Multiclass vector auto-regressive models for multistore sales data

Retailers use the vector auto-regressive (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 not just for one store, but for a whole chain of stores. We propose to study cross-category effects by using a multiclass 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 0, which facilitates the interpretation of the results. A simulation study shows that the multiclass estimator proposed improves estimation accuracy by borrowing strength across classes. Finally, we provide three visual tools showing clustering of stores with similar cross-category effects, networks of product categories and similarity matrices of shared cross-category effects across stores.