# TEFL: Prediction-Residual-Guided Rolling Forecasting for Multi-Horizon Time Series

arXiv: https://arxiv.org/abs/2602.22520 · HTML: https://mlsanity.com/paper/2602.22520/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 52 references that are in the map.
- First posted on arXiv 26 Feb 2026.

## Builds on (most cited first, 27 of 27)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Soft-DTW: a Differentiable Loss Function for Time-Series](https://mlsanity.com/paper/1703.01541/) (2017)
- [TFB: Towards Comprehensive and Fair Benchmarking of Time Series Forecasting Methods](https://mlsanity.com/paper/2403.20150/) (2024)
- [Deep Time Series Models: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2407.13278/) (2024)
- [FreDF: Learning to Forecast in the Frequency Domain](https://mlsanity.com/paper/2402.02399/) (2024)
- [SOFTS: Efficient Multivariate Time Series Forecasting with Series-Core Fusion](https://mlsanity.com/paper/2404.14197/) (2024)
- [Time Series Prediction using Deep Learning Methods in Healthcare](https://mlsanity.com/paper/2108.13461/) (2021)
- [OneNet: Enhancing Time Series Forecasting Models under Concept Drift by Online Ensembling](https://mlsanity.com/paper/2309.12659/) (2023)
- [TimeFilter: Patch-Specific Spatial-Temporal Graph Filtration for Time Series Forecasting](https://mlsanity.com/paper/2501.13041/) (2025)
- [Learning Fast and Slow for Online Time Series Forecasting](https://mlsanity.com/paper/2202.11672/) (2022)
- [Patch-wise Structural Loss for Time Series Forecasting](https://mlsanity.com/paper/2503.00877/) (2025)
- [Temporal Domain Generalization with Drift-Aware Dynamic Neural Networks](https://mlsanity.com/paper/2205.10664/) (2022)
- [Training for the Future: A Simple Gradient Interpolation Loss to Generalize Along Time](https://mlsanity.com/paper/2108.06721/) (2021)
- [Amplifier: Bringing Attention to Neglected Low-Energy Components in Time Series Forecasting](https://mlsanity.com/paper/2501.17216/) (2025)
- [Generalizing to Evolving Domains with Latent Structure-Aware Sequential Autoencoder](https://mlsanity.com/paper/2205.07649/) (2022)
- [Lightweight Online Adaption for Time Series Foundation Model Forecasts](https://mlsanity.com/paper/2502.12920/) (2025)
- [Continuous Temporal Domain Generalization](https://mlsanity.com/paper/2405.16075/) (2024)
- [Learning Robust Spectral Dynamics for Temporal Domain Generalization](https://mlsanity.com/paper/2505.12585/) (2025)
- [Online Test-Time Adaptation of Spatial-Temporal Traffic Flow Forecasting](https://mlsanity.com/paper/2401.04148/) (2024)
- [Selective Learning for Deep Time Series Forecasting](https://mlsanity.com/paper/2510.25207/) (2025)
- [Temporal Test-Time Adaptation with State-Space Models](https://mlsanity.com/paper/2407.12492/) (2024)
- [Online time series prediction using feature adjustment](https://mlsanity.com/paper/2509.03810/) (2025)
- [Leveraging Intra-Period and Inter-Period Features for Enhanced Passenger Flow Prediction of Subway Stations](https://mlsanity.com/paper/2410.14727/) (2024)

## Built on by (most cited first, 2 of 2)

- [Learning the Context of Errors: Black-Box Online Adaptation of Time Series Foundation Models](https://mlsanity.com/paper/2606.14222/) (2026)
- [EPOC: Endpoint-Preserving Online Correction With Compressed Residual State for Multi-Horizon Time Series Forecasting](https://mlsanity.com/paper/2609.30929/) (2026)

## Abstract (arXiv)

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.