  The field of retail analytics has been transformed by the availability of
rich data which can be used to perform tasks such as demand forecasting and
inventory management. However, one task which has proved more challenging is
the forecasting of demand for products which exhibit very few sales. The
sparsity of the resulting data limits the degree to which traditional analytics
can be deployed. To combat this, we represent sales data as a structured sparse
multivariate point process which allows for features such as auto-correlation,
cross-correlation, and temporal clustering, known to be present in sparse sales
data. We introduce a Bayesian point process model to capture these phenomena,
which includes a hurdle component to cope with sparsity and an exciting
component to cope with temporal clustering within and across products. We then
cast this model within a Bayesian hierarchical framework, to allow the
borrowing of information across different products, which is key in addressing
the data sparsity per product. We conduct a detailed analysis using real sales
data to show that this model outperforms existing methods in terms of
predictive power and we discuss the interpretation of the inference.
