Probabilistic forecasting of heterogeneous consumer transaction–sales time series

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

[1]  L. Duncan,et al.  Forecasting intermittent demand: a comparative study , 2009, J. Oper. Res. Soc..

[2]  Andrew Lim,et al.  A greedy aggregation-decomposition method for intermittent demand forecasting in fashion retailing , 2018, Eur. J. Oper. Res..

[3]  T. Willemain,et al.  A new approach to forecasting intermittent demand for service parts inventories , 2004 .

[4]  Commentary on Retail Forecasting , 2018, International Journal of Forecasting.

[5]  Gael M. Martin,et al.  Bayesian predictions of low count time series , 2005 .

[6]  Michael A. West,et al.  Time Series: Modeling, Computation, and Inference , 2010 .

[7]  Jeff Harrison,et al.  Subjective intervention in formal models , 1989 .

[8]  J. Ord,et al.  Forecasting the intermittent demand for slow-moving inventories: A modelling approach , 2012 .

[9]  J. Boylan,et al.  The accuracy of intermittent demand estimates , 2005 .

[10]  J. D. Croston.  Forecasting and Stock Control for Intermittent Demands , 1972 .

[11]  Michael A. West,et al.  Bayesian Forecasting and Dynamic Models (2nd edn) , 1997, J. Oper. Res. Soc..

[12]  Cathy W. S. Chen,et al.  Autoregressive conditional negative binomial model applied to over-dispersed time series of counts , 2016 .

[13]  Mike West,et al.  Bayesian Forecasting of Many Count-Valued Time Series , 2018, Journal of Business & Economic Statistics.

[14]  David Wooff,et al.  Bayes Linear Statistics: Theory and Methods , 2007 .

[15]  S. Kolassa.  Evaluating predictive count data distributions in retail sales forecasting , 2016 .

[16]  Tevfik Aktekin,et al.  Sequential Bayesian Analysis of Multivariate Count Data , 2016, Bayesian Analysis.

[17]  N. Arunraj,et al.  A hybrid seasonal autoregressive integrated moving average and quantile regression for daily food sales forecasting , 2015 .

[18]  Ute Beyer,et al.  Bayesian Forecasting And Dynamic Models , 2016 .

[19]  M. West,et al.  Dynamic Generalized Linear Models and Bayesian Forecasting , 1985 .

[20]  Cathy W. S. Chen,et al.  Bayesian causality test for integer‐valued time series models with applications to climate and crime data , 2017 .

[21]  Brian Seaman.  Considerations of a retail forecasting practitioner , 2018 .

[22]  Nobuhiko Terui,et al.  Multivariate Time Series Model with Hierarchical Structure for Over-Dispersed Discrete Outcomes , 2012 .

[23]  Phillip M. Yelland,et al.  Bayesian Forecasting for Low Count Time Series Using State-Space Models: An Empirical Evaluation for Inventory Management , 2009 .