  We study the $k$-largest eigenvalues of heavy-tailed sample covariance
matrices of the form $\bX\bX^\T$ in an asymptotic framework, where the
dimension of the data and the sample size tend to infinity. To this end, we
assume that the rows of $\bX$ are given by independent copies of some
stationary process with regularly varying marginals with index $\alpha\in(0,2)$
satisfying large deviation and mixing conditions. We apply these general
results to stochastic volatility and GARCH processes.
