Forecasting an aggregate of cointegrated disaggregates

This study examines the problem of forecasting an aggregate of cointegrated disaggregates. It first establishes conditions under which forecasts of an aggregate variable obtained from a disaggregate VECM will be equal to those from an aggregate, univariate time series model, and develops a simple procedure for testing those conditions. The paper then uses Monte Carlo simulations to show, for a finite sample, that the proposed test has good size and power properties and that whether a model satisfies the aggregation conditions is closely related to out-of-sample forecast performance. The paper then shows that ignoring cointegration and specifying the disaggregate model as a VAR in differences can significantly affect analyses of aggregation, with the VAR-based test for aggregation possibly leading to faulty inference and the differenced VAR forecasts potentially under-stating the benefits of disaggregate information. Finally, analysis of an empirical problem confirms the basic results.