Learning from Forecasting Errors: Separating Correctable Errors from Predictive Uncertainty in Time Series Forecasting

Existing time series forecasting methods typically treat forecasting errors as optimization residuals to be minimized, while rarely exploiting the information contained in forecasting failures themselves. However, forecasting errors differ substantially in correctability: some exhibit stable structures that can be further corrected, some recur under similar historical conditions and can be reused as historical evidence, whereas others lack reliable correction evidence and are better represented as predictive uncertainty. We propose EUD-RM (Error-Uncertainty Decoupling with Residual Memory), an error-centric framework that handles forecasting failures through a reduce-correct-reuse-quantify process. A Channel-Aware Mixer (CAM) first strengthens cross-variable interactions to reduce potential systematic errors. Learnability-Gated Error Correction (LGEC) then identifies prediction positions with reliable correction evidence and applies bounded parametric corrections. Residual-Aware Retrieval Memory (RARM) stores historical forecasting residuals and retrieves consistent past failures under similar input and prediction states as non-parametric correction evidence. Finally, an independent LGEC-U branch models the remaining predictive risk after deterministic corrections and produces calibrated prediction intervals without altering point forecasts. Rather than assuming a strict decomposition into deterministic error and random noise, EUD-RM exploits empirical correctability and historical reproducibility to determine how forecasting failures should be handled. Experiments on long-horizon multivariate forecasting benchmarks demonstrate consistent gains, with EUD-RM achieving leading results on most benchmark settings.