If interest centres on forecasting a temporally aggregated multiple time series and the generation process of the disaggregate series is a known vector ARMA (autoregressive moving average) process then forecasting the disaggregate series and temporally aggregating the forecasts is at least as efficient, under a mean squared error measure, as forecasting the aggregated series directly. Necessary and sufficient conditions for equality of the two forecasts are given. In practice the data generation process is usually unknown and has to be determined from the available data. Using asymptotic theory it is shown that also in this case aggregated forecasts from the disaggregate process will usually be superior to forecasts obtained from the aggregated process.
KEY WORDS Forecasting efficiency Vector ARMA processes Temporal aggregation
Theoretical results by ), Lutkepohl (1984a) and others suggest that forecasts from temporally disaggregate data are more efficient in terms of mean squared error (MSE) than forecasts based on aggregated time series if interest centres on future values of the aggregated variable. For example, if monthly observations are available then, based on the above-mentioned theoretical results, a forecasting model should be built for the monthly time series even if interest is focussed on predictions for the corresponding quarterly or annual variable. This result is a consequence of using a larger information set if forecasts are based on the disaggregate rather than the temporally aggregated time series. Here, and in the following, the case of aggregating flow variables is considered where, for instance, the quarterly or annual value of a variable is obtained by adding the monthly figures. Despite the theoretical results, Abraham (1 982) found that in practice the aggregated series may provide better forecasts than the disaggregate series. There are various potential reasons for this discrepancy between theory and practice. First, a forecast being superior in a mean squared error sense does not mean that it is necessarily superior for a single realization of the assumed data generation process. Secondly, the theoretical results are based on the assumption that the data generation process is adequately represented by an ARlMA (autoregressive integrated moving average) or ARMA model. Thus, a very special kind of covariance structure is assumed and many non-stationary processes are excluded. Thirdly, the theory is based on the assumption that the forecasting models are correctly specified. Abraham used the Box and 0277-6693/86/020085-1 1 $05.50