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How to forecast not just the next value, but the uncertainty around it?

Tingting Wang, Yunyi Zhang, Benyou Wang

June 1, 2026

Financial forecasting needs to quantify uncertainty, not just predict point values. ProbRes adds a volatility learning layer on top of any existing forecasting model, separately estimating how confident the prediction should be. It resamples residuals to generate full predictive distributions that work with non-Gaussian noise and multivariate data, with experiments showing better calibrated prediction intervals on real market data.
Published as ProbRes: Volatility Learning for Probabilistic Time-Series Forecasting arXiv:2606.02117
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