Integrated hierarchical forecasting

Forecasts are often made at various levels of aggregation of individual products, which combine into groups at higher hierarchical levels. We provide an alternative to the traditional discussion of bottom-up versus top-down forecasting by examining how the hierarchy of products can be exploited when forecasts are generated. Instead of selecting series from parts of the hierarchy for forecasting, we explore the possibility of using all the series. Moreover, instead of using the hierarchy after the initial forecasts are generated, we consider the hierarchical structure as a defining feature of the data-generating process and use it to instantaneously generate forecasts for all levels of the hierarchy. This integrated approach uses a state space model and the Kalman filter to explicitly incorporate product dependencies, such as complementarity of products and product substitution, which are otherwise ignored. An empirical study shows the substantial gain in forecast and inventory performance of generalizing the bottom-up and top-down forecast approaches to an integrated approach. The integrated approach is applicable to hierarchical forecasting in general, and extends beyond the current application of demand forecasting for manufacturers.