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 forecastingComment: 23 pages, 5 figures, 1 tabl

Multiplicative State-Space Models for Intermittent Time Series

Intermittent demand forecasting is an important supply chain task, which is commonly done using methods based on exponential smoothing. These methods however do not have underlying statistical models, which limits their generalisation. In this paper we propose a general state-space model that takes intermittence of data into account, extending the taxonomy of exponential smoothing models. We show that this model has a connection with conventional non-intermittent state space models and underlies Croston’s and Teunter-Syntetos-Babai (TSB) forecasting methods. We discuss properties of the proposed models and show how a selection can be made between them in the proposed framework. We then conduct experiments on simulated data and on two real life datasets, demonstrating advantages of the proposed approach

An empirical Bayes approach to incorporating demand intermittency and irregularity into inventory control

Article asserts that spare parts inventory management is complex due to the combined impact of intermittent and variable demand patterns. This study proposes a novel nonparametric Bayesian forecasting approach with its roots in the empirical Bayes paradigm

Applications of Bayesian mixture models and self-exciting processes to retail analytics

Retail analytics has been transformed by big data, which has led to many retailers using detailed analytics to improve performance at a range of operational levels. This is the case with the collaborator of this research, dunnhumby, who have large amounts of retailer data derived from the numerous activities that retailers operate at. This thesis focuses on two challenges retailers face; the analysis of products through their price elasticity coefficients and demand forecasting of products known as slow-moving inventory. The analysis of products in terms of their price elasticity coefficients is well studied. Existing approaches are hampered by the challenging nature of cross-elasticity data, as cross-elasticity coefficients typically vary in dimension and exhibit an inherent censoring. We address these problems by developing a systematic model-based approach by reinterpreting the cross-elasticity coefficients as realisations of variable length order statistics sequences, and develop a nonparametric Bayesian methodology to cluster these sequences. Our approach uses the Dirichlet process mixture model that allows data to dictate the appropriate number of clusters and provides interpretable parameters characterising the decay of the leading entries. Slow-moving inventory are characterised by having intermittent demand, in that the demand is populated with an abundance of zero sales and that, when a sale does a occur, it is often followed by a quick succession of sales. This demand intermittency inhibits the use of traditional analytics which crucially affects optimal inventory management. To combat this, we represent intermittent demand as a structured multivariate point process which allows for auto- and cross- correlation frequently observed in sparse sales data. Our approach uses a hurdle component to cope with zero sales inflation, the Hawkes process to capture the temporal clustering and a hierarchal structure to pool information across products. We illustrate our methods on real retailer data, from access granted by dunnhumby