Forecasting a cumulative variable using its partially accumulated data

Several forecasting algorithms have been proposed to forecast a cumulative variable using its partially accumulated data. Some particular cases of this problem are known in the literature as the ‘style goods inventory problem’ or as ‘forecasting shipments using firm orders-to-date’, among other names. Here we summarize some of the most popular techniques and propose a statistical approach to discriminate among them in an objective (data-based) way. Our basic idea is to use statistical models to produce minimum mean square error forecasts and let the data lead us to select an appropriate model to represent their behaviour. We apply our proposal to some published data showing total accumulated values with constant level and then to two actual sets of data pertaining to the Mexican economy, showing a nonconstant level. The forecasting performance of the statistical models was evaluated by comparing their results against those obtained with algorithmic solutions. In general the models produced better forecasts for all lead times, as indicated by the most common measures of forecasting accuracy and precision.