TRACE TEST FOR HIGH-DIMENSIONAL COINTEGRATION

This paper studies Johansen's (1988) 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 non-monotonicity of the power of the test. We comment on the source of such a non-monotonicity.