Title: ProbRes: Volatility Learning for Probabilistic Time-Series Forecasting

Abstract:

The growing requirement to quantify risk and uncertainty in future observations has driven increased interest in probabilistic time series forecasting, particularly within the financial sector. To address this, we introduce ProbRes, a post-hoc probabilistic calibration technique designed to explicitly learn and integrate volatility dynamics into the forecasting process. This approach effectively manages heteroskedastic data. During the training phase, ProbRes utilizes two architecture-agnostic modules that function independently to model the conditional mean and conditional volatility. At the inference stage, predictive distributions are generated through the resampling of normalized residuals. The method is versatile, supporting both univariate and multivariate time series, and demonstrates robustness across various error distributions, including non-Gaussian innovations characterized by conditional heteroskedasticity. Theoretical analysis confirms the validity of ProbRes, while empirical evaluations on synthetic and real-world datasets illustrate its ability to accurately capture predictive distributions and yield well-calibrated prediction intervals.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC