ProbRes: Volatility Learning for Probabilistic Time-Series Forecasting

2026-06-01

AI Summary

This work addresses the challenge of accurately quantifying uncertainty in time series forecasting—particularly in domains like finance—where traditional probabilistic methods often fail to effectively model conditional heteroskedasticity. To this end, the authors propose ProbRes, an architecture-agnostic post-processing framework for probabilistic calibration that, for the first time, explicitly incorporates conditional volatility modeling into this paradigm. ProbRes features a dual-module design that separately learns the conditional mean and volatility, and generates predictive distributions by resampling standardized residuals, thereby avoiding any assumption about the parametric form of the error distribution. Empirical results demonstrate that ProbRes consistently produces well-calibrated prediction intervals on both synthetic and real-world datasets, accurately capturing dynamic uncertainty in both Gaussian and non-Gaussian time series, while maintaining strong theoretical grounding and empirical robustness.

Abstract

Probabilistic time series forecasting has attracted increasing attention in financial applications due to the need to quantify risk and uncertainty in future observations. We propose ProbRes, a post-hoc probabilistic calibration method that explicitly learns and incorporates volatility dynamics into probabilistic forecasting, enabling effective handling of heteroskedastic data. During training, ProbRes employs two architecture-agnostic modules to separately model the conditional mean and conditional volatility. At the inference stage, it generates predictive distributions by resampling normalized residuals. ProbRes is applicable to both univariate and multivariate time series and remains robust under a wide range of error distributions, including non-Gaussian innovations with conditional heteroskedasticity. Theoretical results demonstrate ProbRes's validity and experiments on both synthetic and real-world datasets show that ProbRes accurately captures predictive distributions and produces well-calibrated prediction intervals.

Problem

• probabilistic forecasting
• volatility
• heteroskedasticity
• time series
• uncertainty quantification

Innovation

• probabilistic forecasting
• volatility learning
• conditional heteroskedasticity
• post-hoc calibration
• residual resampling