Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/230291
Authors: 
Makogin, Vitalii
Oesting, Marco
Rapp, Albert
Spodarev, Evgeny
Year of Publication: 
2020
Citation: 
[Journal:] Journal of Time Series Analysis [ISSN:] 1467-9892 [Volume:] [Issue:] [Pages:] n/a-n/a
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.
Subjects: 
long/short memory
long/short range dependence
alpha‐stable
max‐stable
level set
characteristic function
moving average
Brown‐Resnick process
extremal Gaussian process
positive association
extremal coefficient
Persistent Identifier of the first edition: 
Creative Commons License: 
http://creativecommons.org/licenses/by/4.0/
Document Type: 
Article
Document Version: 
Published Version

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