Citation:
[Journal:] Journal of Time Series Analysis [ISSN:] 1467-9892 [Volume:] 42 [Issue:] 2 [Publisher:] John Wiley & Sons, Ltd [Place:] Oxford, UK [Year:] 2021 [Pages:] 161-185
Publisher:
John Wiley & Sons, Ltd, Oxford, UK
Abstract:
We investigate long and short memory in α-stable moving averages and max-stable processes with α-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 α-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.