  We investigate long and short memory in $\alpha$-stable moving averages and
max-stable processes with $\alpha$-Fr\'echet marginal distributions. As these
processes are heavy-tailed, we rely on the notion of long range dependence
suggested by Kulik and Spodarev (2019) based on the covariance of excursions.
Sufficient conditions for the long and short range dependence of
$\alpha$-stable moving averages are proven in terms of integrability of the
corresponding kernel functions. For max-stable processes, the extremal
coefficient function is used to state a necessary and sufficient condition for
long range dependence.
