An expected value approach to forecast reconciliation with forecast targets and under asymmetric costs

A common problem in many business, economic and government organisations is the reconciliation of a group of lower level forecasts to the forecast of the aggregate of that group. Reconciliation may focus on a particular target for the aggregate forecast, or there may be no target. A number of approaches have been suggested, including top-down, bottom-up, hybrid and regression based methods. The reconciliation problem may be for only a single level, but often extends to the entire hierarchy of the organisation. This paper examines a different approach to forecast reconciliation, a minimum expected value approach, both analytically and through examples. Particular concern is the cost implications of forecast errors. Both symmetric cost functions (quadratic) and asymmetric cost functions (linex) are examined. Although the focus is on a single level hierarchy, multilevel and multidimensional reconciliation are also discussed. This paper is unique in that it studies asymmetrical forecast cost functions in an organisational hierarchy through simulations and an actual data example. Both targeted and non-targeted forecasts are considered. It also introduces the minimum expected value method, a new method of forecast reconciliation.