On a spectrum of sample covariation matrices for time series

We study the spectrum of the sample covariance matrix corresponding to an $R^p$-valued time series of length $n$. Under the assumption $p/n\to\rho >0$ conditions are put forward to guarantee the universality property of the limiting spectral distribution of these matrices (it has the same form as in the case of Gaussian time series). These conditions amount to requiring that the quadratic forms of the values of the series be close to its means.