Trace test for high-dimensional cointegration
研究了高维数据中Johansen迹检验的渐近性质，发现当横截面和时间维度同比例增长时，修正后的迹统计量收敛于高斯分布，蒙特卡洛模拟显示该检验在维度与样本量比值较大时优于Bartlett校正版本。
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.