Gaussian fluctuations for sample covariance matrices with dependent data

It is known (Hofmann-Credner and Stolz (2008) [4]) that the convergence of the mean empirical spectral distribution of a sample covariance matrix Wn=1/nYnYnt to the Marčenko-Pastur law remains unaffected if the rows and columns of Yn exhibit some dependence, where only the growth of the number of dependent entries, but not the joint distribution of dependent entries needs to be controlled. In this paper we show that the well-known CLT for traces of powers of Wn also extends to the dependent case.