Hierarchical robust aggregation of sales forecasts at aggregated levels in e-commerce, based on exponential smoothing and Holt's linear trend method

Abstract

We revisit the interest of classical statistical techniques for sales forecasting like exponential smoothing and extensions thereof (as Holt's linear trend method). We do so by considering ensemble forecasts, given by several instances of these classical techniques tuned with different (sets of) parameters, and by forming convex combinations of the elements of ensemble forecasts over time, in a robust and sequential manner. The machine-learning theory behind this is called "robust online aggregation", or "prediction with expert advice", or "prediction of individual sequences" (see Cesa-Bianchi and Lugosi, 2006). We apply this methodology to a hierarchical data set of sales provided by the e-commerce company Cdiscount and output forecasts at the levels of subsubfamilies, subfamilies and families of items sold, for various forecasting horizons (up to 6-week-ahead). The performance achieved is better than what would be obtained by optimally tuning the classical techniques on a train set and using their forecasts on the test set. The performance is also good from an intrinsic point of view (in terms of mean absolute percentage of error). While getting these better forecasts of sales at the levels of subsubfamilies, subfamilies and families is interesting per se, we also suggest to use them as additional features when forecasting demand at the item level.

Hierarchical forecasting for aggregated curves with an application to day-ahead electricity price auctions

“…Most notable is the optimal minimum trace reconciling method Wickramasuriya et al [2019]. Other methods have also been proposed, such as a game-theoretically optimal reconciliation approach [ Van Erven and Cugliari, 2015], averaging approaches called level conditional coherent (LCC) and combined conditional coherent (CCC) point forecasts [Di Fonzo andGirolimetto, 2021, Hollyman et al, 2021] and machine-learning based reconciliation [Spiliotis et al, 2021], [Brégère and Huard, 2022], [Huard et al, 2020].…”