AI 中文总结
该研究提出结合预测误差后处理与模型特定不确定性缩放的混合概率预测框架，在 M4 竞赛数据集上验证后处理方法可提升预测分布性能，且样本内校准多数场景优于样本外，为机构扩展点预测系统提供高效不确定性量化方案。
AI 中文摘要
许多预测系统会生成点预测，即便决策需要不确定性相关信息。本文研究后处理方法能否系统性改进由样本内残差构建的传统高斯预测分布。我们提出一种混合框架，将预测误差后处理与跨预测 horizon 的模型特定预测不确定性缩放相结合。为开展全面评估，我们对 Theta、指数平滑和 ARIMA 模型生成的点预测，应用历史模拟、共形预测、分位数回归及基于 GARCH 的后处理方法。利用来自 M4 竞赛的 14407 个月度序列，以及 1 至 12 个月的预测 horizon，我们采用连续排名概率得分和基于排名的统计比较来评估性能。按 horizon 取平均，所有后处理变体均优于基准预测分布，提升幅度最高达 4.6%。在 12 种模型-方法组合中，有 11 种的样本内校准优于样本外对应方法，不过优选的后处理方法取决于基础模型和预测 horizon。样本内校准的优势通常随 horizon 延长而增大。研究结果表明，各机构可扩展现有点预测系统，以提供有用的不确定性量化，而无需计算密集型的重复模型重新估计。
英文摘要
Many forecasting systems produce point forecasts even when decisions require information about uncertainty. We investigate whether post-processing methods can systematically improve upon traditional Gaussian predictive distributions constructed from in-sample residuals. We propose a hybrid framework that combines forecast error post-processing with model-specific scaling of forecast uncertainty across horizons. For a comprehensive evaluation, we apply historical simulation, conformal prediction, quantile regression, and GARCH-based post-processing to point forecasts generated by Theta, exponential smoothing, and ARIMA models. Using 14,407 monthly series from the M4 competition and forecast horizons of 1 to 12 months, we evaluate performance using the continuous ranked probability score and rank-based statistical comparisons. Averaged across horizons, all post-processing variants improve upon the benchmark predictive distributions, with gains of up to 4.6%. In-sample calibration outperforms its out-of-sample counterpart in 11 of the 12 model-method combinations, although the preferred post-processing method depends on the base model and forecast horizon. The advantage of in-sample calibration generally increases at longer horizons. Our results show that organisations can extend existing point-forecasting systems to provide useful uncertainty quantification without computationally intensive repeated model re-estimation.
Comments25 pages
