Best Approximate Aggregation of Input—Output Systems

Abstract

A method of constructing aggregate input—output systems is proposed. The procedure minimizes the mean squared error of aggregate predictions. The range of data on which the aggregate model is to be applied influences the best approximate aggregate. Best approximate aggregate models maximize Ijiri's coefficient of aggregation. In a special case, Fisher's aggregated model emerges: if consistent aggregation is possible it gives the best approximate aggregate. Computations reveal best approximate aggregations to be feasible and to yield considerably better predictions than alternative methods in realistic cases.