What do we know about comparing aggregate and disaggregate forecasts?

This paper compares the performance of "aggregate" and "disaggregate" predictors in forecasting contemporaneously aggregated vector ARMA processes. An aggregate predictor is built by forecasting directly the aggregate process, as it results from contemporaneous aggregation of the data generating vector process. A disaggregate predictor is obtained by aggregating univariate forecasts for the individual components of the data generating vector process. The necessary and sufficient condition for the equality of mean squared errors associated with the two competing methods is provided in the bivariate VMA(1) case. Furthermore, it is argued that the condition of equality of predictors as stated in Lütkepohl (1984b, 1987, 2004) is only sufficient (not necessary) for the equality of mean squared errors. Finally, it is shown that the equality of forecasting accuracy for the two predictors can be achieved using specific assumptions on the parameters of the VMA(1) structure. Monte Carlo simulations are in line with the analytical results. An empirical application that involves the problem of forecasting the Italian monetary aggregate M1 in the pre-EMU period is presented to illustrate the main findings.