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Johansen's (1988, 1991) likelihood ratio test for cointegration rank of aGaussian VAR depends only on the squared sample canonical correlations betweencurrent changes and past levels of a simple transformation of the data. Westudy the asymptotic behavior of the empirical distribution of those squaredcanonical correlations when the number of observations and the dimensionalityof the VAR diverge to infinity simultaneously and proportionally. We find thatthe distribution almost surely weakly converges to the so-called Wachterdistribution. This finding provides a theoretical explanation for the observedtendency of Johansen's test to find "spurious cointegration". It also shedslight on the workings and limitations of the Bartlett correction approach tothe over-rejection problem. We propose a simple graphical device, similar tothe scree plot, for a preliminary assessment of cointegration inhigh-dimensional VARs.

Alternative asymptotics for cointegration tests in large VARs