  We present new Bayesian methodology for consumer sales forecasting. With a
focus on multi-step ahead forecasting of daily sales of many supermarket items,
we adapt dynamic count mixture models to forecast individual customer
transactions, and introduce novel dynamic binary cascade models for predicting
counts of items per transaction. These transactions-sales models can
incorporate time-varying trend, seasonal, 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 sharing across items with related
patterns over time to improve prediction while maintaining scalability to many
items. A motivating case study in many-item, multi-period, multi-step ahead
supermarket sales forecasting provides examples that demonstrate improved
forecast accuracy in multiple metrics, and illustrates the benefits of full
probabilistic models for forecast accuracy evaluation and comparison.
  Keywords: Bayesian forecasting; decouple/recouple; dynamic binary cascade;
forecast calibration; intermittent demand; multi-scale forecasting; predicting
rare events; sales per transaction; supermarket sales forecasting
