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Forecasting and testing in co-integrated systems. (English) Zbl 0649.62108
This paper examines the behavior of forecasts made from a co-integrated system as introduced by C. W. J. Granger and A. A. Weiss [Studies in econometrics, time series, and multivariate statistics, Commem. T. W. Anderson’s 65th Birthday, 255-278 (1983; Zbl 0547.62060)] and R. F. Engle and C. W. J. Granger [Econometrica 55, 251- 276 (1987; Zbl 0613.62140)]. It is established that a multi-step forecast will satisfy the co-integrating relation exactly and that this particular linear combination of forecasts will have a finite limiting forecast error variance. A simulation study compares the multistep forecast accuracy of unrestricted vector autoregression with the two-step estimation of the vector autoregression imposing the co-integration restriction. To test whether a system exhibits co-integration, the procedures introduced in Engle and Granger are extended to allow different sample sizes and numbers of variables.

MSC:
62P20 Applications of statistics to economics
62M20 Inference from stochastic processes and prediction
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