TEFL: Prediction-Residual-Guided Rolling Forecasting for Multi-Horizon Time Series
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arXiv
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| Format: | Preprint |
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2026
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| author | Huang, Xiannan Fang, Shen Qiu, Shuhan Yu, Chengcheng Du, Jiayuan Yang, Chao |
| author_facet | Huang, Xiannan Fang, Shen Qiu, Shuhan Yu, Chengcheng Du, Jiayuan Yang, Chao |
| contents | Time series forecasting plays a critical role in domains such as transportation, energy, and meteorology. Despite their success, modern deep forecasting models are typically trained to minimize point-wise prediction loss without leveraging the rich information contained in past prediction residuals from rolling forecasts - residuals that reflect persistent biases, unmodeled patterns, or evolving dynamics. We propose TEFL (Temporal Error Feedback Learning), a unified learning framework that explicitly incorporates these historical residuals into the forecasting pipeline during both training and evaluation. To make this practical in deep multi-step settings, we address three key challenges: (1) selecting observable multi-step residuals under the partial observability of rolling forecasts, (2) integrating them through a lightweight low-rank adapter to preserve efficiency and prevent overfitting, and (3) designing a two-stage training procedure that jointly optimizes the base forecaster and error module. Extensive experiments across 10 real-world datasets and 5 backbone architectures show that TEFL consistently improves accuracy, reducing MAE by 5-10% on average. Moreover, it demonstrates strong robustness under abrupt changes and distribution shifts, with error reductions exceeding 10% (up to 19.5%) in challenging scenarios. By embedding residual-based feedback directly into the learning process, TEFL offers a simple, general, and effective enhancement to modern deep forecasting systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22520 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | TEFL: Prediction-Residual-Guided Rolling Forecasting for Multi-Horizon Time Series Huang, Xiannan Fang, Shen Qiu, Shuhan Yu, Chengcheng Du, Jiayuan Yang, Chao Machine Learning Time series forecasting plays a critical role in domains such as transportation, energy, and meteorology. Despite their success, modern deep forecasting models are typically trained to minimize point-wise prediction loss without leveraging the rich information contained in past prediction residuals from rolling forecasts - residuals that reflect persistent biases, unmodeled patterns, or evolving dynamics. We propose TEFL (Temporal Error Feedback Learning), a unified learning framework that explicitly incorporates these historical residuals into the forecasting pipeline during both training and evaluation. To make this practical in deep multi-step settings, we address three key challenges: (1) selecting observable multi-step residuals under the partial observability of rolling forecasts, (2) integrating them through a lightweight low-rank adapter to preserve efficiency and prevent overfitting, and (3) designing a two-stage training procedure that jointly optimizes the base forecaster and error module. Extensive experiments across 10 real-world datasets and 5 backbone architectures show that TEFL consistently improves accuracy, reducing MAE by 5-10% on average. Moreover, it demonstrates strong robustness under abrupt changes and distribution shifts, with error reductions exceeding 10% (up to 19.5%) in challenging scenarios. By embedding residual-based feedback directly into the learning process, TEFL offers a simple, general, and effective enhancement to modern deep forecasting systems. |
| title | TEFL: Prediction-Residual-Guided Rolling Forecasting for Multi-Horizon Time Series |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.22520 |