Predictive-sequential forecasting system development for cash machine stocking

The development of a system for predicting the daily amounts withdrawn from automated teller machines (ATMs) for inventory control is considered, using data from 190 ATMs in the United Kingdom over a two-year period. We argue that density forecasts are more appropriate than point forecasts and that a good forecasting system might choose a different model for each ATM. An analysis of the data finds that seasonal structure, first-order autocorrelation and cash-out days are important aspects of the data. Predictive sequential (prequential) comparisons between linear models, autoregressive models, structural time series models and Markov-switching models are made. The Markov-switching models are preferred because they are found to produce better density forecasts, and might also be more useful for inventory control because they separate the demand for cash from 'out-of-service' effects. A logarithmic scoring rule is used to choose the most appropriate seasonal and distributional assumptions for each ATM.