ProbRes: Volatility Learning for Probabilistic Time-Series Forecasting
2026-06-01 • Machine Learning
Machine Learning
AI summaryⓘ
The authors introduce ProbRes, a method to improve the accuracy of forecasting uncertain future values in time series data, especially when the variability changes over time. ProbRes works by separately learning the average trend and the changing volatility, then uses these to better model the range of possible outcomes. This approach works for both single and multiple related time series and handles complex data behaviors that don't follow simple patterns. Their tests show that ProbRes provides reliable estimates of uncertainty and good predictions.
Probabilistic forecastingTime seriesVolatilityHeteroskedasticityConditional meanConditional volatilityCalibrationResidual resamplingPredictive distributionNon-Gaussian errors
Authors
Tingting Wang, Yunyi Zhang, Benyou Wang
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.