Alternative Asymptotics for Cointegration Tests in Large VARs
研究了当观测数和变量维数同时趋于无穷时，Johansen协整检验中平方典型相关系数的经验分布收敛到Wachter分布，解释了该检验容易发现“伪协整”的现象。
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.”