Long Range Dependence for Stable Random Processes
Probability
2020-06-01 v2
Abstract
We investigate long and short memory in -stable moving averages and max-stable processes with -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 -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.
Cite
@article{arxiv.1908.11187,
title = {Long Range Dependence for Stable Random Processes},
author = {Vitalii Makogin and Marco Oesting and Albert Rapp and Evgeny Spodarev},
journal= {arXiv preprint arXiv:1908.11187},
year = {2020}
}