提出一种后处理校准方法，显式建模时间序列波动率，提升不确定性预测精度。
ProbRes: Volatility Learning for Probabilistic Time-Series Forecasting
- 分离建模均值与波动率，通过归一化残差重采样生成预测分布
- 在真实和合成数据上准确捕捉预测分布，预测区间校准度显著提升
- 适用于单变量/多变量序列，对非高斯、异方差误差鲁棒，适合金融风险分析
概率时间序列预测在金融领域日益受到关注，因其能量化未来观测的不确定性与风险。本文提出 ProbRes，一种后处理的概率校准方法，显式学习并融入波动率动态，有效处理异方差数据。训练阶段，ProbRes 使用两个与架构无关的模块分别建模条件均值与条件波动率；推理时，通过重采样归一化残差生成预测分布。ProbRes 适用于单变量与多变量时间序列，在多种误差分布下保持稳健，包括具有条件异方差性的非高斯创新项。理论分析证明了 ProbRes 的有效性，合成与真实数据实验表明，其能准确捕捉预测分布，并生成校准良好的预测区间。
原文摘要 · Abstract (English)
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.
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