Long range dependence for stable random processes

Abstract

We investigate long and short memory in (Formula presented.) -stable moving averages and max-stable processes with (Formula presented.) -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 (Formula presented.) -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.