The Forecast After the Forecast: A Post-Processing Shift in Time Series
Daojun Liang, Qi Li, Yinglong Wang, Jing Chen, Hu Zhang, Xiaoxiao Cui, Qizheng Wang, Shuo Li
TL;DR
This paper tackles the last-mile challenge in time series forecasting by introducing δ-Adapter, a lightweight, architecture-agnostic post-processing module that augments a frozen forecaster through input nudging and output residual correction with a small trust region δ. It additionally provides a horizon-aware feature-selector mask and two uncertainty calibrators—Quantile Calibrator and Conformal Calibrator—to deliver calibrated, personalized prediction intervals without retraining the backbone. The authors establish stability and descent guarantees for both input- and output-edits, along with compositional stability when combining the two placements, and show how a tiny, high-signal adapter can yield consistent gains across diverse backbones and datasets with negligible compute. Empirically, δ-Adapter improves both accuracy and calibration, while offering interpretability through the feature-selector mask and finite-sample uncertainty guarantees, making it practical for real-world deployment. Overall, the approach provides a principled, efficient pathway to enhance deployed forecasting systems without touching established models.
Abstract
Time series forecasting has long been dominated by advances in model architecture, with recent progress driven by deep learning and hybrid statistical techniques. However, as forecasting models approach diminishing returns in accuracy, a critical yet underexplored opportunity emerges: the strategic use of post-processing. In this paper, we address the last-mile gap in time-series forecasting, which is to improve accuracy and uncertainty without retraining or modifying a deployed backbone. We propose $δ$-Adapter, a lightweight, architecture-agnostic way to boost deployed time series forecasters without retraining. $δ$-Adapter learns tiny, bounded modules at two interfaces: input nudging (soft edits to covariates) and output residual correction. We provide local descent guarantees, $O(δ)$ drift bounds, and compositional stability for combined adapters. Meanwhile, it can act as a feature selector by learning a sparse, horizon-aware mask over inputs to select important features, thereby improving interpretability. In addition, it can also be used as a distribution calibrator to measure uncertainty. Thus, we introduce a Quantile Calibrator and a Conformal Corrector that together deliver calibrated, personalized intervals with finite-sample coverage. Our experiments across diverse backbones and datasets show that $δ$-Adapter improves accuracy and calibration with negligible compute and no interface changes.