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

Estimating Product Cannibalisation in Wholesale using Multivariate Hawkes Processes with Inhibition