Lindsay R. Berry

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

This paper develops forecasting methodology and application of new classes of dynamic models for time series of non-negative counts. Novel univariate models synthesise dynamic generalized linear models for binary and conditionally Poisson time series, with dynamic random effects for over-dispersion. These models allow use of dynamic covariates in both binary and non-zero count components. Sequential Bayesian analysis allows fast, parallel analysis of sets of decoupled time series. New multivariate models then enable information sharing in contexts when data at a more highly aggregated level provide more incisive inferences on shared patterns such as trends and seasonality. A novel multi-scale approach-- one new example of the concept of decouple/recouple in time series-- enables information sharing across series. This incorporates cross-series linkages while insulating parallel estimation of univariate models, hence enables scalability in the number of series. The major motivating context is supermarket sales forecasting. Detailed examples drawn from a case study in multi-step forecasting of sales of a number of related items showcase forecasting of multiple series, with discussion of forecast accuracy metrics and broader questions of probabilistic forecast accuracy assessment.