Probabilistic forecasting of heterogeneous consumer transaction–sales time series

We present new Bayesian methodology for consumer sales forecasting. Focusing on the multi-step-ahead forecasting of daily sales of many supermarket items, we adapt dynamic count mixture models for forecasting individual customer transactions, and introduce novel dynamic binary cascade models for predicting counts of items per transaction. These transaction–sales models can incorporate time-varying trends, seasonality, price, promotion, random effects and other outlet-specific predictors for individual items. Sequential Bayesian analysis involves fast, parallel filtering on sets of decoupled items, and is adaptable across items that may exhibit widely-varying characteristics. A multi-scale approach enables information to be shared across items with related patterns over time in order to improve prediction, while maintaining the scalability to many items. A motivating case study in many-item, multi-period, multi-step-ahead supermarket sales forecasting provides examples that demonstrate an improved forecast accuracy on multiple metrics, and illustrates the benefits of full probabilistic models for forecast accuracy evaluation and comparison.