Optimally Reconciling Forecasts in a Hierarchy

42 HIERARCHICAL STRUCTURES T series can often be naturally disaggregated using attributes such as product type. The total number of bicycles sold by a cycling warehouse, for example, can be disaggregated into a hierarchy of bicycle types. Such a warehouse will sell road bikes, mountain bikes, children’s bikes, and hybrids. Each of these can be disaggregated further into finer categories. Children’s bikes can be divided into balance bikes for children under 4 years old, single-geared bikes for children between 4 and 6, and multigeared bikes for children over the age of 6. Hybrid bikes can be divided into city, commuting, comfort, and trekking bikes; and so on. Such disaggregation imposes a hierarchical structure and we refer to these as hierarchical time series.