Abstract
This paper compares the small sample properties of different tests for multivariate cointegration like Johansen's trace test, stock & Watson's common trend test, Phillips & Ouliaris' principal component test, as well as cointegration rank decisions based on order selection criteria. Under the null hypothesis of non-cointegration we find a slow convergence rate of the test statistics. In bivariate models the Phillips & Ouliaris test is extremely dependent on the specification and is outperformed by the other procedures. For trivariate processes we find dependence of the power results on the dynamic specification. The lag order is successfully estimated by order selection criteria.
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The paper was written during the time the author was at the Institute of Statistic and Econometrics of the Christian-Albrechts-Universität Kiel. The author is grateful to Prof. Helmut Lütkepohl and Wolfgang Hauschulz for helpful comments and criticisms and has also benefited from the comments of an anonymous referee.
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Reimers, H.E. Comparisons of tests for multivariate cointegration. Statistical Papers 33, 335–359 (1992). https://doi.org/10.1007/BF02925336
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DOI: https://doi.org/10.1007/BF02925336