On the effectiveness of top-down strategy for forecasting autoregressive demands

We investigate the relative effectiveness of top-down versus bottom-up strategies for forecasting the demand of an item that belongs to a product family. The demand for each item in the family is assumed to follow a first-order univariate autoregressive process. Under the top-down strategy, the aggregate demand is forecasted by using the historical data of the family demand. The demand forecast for the items is then derived by proportional allocation of the aggregate forecast. Under the bottom-up strategy, the demand forecast for each item is directly obtained by using the historical demand data of the particular item. In both strategies, the forecasting technique used is exponential smoothing. We analytically evaluate the condition under which one forecasting strategy is preferred over the other when the lag-1 autocorrelation of the demand time series for all the items is identical. We show that when the lag-1 autocorrelation is smaller than or equal to 1/3, the maximum difference in the performance of the two forecasting strategies is only 1%. However, if the lag-1 autocorrelation of the demand for at least one of the items is greater than 1/3, then the bottom-up strategy consistently outperforms the top-down strategy, irrespective of the items' proportion in the family and the coefficient of correlation between the item demands. A simulation study reveals that the analytical findings hold even when the lag-1 autocorrelation of the demand processes is not identical.