Trace test for high-dimensional cointegration
The Annals of Statistics · 2026 · Volume 54 · Issue 2
Abstract
This paper studies Johansen’s (J. Econom. Dynam. Control 12 (1988) 231–254) trace test for cointegration in high-dimensional data. We show that when both cross-sectional and temporal dimension of the data go to infinity proportionally, the shifted and scaled modified trace statistic converges to a Gaussian random variable. We give explicit formulae for the shift and scale parameters as well as for the mean and variance of the Gaussian limit. Monte Carlo analysis shows excellent size properties of the asymptotic test, which is an improvement over the Bartlett-corrected versions of the original trace test, especially for relatively large ratios of the dimensionality to the sample size. The Monte Carlo also reveals a nonmonotonicity of the power of the test. We comment on the source of such a nonmonotonicity.
Keywords
60B20; 60F05; 62M10; central limit theorem; cointegration test; High-dimensional VAR; Johansen’s trace statistic; Linear spectral statistics;
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