Long range dependence for stable random processes

Abstract

We investigate long and short memory in ‐stable moving averages and max‐stable processes with ‐Fréchet marginal distributions. As these processes are heavy‐tailed, we rely on the notion of long range dependence based on the covariance of indicators of excursion sets. Sufficient conditions for the long and short range dependence of ‐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.