A number of papers in recent years have investigated the problems of forecasting contemporaneously aggregated time series and of combining alternative forecasts of a time series. This paper considers the integration of both approaches within the example of assessing the forecasting performance of models for two of the U.K. monetary aggregates, f M 3 and MO. It is found that forecasts from a time series model for aggregate fM3 are superior to aggregated forecasts from individual models fitted to either the components or counterparts of f M 3 and that an even better forecast is obtained by forming a linear combination of the three alternatives. For MO, however, aggregated forecasts from its components prove superior to either the forecast from the aggregate itself or from a linear combination of the two.
KEY WORDS Contemporaneously aggregated time series
Combination of forecasts Time series models U.K. money supply A number of papers in recent years have investigated the problem of forecasting contemporaneously aggregated time series: see, for example, , Tiao and Guttman (1980), Wei and Abraham (1981), Kohn (1982) and . This body of research has shown that, in general, if disaggregated data are generated by a known vector ARMA process, then it is preferable to forecast the disaggregated series first and then aggregate these forecasts, rather than forecast the aggregate time series directly.
In practice, of course, the data generation process will be unknown and, in these more usual circumstances, Lutkepohl (1984b) has shown that it may be better to forecast the aggregate directly rather than attempt to forecast from an empirically identified multiple time series model. A further argument in favour of this approach is that multiple time series modelling is still in its infancy, with no consensus having yet been reached as to the most effective identification procedure (see, for example, Tiao and Box (1981) and Jenkins and Alavi (1981)) and with appropriate computing software still to be made widely available. However, a yet more attractive forecasting procedure in such circumstances, at least when more than, say, three time series are