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By Helmut Lütkepohl

This examine is anxious with forecasting time sequence variables and the impression of the extent of aggregation at the potency of the forecasts. because temporally and contemporaneously disaggregated info at quite a few degrees became on hand for lots of nations, areas, and variables over the last many years the query which facts and systems to take advantage of for prediction has develop into more and more very important in recent times. This research goals at stating many of the difficulties concerned and at seasoned­ viding a few feedback find out how to continue specifically occasions. some of the effects were circulated as operating papers, a few were released as magazine articles, and a few were awarded at meetings and in seminars. I convey my gratitude to all those that have commented on elements of this learn. they're too various to be in this article and lots of of them are nameless referees and are hence unknown to me. a few early effects regarding the current examine are contained in my monograph "Prognose aggregierter Zeitreihen" (Lutkepohl (1986a)) which was once basically accomplished in 1983. the current research comprises significant extensions of that examine and in addition summarizes the sooner effects to the level they're of curiosity within the context of this study.

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Extra resources for Forecasting Aggregated Vector ARMA Processes

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Thus, the variances of the components of ~t are upper bounds for the forecast MSEs. The upper bounds are attained for h ~ 00, that is, ~x(h)~~x. 1, processes with this property are called nondeterministic. 1) if ~ x (h) --+h ~. That is, x t has an +00 x MA representation if it is nondeterministic. 9) This fact can be used to construct confidence intervals for the forecasts. , for a standard normal random variable z. t = ~t -~. 111 where is the optimal h-step predictor of the zero mean process ~t(h) That is, the mean vector is simply added to the optimal predictor ~t' of the zero mean part.

47) holds for T approaching infinity. Therefore, in practice, it is desirable to have a rule for choosing pIT) in a finite sample situation. 1) 37 In HQ(p) ? 15) that results when an AR(p) is fitted. The only difference here is that always (for each p) the first P observed ~t vectors, x 1 , ••• ,x , are treated as presample vectors. 15) T-P is used for T-p. Using any of the three criteria, AR(p) models are fitted to the data ~p = 0,1, ••• ,P and the AR order p is chosen so as to minimize the selected criterion.

It will now be described how a further reduction in the number of parameters can be obtained. 11). A generalization of the specification procedure will be obvious. Also, since the two equations may be treated separately, the method is described only for the first equation. The second equation can again be treated analogously. •. ,pp)' be a vector with elements Pi and S. {: i f /)11 , i f- 0 i f /)11, i 0 i 1, ... 13) 0,1, ... ,P, i =0 if 012,i and P is the maximum lag length that is considered for the time series under consideration.

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