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

Jize Li; Jiani He; Dishu Yang; Dingyan Shang; Jingjing Liu; Shiqi Huang

cs.LGJul 14, 2026

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

Authors: Jize Li, Jiani He, Dishu Yang, Dingyan Shang, Jingjing Liu, Shiqi Huang

Organizations: Boston University, Boston, MA, USA · Massachusetts Institute of Technology, Cambridge, MA, USA · Northeastern University, San Jose, CA, USA · University of Southern California, Los Angeles, CA, USA · University of California, Berkeley, Berkeley, CA, USA · Washington University in St. Louis, St. Louis, MO, USA

Abstract

Retail demand forecasts are reused across replenishment, capacity, labor, and transportation planning cycles. Point-error objectives do not constrain abrupt movement between adjacent forecasts, while post-hoc smoothing acts only after model fitting. We ask whether a training-time penalty on consecutive within-series movement can improve horizontal forecast-path stability without materially changing point accuracy. The penalty is evaluated in a temporal-structured pipeline combining recent-demand embeddings with calendar, price, hierarchy, item, and store features. On selected M5 demand series at 1000, 3000, and 4000-series scales, the stability-aware hybrid model improves Forecast Stability Score over XGBoost by 6.91%, 6.66%, and 7.68%, respectively, while RMSE changes remain within 0.72% across three random seeds. Post-hoc exponential smoothing attains lower raw movement but incurs a larger RMSE cost; training-time regularization preserves more point accuracy and performs favorably under normalized stability. These findings extend forecast evaluation from point-error minimization toward an accuracy-stability trade-off perspective for operational retail forecasting.

Explore similar work

Stabilizing distribution-free probabilistic forecasts
May 27, 2026Jente Van Belle, Honglin Wen, Wouter Verbeke +1Retrieval-Augmented Forecasting Time Series Forecasting
Stationarity-Aware Retrieval-Augmented Time Series Forecasting
Jun 2, 2026Shiqiao Zhou, Holger Schöner, Zipeng Wu +3Time Series Forecasting Time Series
RATL: Learning from Retrieved Residuals for Robust Multivariate Time-Series Forecasting
Sep 3, 2026Yuchen He, Yueyang Cang, Zhiyuan Ning +2Residual Learning Time Series

May 27, 2026 · cs.LGJ/K move · Enter open · S save

Stabilizing distribution-free probabilistic forecasts

Jente Van Belle, Honglin Wen, Wouter Verbeke, Pierre Pinson

Faculty of Economics and Business, KU Leuven, Belgium · Department of Electrical Engineering, Shanghai Jiao Tong University, China · Dyson School of Design Engineering, Imperial College London, United Kingdom · Halfspace, Denmark · Department of Technology, Management and Economics, Technical University of Denmark, Denmark

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.

Retrieval-Augmented Forecasting Time Series Forecasting Long-Horizon Forecasting Quantile Regression Predictive Uncertainty Non-Stationarity Stability Analysis

Open paper Ask about it PDF

Abstract

Explore similar work

Stabilizing distribution-free probabilistic forecasts

Stationarity-Aware Retrieval-Augmented Time Series Forecasting

RATL: Learning from Retrieved Residuals for Robust Multivariate Time-Series Forecasting