Econometrica: Jul 2018, Volume 86, Issue 4
Alternative Asymptotics for Cointegration Tests in Large VARs
Alexei Onatski, Chen Wang
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.”
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Supplement to "Alternative Asymptotics for Cointegration Tests in Large VARs"
This zip file contains all MATLAB files used in the Monte Carlo analysis. It also contains supplementary material for Onatski and Wang (2017). The appendix is lined up with sections in the main text to make it easy to locate the required proofs.