Optimally reconciling forecasts in a hierarchy

We know that when forecasting the product hierarchy, reconciliation is invariably needed to make the sum of lower-level forecasts equate to the upperlevel forecasts. The authors argue that the traditional Bottom-Up, Top-Down, and Middle-Out procedures for reconciliation all fail to make best use of the available data. They show we can do better by taking weighted averages of the forecasts from different levels, an approach they call optimal reconciliation.