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

2026-02-25

AI Summary

Existing deep time series forecasting models fail to effectively leverage the dynamic bias information embedded in historical prediction residuals during rolling forecasts, limiting their accuracy and robustness in multi-step predictions. This work proposes the TEFL framework, which systematically integrates multi-step observable residuals into the deep forecasting pipeline for the first time. TEFL employs a lightweight low-rank adapter to fuse residual information and introduces a two-stage joint training strategy to co-optimize the base forecaster and the error correction module. Notably, the approach enhances performance universally without modifying the backbone architecture. Evaluated across ten real-world datasets and five state-of-the-art models, TEFL consistently reduces MAE by 5–10% on average, with error reductions exceeding 10%—and reaching up to 19.5%—under distribution shifts or abrupt changes.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Intelligent Robots: State Estimation
• Natural Language Processing: Language Grounding & Multi-modal NLP

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

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.

Problem

• time series forecasting
• prediction residuals
• multi-horizon forecasting
• rolling forecast
• distribution shift

Innovation

• Temporal Error Feedback Learning
• prediction residuals
• multi-horizon forecasting
• low-rank adapter
• rolling forecast