  We study the joint limit behavior of sums, maxima and $\ell^p$-type moduli
for samples taken from an $\mathbb{R}^d$-valued regularly varying stationary
sequence with infinite variance. As a consequence, we can determine the
distributional limits for ratios of sums and maxima, studentized sums, and
other self-normalized quantities in terms of hybrid characteristic functions
and Laplace transforms. These transforms enable one to calculate moments of the
limits and to characterize the differences between the iid and stationary cases
in terms of indices which describe effects of extremal clustering on
functionals acting on the dependent sequence.
