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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.

62P20 Applications of statistics to economics
62M20 Inference from stochastic processes and prediction
Full Text: DOI
[1] Beveridge, S.; Nelson, C.R., A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the business cycle, Journal of monetary economics, 7, 151-174, (1981)
[2] Cox, D.R.; Hinkley, C.V., Theoretical statistics, (1974), Chapman and Hall London · Zbl 0334.62003
[3] Dickey, David A.; Fuller, W.A., Distribution of estimates for autoregressive time series with unit root, Journal of the American statistical association, 74, 427-431, (1979) · Zbl 0413.62075
[4] Engle, Robert F.; Granger, C.W.J., Cointegration and error correction: representation, estimation and testing, Econometrica, 55, 251-276, (1987) · Zbl 0613.62140
[5] Fuller, W.A., Introduction to statistical time series, (1976), Wiley New York · Zbl 0353.62050
[6] Granger, C.W.J., Some properties of time series data and their use in econometric model specification, Journal of econometrics, 16, 121-130, (1981)
[7] Granger, C.W.J., Cointegrated variables and error-correcting models, () · Zbl 0533.62095
[8] Granger, C.W.J., Developments in the study of cointegrated economic variables, Oxford bulletin of economics and statistics, 48, 213-228, (1986)
[9] Granger, C.W.J.; Weiss, A.A., Time series analysis of error-correcting models, (), 255-278 · Zbl 0547.62060
[10] Litterman, R.B., Forecasting with Bayesian vector autoregressions: five years of experience, Journal of business and economic statistics, 4, 25-38, (1986)
[11] Phillips, P.C.B., Time series regression with unit roots, () · Zbl 0613.62109
[12] Phillips, P.C.B., Understanding spurious regressions in econometrics, () · Zbl 0602.62098
[13] Phillips, P.C.B.; Durlauf, S.N., Multiple time series regression with integrated processes, Review of economic studies, 53, 473-495, (1986) · Zbl 0599.62103
[14] Rohatgi, V.K., Statistical inference, (1984), Wiley New York · Zbl 0537.62001
[15] Said, S.E.; Dickey, D.A., Testing for unit roots in autoregressive-moving average models of unknown order, Biometrica, 71, 599-607, (1984) · Zbl 0564.62075
[16] Sims, C.A., Macroeconomics and reality, Econometrica, 48, 1-48, (1980)
[17] Stock, J., Asymptotic properties of least squares estimators of cointegrating vectors, (1984), Harvard University Cambridge, MA, Mimeo
[18] Stock, J.H.; Watson, M.W., Testing for common trends, (1986), Harvard University Cambridge, MA, Mimeo
[19] Watson, M.W., Univariate detrending methods with stochastic trends, Journal of monetary economics, 18, 49-75, (1986)
[20] White, J.S., The limiting distribution of the serial correlation coefficient in the explosive case, Annals of mathematical statistics, 29, 1188-1197, (1958) · Zbl 0099.13004
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