Abstract
This paper proposes a new unit-root test for the case where a high-dimensional vector of nonstationary time series is considered. A new CLT is being established and studied both theoretically and numerically.
Highlights
There have been an increasing interest and significant developments on the theory and methodologies for handling high-dimensional data in recent years
Zhang [29] investigated the empirical spectral distribution (ESD) of the sample covariance for the case where the data matrices are of the form A1ZA2, where A1 and A2 are positive semidefinite matrices and Z has independent entries satisfying some moment assumptions
A key observation is that Theorem 2 indicates that the largest eigenvalue of B is of order T 2 in probability, while Theorem 1 and Assumption (A4) imply that when 0 ≤ φ < 1, B 2 = op(T )
Summary
There have been an increasing interest and significant developments on the theory and methodologies for handling high-dimensional data in recent years. Empirical data from wireless communication, finance and speech recognition often suggest that some extreme eigenvalues of sample covariance matrices are well separated from the rest This intrigues the second line of research about the spiked eigenvalues, which was first proposed in Johnstone [14]. Zhang [29] investigated the empirical spectral distribution (ESD) of the sample covariance for the case where the data matrices are of the form A1ZA2, where A1 and A2 are positive semidefinite matrices and Z has independent entries satisfying some moment assumptions This model is referred to as the separable covariance model and allows for some dependence among observations recorded over different time points.
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