Multiclass vector auto-regressive models for multistore sales data

Ines Wilms*, Luca Barbaglia, Christophe Croux

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)435-452
Number of pages18
JournalJournal of the Royal Statistical Society Series C-Applied Statistics
Volume67
Issue number2
DOIs
Publication statusPublished - Feb 2018

Keywords

  • Fused lasso
  • Multiclass estimation
  • Multistore sales application
  • Sparse estimation
  • Vector auto-regressive model
  • JOINT GRAPHICAL LASSO
  • SPARSE REGRESSION
  • SELECTION
  • CATEGORIES
  • SHRINKAGE
  • NETWORK

Cite this

@article{23127c16a32347b2b5406c96027140df,
title = "Multiclass vector auto-regressive models for multistore sales data",
abstract = "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.",
keywords = "Fused lasso, Multiclass estimation, Multistore sales application, Sparse estimation, Vector auto-regressive model, JOINT GRAPHICAL LASSO, SPARSE REGRESSION, SELECTION, CATEGORIES, SHRINKAGE, NETWORK",
author = "Ines Wilms and Luca Barbaglia and Christophe Croux",
note = "data source: We use Dominick's Finer Food database, publicly available at https://www.chicagobooth.edu/research/kilts/datasets/dominicks.",
year = "2018",
month = "2",
doi = "10.1111/rssc.12231",
language = "English",
volume = "67",
pages = "435--452",
journal = "Journal of the Royal Statistical Society Series C-Applied Statistics",
issn = "0035-9254",
publisher = "Wiley",
number = "2",

}

Multiclass vector auto-regressive models for multistore sales data. / Wilms, Ines; Barbaglia, Luca; Croux, Christophe.

In: Journal of the Royal Statistical Society Series C-Applied Statistics, Vol. 67, No. 2, 02.2018, p. 435-452.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Multiclass vector auto-regressive models for multistore sales data

AU - Wilms, Ines

AU - Barbaglia, Luca

AU - Croux, Christophe

N1 - data source: We use Dominick's Finer Food database, publicly available at https://www.chicagobooth.edu/research/kilts/datasets/dominicks.

PY - 2018/2

Y1 - 2018/2

N2 - 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.

AB - 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.

KW - Fused lasso

KW - Multiclass estimation

KW - Multistore sales application

KW - Sparse estimation

KW - Vector auto-regressive model

KW - JOINT GRAPHICAL LASSO

KW - SPARSE REGRESSION

KW - SELECTION

KW - CATEGORIES

KW - SHRINKAGE

KW - NETWORK

U2 - 10.1111/rssc.12231

DO - 10.1111/rssc.12231

M3 - Article

VL - 67

SP - 435

EP - 452

JO - Journal of the Royal Statistical Society Series C-Applied Statistics

JF - Journal of the Royal Statistical Society Series C-Applied Statistics

SN - 0035-9254

IS - 2

ER -