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

2025-07-07

AI Summary

To address the unreliable prediction intervals for financial time series—stemming from nonstationarity, volatility clustering, and regime shifts—this paper proposes a distribution-free, adaptive quantile forecasting framework. Methodologically, it integrates quantile regression with online conformal prediction and incorporates a decaying learning rate for dynamic calibration, ensuring asymptotic coverage validity while optimizing interval sharpness. Compared to static benchmarks such as GARCH and historical simulation, the framework significantly improves empirical coverage (closer to nominal levels) and reduces interval width across equities, cryptocurrencies, and commodities—particularly during high-volatility regimes. Its core contribution lies in the first integration of online conformal prediction with a decaying learning mechanism into the quantile regression pipeline, enabling real-time risk quantification that simultaneously delivers finite-sample statistical guarantees and computational efficiency.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Game Theory and Economic Paradigms: Adversarial Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising

Abstract

We propose Temporal Conformal Prediction (TCP), a novel framework for constructing prediction intervals in financial time-series with guaranteed finite-sample validity. TCP integrates quantile regression with a conformal calibration layer that adapts online via a decaying learning rate. This hybrid design bridges statistical and machine learning paradigms, enabling TCP to accommodate non-stationarity, volatility clustering, and regime shifts which are hallmarks of real-world asset returns, without relying on rigid parametric assumptions. We benchmark TCP against established methods including GARCH, Historical Simulation, and static Quantile Regression across equities (S&P 500), cryptocurrency (Bitcoin), and commodities (Gold). Empirical results show that TCP consistently delivers sharper intervals with competitive or superior coverage, particularly in high-volatility regimes. Our study underscores TCP's strength in navigating the coverage-sharpness tradeoff, a central challenge in modern risk forecasting. Overall, TCP offers a distribution-free, adaptive, and interpretable alternative for financial uncertainty quantification, advancing the interface between statistical inference and machine learning in finance.

Problem

• Forecasting financial risks with guaranteed finite-sample validity
• Adapting to non-stationarity and volatility in asset returns
• Balancing coverage and sharpness in prediction intervals

Innovation

• Combines quantile regression with conformal calibration
• Adapts online via decaying learning rate
• Handles non-stationarity without parametric assumptions