Abstract
In this paper, we consider the separable covariance model, which plays an important role in wireless communications and spatio-temporal statistics and describes a process where the time correlation does not depend on the spatial location and the spatial correlation does not depend on time. We established a central limit theorem for linear spectral statistics of general separable sample covariance matrices in the form of Sn=1nT1nXnT2nXn∗T1n∗ where Xn=(xjk) is of m1×m2 dimension, the entries {xjk,j=1,…,m1,k=1,…,m2} are independent and identically distributed complex variables with zero means and unit variances, T1n is a p×m1 complex matrix and T2n is an m2×m2 Hermitian matrix. We then apply this general central limit theorem to the problem of testing white noise in time series.
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