Calculating the accuracy of hierarchical estimation

Instead of forecasting demand for individual items separately, hierarchical forecasting is often used: total demand is forecasted for a collection of items; this total forecast then is broken down to produce the desired individual demand forecasts. To allow analytical analyses, we considered in a previous paper the simpler problem of hierarchical estimation. So from a random sample of demand periods, we estimated both the total demand for a number of items and the fraction of this total that an individual item takes; multiplying these two quantities gives the hierarchical estimate for each individual demand. From the joint distribution of the individual demands, we here present a fast and general method for finding the bias and variance of the corresponding hierarchical estimator. The method is compared with our previous results and two new applications are added.