Dirichlet Proportions Model for Hierarchically Coherent Probabilistic Forecasting

A central problem in multivariate forecasting is the need to forecast a large group of time series arranged in a natural hierarchical structure, such that time series at higher levels of the hierarchy are aggregates of time series at lower levels. For example, hierarchical time series are common in retail forecasting applications [Fildes et al., 2019], where the time series may capture retail sales of a company at different granularities such as item-level sales, category-level sales, and department-level sales. In electricity demand forecasting [Van Erven and Cugliari, 2015], the time series may correspond to electricity consumption at different granularities, starting with individual households, which could be progressively grouped into city-level, and then state-level consumption time-series. The hierarchical structure among the time series is usually represented as a tree, with leaf-level nodes corresponding to time series at the finest granularity, while higher-level nodes represent coarser-granularities and are obtained by aggregating the values from its children nodes. Since businesses usually require forecasts at various different granularities, the goal is to obtain accurate forecasts for time series at every level of the hierarchy. Furthermore, to ensure decisionmaking at different hierarchical levels are aligned, it is essential to generate predictions that are coherent [Hyndman et al., 2011] with respect to the hierarchy, that is, the forecasts of a parent time-series should be equal to the sum of forecasts of its children time-series.