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标题: "Probabilistic forecasting via post-processing prediction errors: In- or out-of-sample?"
原文链接: "https://arxiv.org/abs/2608.10620"
发布日期: "2026-08-11"
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---

## Statistics > Applications

## Title:Probabilistic forecasting via post-processing prediction errors: In- or out-of-sample?

[View PDF](https://arxiv.org/pdf/2608.10620) [HTML (experimental)](https://arxiv.org/html/2608.10620v1)

> Abstract: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.

| Comments: |  |
| --- | --- |
| Subjects: | Applications (stat.AP) |
| Cite as: | [arXiv:2608.10620](https://arxiv.org/abs/2608.10620) \[stat.AP\] |
|  | (or [arXiv:2608.10620v1](https://arxiv.org/abs/2608.10620v1) \[stat.AP\] for this version) |
|  | [https://doi.org/10.48550/arXiv.2608.10620](https://doi.org/10.48550/arXiv.2608.10620) |

## Submission history

From: Rafał Weron \[[view email](https://arxiv.org/show-email/411e75b9/2608.10620)\]  
**\[v1\]** Tue, 11 Aug 2026 08:06:11 UTC (368 KB)

[Which authors of this paper are endorsers?](https://arxiv.org/auth/show-endorsers/2608.10620) | Disable MathJax ([What is MathJax?](https://info.arxiv.org/help/mathjax.html))
