ProbRes: Volatility Learning for Probabilistic Time-Series Forecasting
For financial and other applications requiring risk quantification, ProbRes offers a simple, architecture-agnostic way to improve probabilistic forecast calibration, though it is an incremental improvement over existing methods.
ProbRes is a post-hoc calibration method for probabilistic time series forecasting that explicitly models volatility dynamics, enabling accurate handling of heteroskedastic data. Experiments show it produces well-calibrated prediction intervals across various error distributions.
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.