Many applications require forecasts for a hierarchy comprising a set of time series along with aggregates of subsets of these series. Although forecasts can be produced independently for each series in the hierarchy, typically this does not lead to coherent forecasts — the property that forecasts add up appropriately across the hierarchy. State-of-the-art hierarchical forecasting methods usually reconcile these independently generated forecasts to satisfy the aggregation constraints. A fundamental limitation of prior research is that it has looked only at the problem of forecasting the mean …