Coherent probabilistic forecasts for hierarchical time series

Many applications require forecasts for a hierarchy comprising a set of time series along with aggregates of subsets of these series. Hierarchical forecasting require not only good prediction accuracy at each level of the hierarchy, but also the coherency between different levels --- the property that forecasts add up appropriately across the hierarchy. A fundamental limitation of prior research is the focus on forecasting the mean of each time series. We consider the situation where probabilistic forecasts are needed for each series in the hierarchy, and propose an algorithm to compute predictive distributions rather than mean forecasts only. Our algorithm has the advantage of synthesizing information from different levels in the hierarchy through a sparse forecast combination and a probabilistic hierarchical aggregation. We evaluate the accuracy of our forecasting algorithm on both simulated data and large-scale electricity smart meter data. The results show consistent performance gains compared to state-of-the art methods.