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Onatski, A. and Wang, C.

Alternative Asymptotics for Cointegration Tests in Large VARs


Vol. 86(4) pp. 1465-1478 (2018)

Abstract: 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 socalled 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.

Keywords: High‐dimensional, VAR cointegration tests, canonical correlations, empirical distribution, Wachter distribution

Author links: Alexey Onatskiy  

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Cambridge-INET Working Paper Version of Paper: Alternative Asymptotics for Cointegration Tests in Large VARs, Onatski, A. and Wang, C., (2016)