Time series forecasts improved with historical data and error corrections
ECHO: Correcting Time Series Foundation Model Forecasts with Historical Analogues and Errors
Machine Learning
Summary
Forecasting models that predict future data points sometimes make systematic mistakes or don’t match the specific patterns of the data they are used on. The authors noticed that looking at similar past situations and remembering previous mistakes can help fix these forecasts. They built a method called ECHO that adjusts forecasts by learning from both similar past cases and past errors, even without knowing how the original model works inside. Testing on multiple datasets and models, they showed ECHO consistently reduces forecasting errors, especially for longer-range predictions.
What this means in practice
- •For data science teams: Improve prediction accuracy for business and operational data by correcting forecasts using past error patterns and similar historical instances.
- •For energy load forecasters: Enhance energy demand forecasts by applying ECHO to adjust foundation model outputs with domain-specific error corrections and analogous historical events.
Authors
Boya Zhang, Xilin Dai, Yilin Wang, Qiang Xu, Luyao Dong, Xing He, Wen Wu
Abstract
Time Series Foundation Models (TSFMs) provide general-purpose forecasting capabilities, yet their forecasts can remain misaligned with the temporal characteristics of a target domain. This motivates lightweight forecast correction even when only black-box access to the TSFM is available. Our key observation is that two forms of historical information provide complementary correction signals: historical analogues reveal how similar contexts evolved, while past forecast errors reveal a TSFM's characteristic deviations in the target domain. Based on this observation, we propose ECHO, a black-box forecast correction framework that learns from both sources. ECHO uses AnalogE to assess retrieved historical analogues together with the current context and base forecast, learning transferable corrections through cross-domain pretraining. In parallel, RecentE learns target-specific residual corrections from past forecast errors and refines them as causally available feedback accumulates. ECHO dynamically combines the two corrections according to their observed forecasting performance. Across 5 representative TSFMs and 9 real-world datasets, ECHO reduces MSE in all 45 backbone--dataset settings, yielding an average relative reduction of 9.26\% in macro-average MSE. Its gains also extend to long-horizon forecasting.