Multivariate dynamic modeling for Bayesian forecasting of business revenue

Abstract

Forecasting enterprise‐wide revenue is critical to many companies and presents several challenges and opportunities for significant business impact. This case study is based on model developments to address these challenges for forecasting in a large‐scale retail company. Focused on multivariate revenue forecasting across collections of supermarkets and product categories, hierarchical dynamic models are natural: these are able to couple revenue streams in an integrated forecasting model, while allowing conditional decoupling to enable relevant and sensitive analysis together with scalable computation. Structured models exploit multi‐scale modeling to cascade information on price and promotion activities as predictors relevant across categories and groups of stores. With a context‐relevant focus on forecasting revenue 12 weeks ahead, the study highlights product categories that benefit from multi‐scale information, defines insights into when, how, and why multivariate models improve forecast accuracy, and shows how cross‐category dependencies can relate to promotion decisions in one category impacting others. Bayesian modeling developments underlying the case study are accessible in custom code for interested readers.

Discussion of “Multivariate dynamic modeling for Bayesian forecasting of business revenue”

“…It would be interesting to explore more predictors, and also allow different predictors to have different importance for forecasting each week's sales. Within the context of DLM that the authors present (see Yanchenko et al, 1 equation ( 1)) our suggestion implies that some of the coefficients 𝜽 t may be zero in some time periods but not in others. This is the so-called dynamic variable selection problem in statistics, and recently Koop and Korobilis 4 have developed a fast variational Bayes algorithm that allows to select among hundreds of predictors each time period.…”

“…The paper by Yanchenko et al 1 presents a long‐term business revenue forecast effort for a large retail company. We congratulate the authors for elaborating on a framework that is of theoretical interest while responding to specific needs of business revenue forecasting and the retail sector.…”

Discussion of “Multivariate Dynamic Modeling for Bayesian Forecasting of Business Revenue”

“…This task requires not only forecasting accuracy, but also hierarchical coherence of the forecasts. To achieve this goal, Yanchenko et al 1 develop multiscale modeling to spread information on price and promotion activities as explanatory variables across categories and groups of stores.…”

“…This study proposes a multiscale approach for modeling business revenue and forecasting revenue 12 weeks ahead. Yanchenko et al 1 successfully demonstrate how to share information among LSG (Local Store Group) and category groups while keeping the computation highly scalable. One of the main innovations is to extend the idea of Berry and West 2 and Yanchenko et al 3 to allow the sharing of discount information in the modeling and to apply decoupled/recoupled steps to facilitate parallel statistical computation in univariate modeling.…”

“…Yanchenko et al 1 consider $$$ 9\times 100 $$$ LSG‐category combinations and show enhanced predictive power of the multiscale model.…”