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.
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References
Granger CWJ, Morris MJ (1976) Time series modelling and interpretation. J Roy Stat Soc A 139: 246–257
Kohn R (1982) When is an aggregate of a time series efficiently forecast by its past?. J Econ 18: 337–349
Ku S, Seneta E (1998) Practical estimation from the sum of AR(1) processes. Commun Stat Simul Comput 27: 981–998
Lütkepohl H (1984a) Linear aggregation of vector autoregressive moving average processes. Econ Lett 14: 345–350
Lütkepohl H (1984b) Linear transformations of vector ARMA processes. J Econ 26: 283–293
Lütkepohl H (1984c) Forecasting contemporaneously aggregated vector ARMA processes. J Bus Econ Stat 2: 201–214
Lütkepohl H (1987) Forecasting aggregated vector ARMA processes. Springer, Berlin
Lütkepohl H (2006) Forecasting with VARMA Models. In: Elliott G, Granger CWJ, Timmermann A (eds) Handbook of economic forecasting, vol 1. Elsevier, Amsterdam
Rose DE (1977) Forecasting aggregates of independent ARIMA processes. J Econ 5: 323–345
Sbrana G, Silvestrini A (2009) What do we know about comparing aggregate and disaggregate forecasts? CORE DP 2009/20, Université catholique de Louvain, Belgium
Tiao GC, Guttman I (1980) Forecasting contemporal aggregates of multiple time series. J Econ 12: 219–230
Wei WWS, Abraham B (1981) Forecasting contemporal time series aggregates. Commun Stat Theory Methods A10: 1335–1344
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Sbrana, G., Silvestrini, A. Comparing aggregate and disaggregate forecasts of first order moving average models. Stat Papers 53, 255–263 (2012). https://doi.org/10.1007/s00362-010-0333-6
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DOI: https://doi.org/10.1007/s00362-010-0333-6