  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.
