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

• URL: http://arxiv.org/abs/2608.11114v1
• Date: Tue, 11 Aug 2026 16:22:47 GMT
• Title: Two-stage Odd Residual Flows for Mean-Preserving Probabilistic Time Series Forecasting
• Abstract summary: Two-stage Odd Residual Flows (TORF) is a framework that decouples mean forecasting from uncertainty estimation.<n>TORF achieves state-of-the-art deterministic accuracy (NMAE) while providing strong density estimation performance (CRPS) on short and long-horizon forecasting.
• Score: 9.992963275755159
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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