Long Range Dependence for Stable Random Processes

Vitalii Makogin; Marco Oesting; Albert Rapp; Evgeny Spodarev

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arXiv · 1908.11187

Long Range Dependence for Stable Random Processes

Vitalii Makogin·Marco Oesting·Albert Rapp·Evgeny Spodarev

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Abstract

We investigate long and short memory in $\alpha$-stable moving averages and max-stable processes with $\alpha$-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 $\alpha$-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.

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BibTeX RIS

Vitalii Makogin, Marco Oesting, Albert Rapp, Evgeny Spodarev. 2019-08-29. Long Range Dependence for Stable Random Processes. https://arxiv.org/abs/1908.11187

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