Look Back, Correct Forward: Error Feedback Calibration for Time Series Forecasting

Abstract

Time series forecasting models are increasingly deployed in continuously evolving environments. After a forecast is issued, future observations gradually arrive and reveal how the model has failed. Existing methods mainly treat such observations as supervision for parameter updates. However, it remains unclear whether verified forecasting errors can themselves provide causal feedback for correcting future predictions. To address this, we introduce Error Feedback Calibration (EFC), a fully test-time framework for deterministic post-hoc correction of time series forecasting. EFC constructs a Causal Error Diagonal (CED) from revealed errors of overlapping historical forecasts, providing a fresh view of the frozen forecaster's recent failure behavior. Then Cumulative Error Transport (CET) maps this error state to future residuals using cumulative estimation, while temporal out-of-sample validation controls the correction strength. Temporal Residual Learning (TRL) further predicts only the residual structure left after CET from recent CED trajectories, rather than relearning the entire forecasting error. Extensive experiments across forecasting backbones and datasets show that EFC broadly improves forecasting performance while substantially controlling harmful over correction.