Long Range Dependence for Stable Random Processes

2019/08/29 by Makogin, Vitalii, Oesting, Marco, Rapp, Albert +1
#60G10 #60G52 #60G70 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1908.11187

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 suggested by Kulik and Spodarev (2019) based on the covariance of excursions. 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.

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