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Multi-class vector autoregressive models for multi-store sales data

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  • Ines Wilms
  • Luca Barbaglia
  • Christophe Croux

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.

Suggested Citation

  • Ines Wilms & Luca Barbaglia & Christophe Croux, 2016. "Multi-class vector autoregressive models for multi-store sales data," Working Papers of Department of Decision Sciences and Information Management, Leuven 540947, KU Leuven, Faculty of Economics and Business (FEB), Department of Decision Sciences and Information Management, Leuven.
  • Handle: RePEc:ete:kbiper:540947
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    Cited by:

    1. Baek, Changryong & Gates, Katheleen M. & Leinwand, Benjamin & Pipiras, Vladas, 2021. "Two sample tests for high-dimensional autocovariances," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).

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    Keywords

    Fused Lasso; Multi-class estimation; Multi-store sales application; Sparse estimation; Vector AutoRegressive model;
    All these keywords.

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