Geometric Log-Space Ensembling for MAPE-Optimal Retail Revenue Forecasting: A Large-Scale Case Study

Abstract

Forecasting monthly store-level turnover across tens of thousands of retail locations is a canonical large-scale retail analytics problem: the panel is wide and heterogeneous, and the dominant variance is multiplicative, driven by calendar effects, macro-economic cycles, and local competition. We report a forecasting pipeline built for a public retail-forecasting challenge for a grocery retailer operating more than 18,000 stores, predicting each store’s revenue (PTO) for a target month from prior sales history, store metadata, and a calendar of events. Performance is evaluated with the multiplicative score S = 100(1 − MAPE/100)², minimised by forecasters that are geometrically, not arithmetically, unbiased. We show analytically, and confirm via synthetic simulation, that for log-normal targets the geometric (log-space) ensemble is the MAPE-optimal aggregator of unbiased predictors. Guided by this, we (i) reparameterise the target as a multiplicative residual relative to the previous month; (ii) train CatBoost models on log-turnover with calendar features; and (iii) combine these with an independently developed external gradient-boosting model via a weighted geometric blend under a global mass-preservation constraint. This pipeline reaches a confirmed public-leaderboard score of 90.68 (MAPE ≈ 4.77%), up from a 90.28 baseline, within 0.14 of the best observed public score (90.82). We additionally report a submission-log-grounded ablation of what did not work, and discuss why common ensembling and calibration heuristics fail to transfer to this metric.