Multi-class Vector AutoRegressive Models for Multi-store Sales Data

TL;DR

This paper introduces a multi-class VAR model for multi-store sales data, capturing cross-category effects across stores with a sparse, interpretable estimator that improves accuracy and reveals store and category relationships.

Contribution

It proposes a novel multi-class VAR approach that models multiple stores simultaneously, encouraging effect similarity, sparsity, and interpretability, advancing sales data analysis.

Findings

Improved estimation accuracy through borrowing strength across stores.

Effective visualization tools for store clustering and category networks.

Sparse estimator identifies key cross-category effects.

Abstract

Retailers use the Vector AutoRegressive (VAR) model as a standard tool to estimate the effects of prices, promotions and sales in one product category on the sales of another product category. Besides, these price, promotion and sales data are available for not just one store, but a whole chain of stores. We propose to study cross-category effects using a multi-class VAR model: we jointly estimate cross-category effects for several distinct but related VAR models, one for each store. Our methodology encourages effects to be similar across stores, while still allowing for small differences between stores to account for store heterogeneity. Moreover, our estimator is sparse: unimportant effects are estimated as exactly zero, which facilitates the interpretation of the results. A simulation study shows that the proposed multi-class estimator improves estimation accuracy by borrowing strength across classes. Finally, we provide three visual tools showing (i) the clustering of stores on identical cross-category effects, (ii) the networks of product categories and (iii) the similarity matrices of shared cross-category effects across stores.