  We study the joint limit distribution of the $k$ largest eigenvalues of a
$p\times p$ sample covariance matrix $XX^\T$ based on a large $p\times n$
matrix $X$. The rows of $X$ are given by independent copies of a linear
process, $X_{it}=\sum_j c_j Z_{i,t-j}$, with regularly varying noise $(Z_{it})$
with tail index $\alpha\in(0,4)$. It is shown that a point process based on the
eigenvalues of $XX^\T$ converges, as $n\to\infty$ and $p\to\infty$ at a
suitable rate, in distribution to a Poisson point process with an intensity
measure depending on $\alpha$ and $\sum c_j^2$. This result is extended to
random coefficient models where the coefficients of the linear processes
$(X_{it})$ are given by $c_j(\theta_i)$, for some ergodic sequence
$(\theta_i)$, and thus vary in each row of $X$. As a by-product of our
techniques we obtain a proof of the corresponding result for matrices with iid
entries in cases where $p/n$ goes to zero or infinity and $\alpha\in(0,2)$.
