# Estimating Product Cannibalisation in Wholesale using Multivariate Hawkes Processes with Inhibition

arXiv: https://arxiv.org/abs/2201.05009 · HTML: https://mlsanity.com/paper/2201.05009/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jan 2022.

## Built on by (most cited first, 2 of 2)

- [Nonparametric estimation of Hawkes processes with RKHSs](https://mlsanity.com/paper/2411.00621/) (2024)
- [Scalable and adaptive variational Bayes methods for Hawkes processes](https://mlsanity.com/paper/2212.00293/) (2022)

## Abstract (arXiv)

Product cannibalisation in the marketplace refers to the decrease in the sales of one product due to competition from another product. We examine this phenomenon in a wholesale data set provided by an international company. We use a multivariate Hawkes process where each product is represented by a dimension, with cross-inhibition effects that model product cannibalisation. To implement the Hawkes process with inhibition we resolve challenges regarding the integration of the intensity function and introduce a new, stronger conditions for stability as existing conditions are unnecessarily strict under inhibition. We conduct our analysis in a Bayesian framework, for which we design a dimension-independent prior on the cross-inhibition based on a reparametrisation.