Abstract
In this paper interval forecasting of cointegrated systems is examined. If the estimated coefficients are used to construct the forecasting intervals the error component due to the estimation of the coefficients is omitted in most cases. Analogous to the stationary case of vectorautoregressive models a correction term is derived basing on Johansen’s error correction representation of cointegrated systems. Its usefulness is analysed by means of a Monte Carlo study. The Monte Carlo study firstly demonstrates the difference between the nominal level of the confidence interval of forecasting and the observed level of the interval construction with known coefficients of variance calculation. Secondly, the forecast interval with estimated coefficients is investigated. Thirdly, it is illustrated that the approximation of forecast intervals can be improved by the proposed correction term for a small sample size, if the true cointegration rank is specified.
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The main parts of the paper were written while the author was at the institute of Statistic and Econometrics of the Christian-Albrechts-Universität. Kiel. The author is grateful to Prof. Helmut Lütkepohl for nelpful comments and discussion and thanks an anonymous referee for comments. Michael Scharnagl revised the English version.
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Reimers, HE. Interval forecasting in cointegrated systems. Stat Papers 36, 349–369 (1995). https://doi.org/10.1007/BF02926048
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DOI: https://doi.org/10.1007/BF02926048