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.

翻译：产品蚕食指的是市场上某一产品因其他产品竞争而导致销售额下降的现象。我们基于一家跨国企业提供的批发数据集研究了这一现象。采用多元霍克斯过程建模，其中每个产品对应一个维度，通过交叉抑制效应刻画产品蚕食。为实施含抑制机制的霍克斯过程，我们解决了强度函数积分中的难点，并提出了新的更强稳定性条件——现有条件在抑制场景下过于严苛。我们在贝叶斯框架下展开分析，为此基于重参数化方法设计了一种与维度无关的交叉抑制先验。