Optimal aggregation of linear time series models

Aggregation is a central and mainly unsolved problem in econometrics. When considering linear time series models, a widely used method is to replace the disaggregate model by an aggregative one in which the variables are grouped and replaced by sums or weighted averages of the variables in each group. Choosing the modes of aggregation optimally with regard to a measure of mean-square forecast error results in a highly complex integer optimization problem, an implementation of the threshold accepting heuristic for this problem is presented. It is applied to the problem of optimal aggregation of price indices in a model of international price transmission using German data. Furthermore, methods for assessing the quality of the results are introduced comparing optimization results with some ad hoc (“official”) modes of aggregation. It turns out that optimized groupings significantly improve the quality of the aggregative model.