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标题: "Two-stage Odd Residual Flows for Mean-Preserving Probabilistic Time Series Forecasting"
原文链接: "https://arxiv.org/abs/2608.11114"
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---

## Computer Science > Machine Learning

## Title:Two-stage Odd Residual Flows for Mean-Preserving Probabilistic Time Series Forecasting

[View PDF](https://arxiv.org/pdf/2608.11114) [HTML (experimental)](https://arxiv.org/html/2608.11114v1)

> Abstract:Probabilistic forecasting plays an essential role in risk-sensitive decision-making, particularly in long-horizon settings. However, existing approaches often face a fundamental trade-off between distributional flexibility and accurate mean prediction. Traditional parametric methods, such as Mean Variance Estimation (MVE), can suffer from degraded point accuracy when trained under joint Negative Log-Likelihood (NLL) objectives, while modern-flexible generative models, including Normalizing Flows and Diffusion Models, typically rely on costly Monte Carlo sampling and may yield suboptimal mean estimates. To address this limitation, we propose Two-stage Odd Residual Flows (TORF), a framework that decouples mean forecasting from uncertainty estimation. In the first stage, a pre-trained deterministic model is used to produce an accurate mean prediction. In the second stage, a Restricted Normalizing Flow, with strictly odd functions learns flexible residual distributions around the point forecast, guaranteeing mean preservation from the first stage without sampling. Experiments show that TORF achieves state-of-the-art deterministic accuracy (NMAE) while providing strong density estimation performance (CRPS) on short and long-horizon forecasting.

| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| --- | --- |
| Cite as: | [arXiv:2608.11114](https://arxiv.org/abs/2608.11114) \[cs.LG\] |
|  | (or [arXiv:2608.11114v1](https://arxiv.org/abs/2608.11114v1) \[cs.LG\] for this version) |
|  | [https://doi.org/10.48550/arXiv.2608.11114](https://doi.org/10.48550/arXiv.2608.11114) |

## Submission history

From: Kiran Madhusudhanan \[[view email](https://arxiv.org/show-email/c7568ede/2608.11114)\]  
**\[v1\]** Tue, 11 Aug 2026 16:22:47 UTC (2,143 KB)

[Which authors of this paper are endorsers?](https://arxiv.org/auth/show-endorsers/2608.11114) | Disable MathJax ([What is MathJax?](https://info.arxiv.org/help/mathjax.html))
