Alternative Asymptotics For Cointegration Tests In Large Vars

Abstract

Johansen's (1988,1991) likelihood ratio test for cointegration rank of a vector autoregression (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 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.”