Comparing aggregate and disaggregate forecasts of first order moving average models

Abstract

This paper compares the performance of "aggregate" and "disaggregate" predictors in forecasting contemporaneously aggregated vector MA(1) processes. The necessary and sufficient condition for the equality of mean squared errors associated with the two competing predictors is provided in the bivariate MA(1) case. Furthermore, it is argued that the condition of equality of predictors as stated by Lütkepohl (Forecasting aggregated vector ARMA processes, Springer, Berlin, 1987) 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 vector MA(1) structure.

Forecasting Aggregated Moving Average Processes with an Application to the Euro Area Real Interest Rate

“…This paper shows that aggregating across second (or first)‐order (integrated) moving average processes leads to an aggregate process whose parameters are direct functions of the micro processes. That is, no iteration procedure is needed to recover the parameters of the aggregate process provided that the data generation process is known (similar results relative to the aggregation of first‐order moving average processes have been achieved by Ku and Seneta, , and Sbrana and Silvestrini, , ). Those results are shown in the next section, which considers the aggregation of both independent and dependent processes.…”