  Johansen's (1988, 1991) likelihood ratio test for cointegration rank of a
Gaussian VAR depends only on the squared sample canonical correlations between
current changes and past levels of a simple transformation of the data. We
study the asymptotic behavior of the empirical distribution of those squared
canonical correlations when the number of observations and the dimensionality
of the VAR diverge to infinity simultaneously and proportionally. We find that
the distribution almost surely weakly converges to the so-called Wachter
distribution. This finding provides a theoretical explanation for the observed
tendency of Johansen's test to find "spurious cointegration". It also sheds
light on the workings and limitations of the Bartlett correction approach to
the over-rejection problem. We propose a simple graphical device, similar to
the scree plot, for a preliminary assessment of cointegration in
high-dimensional VARs.
