Forecasting Aggregated Vector ARMA Processes

This study is concerned with forecasting time series variables and the impact of the level of aggregation on the efficiency of the forecasts. Since temporally and contemporaneously disaggregated data at various levels have become available for many countries, regions, and variables during the last decades the question which data and procedures to use for prediction has become increasingly important in recent years. This study aims at pointing out some of the problems involved and at pro viding some suggestions how to proceed in particular situations. Many of the results have been circulated as working papers, some have been published as journal articles, and some have been presented at conferences and in seminars. I express my gratitude to all those who have commented on parts of this study. They are too numerous to be listed here and many of them are anonymous referees and are therefore unknown to me. Some early results related to the present study are contained in my monograph "Prognose aggregierter Zeitreihen" (Lutkepohl (1986a)) which was essentially completed in 1983. The present study contains major extensions of that research and also summarizes the earlier results to the extent they are of interest in the context of this study.