (TCP), a principled framework for constructing well-calibrated prediction intervals for non-stationary time series. TCP integrates a machine learning-based quantile forecaster with an online conformal calibration layer. This layer's thresholds are updated via a modified Robbins-Monro scheme, allowing the model to dynamically adapt to volatility clustering and regime shifts without rigid parametric assumptions. We benchmark TCP against GARCH, Historical Simulation, and static Quantile Regression across diverse financial assets. Our empirical results reveal a critical flaw in static methods: while sharp, Quantile Regression is poorly calibrated, systematically over-covering the nominal 95% target. In contrast, TCP's adaptive mechanism actively works to achieve the correct coverage level, successfully navigating the coverage-sharpness tradeoff. Visualizations during the 2020 market crash confirm TCP's superior adaptive response, and a comprehensive sensitivity analysis demonstrates the framework's robustness to hyperparameter choices. Overall, TCP offers a practical and theoretically-grounded solution to the central challenge of calibrated uncertainty quantification for time series under distribution shift, advancing the interface between statistical inference and machine learning.