  The paper analyses cointegration in vector autoregressive processes (VARs)
for the cases when both the number of coordinates, $N$, and the number of time
periods, $T$, are large and of the same order. We propose a way to examine a
VAR of order $1$ for the presence of cointegration based on a modification of
the Johansen likelihood ratio test. The advantage of our procedure over the
original Johansen test and its finite sample corrections is that our test does
not suffer from over-rejection. This is achieved through novel asymptotic
theorems for eigenvalues of matrices in the test statistic in the regime of
proportionally growing $N$ and $T$. Our theoretical findings are supported by
Monte Carlo simulations and an empirical illustration. Moreover, we find a
surprising connection with multivariate analysis of variance (MANOVA) and
explain why it emerges.
