Accuracy-Preserving Stability Regularization for Large-Scale Retail Demand Forecasting

Multi-step-ahead forecasts are often updated as new observations become available, since shorter forecast horizons typically improve forecast quality. However, such improvements come at the cost of forecast instability, i.e., variability in forecasts for the same target period. This instability can trigger costly changes to plans formulated based on the forecasts and may erode trust in the forecasting system. In this work, we integrate forecast stability alongside forecast quality into the training of distribution-free probabilistic time-series forecasting models, allowing us to control this trade-off. We propose a method for generating stabilized forecasted conditional quantile functions using regression splines parameterized by a neural network. This approach enables joint optimization of quality and stability, as it allows us to directly penalize dissimilarities arising from forecast updates. Furthermore, it allows assigning varying importance to stabilizing different parts of the forecast distributions (e.g., central parts vs. tails) to focus on the parts most relevant for the intended downstream use (e.g., the upper tail for inventory management). We empirically evaluate the proposed method on two datasets with different statistical properties and show that it can effectively reduce forecast instability without a substantial loss in forecast quality, and that it can target stabilization effort toward specific parts of the forecast distributions.

Time series forecasting relies on historical patterns, but real-world series often exhibit non-stationarity and regime shifts that challenge fully parametric forecasters. Inspired by Retrieval-Augmented Generation (RAG), recent work augments forecasters by retrieving relevant historical segments and using them as external evidence at inference time. However, due to the intrinsic non-stationarity of real-world time series, a highly similar past segment does not necessarily imply a similar future, rendering similarity-only retrieval brittle and prone to redundancy. We propose Stationarity-Aware Retrieval-Augmented Time Series Forecasting (SARAF), a framework that adaptively balances relevance and diversity in retrieval. SARAF first forms a candidate pool via temporal similarity with time-aligned enhancement, then applies a diversity-aware selection strategy to cover heterogeneous historical regimes, with the diversification strength automatically modulated by dataset-level stationarity. Moreover, SARAF uses stationarity-aware aggregation to fuse the retrieved futures. Extensive experiments on eight real-world datasets show that SARAF achieves competitive forecasting performance and improves average accuracy and robustness over strong baselines, with particularly clear benefits under challenging non-stationary settings. Code: https://github.com/ShiqiaoZhou/SARAF.

Retrieval-augmented generation (RAG) complements parametric models with retrieved external evidence. The same idea is attractive for continuous-output regression, but directly reusing retrieved target values is often not robust when samples differ in output level, numerical scale, or local dynamics. Moreover, conventional forecasting pipelines generally use residuals for model optimization and error diagnosis, but do not retain individual historical residual examples as memory that can be accessed at inference time.For multivariate time-series forecasting, we propose RATL, a plug-in residual-retrieval and feedback-correction method. RATL freezes a base forecaster to construct retrieval keys and turns its historical forecast residuals into a train-only memory specific to that base model. At inference time, RATL retrieves residual trajectories from similar historical contexts subject to causal availability constraints, then uses a set-aware router operating over forecast blocks and variables to select and combine these trajectories. Experiments show that historical residuals matched to the current context contain reusable forecasting information and that RATL improves frozen base forecasters in most experimental settings. Ablations further show that learned routing strengthens raw residual feedback, while validation-based correction-strength selection limits residual over-injection.On real-world benchmarks, we use iTransformer as the primary frozen base forecaster, compare against multiple strong forecasting baselines, and test transferability across backbones. The results show that RATL can further improve base-forecaster performance in most settings.Overall, RATL shifts the retrieved object from historical target values to base-model-specific historical forecast errors, providing a plug-in, residual-memory-based paradigm for learned feedback correction in continuous-output forecasting.