# Long range dependence of heavy-tailed random functions

@article{Kulik2021LongRD, title={Long range dependence of heavy-tailed random functions}, author={Rafal Kulik and E. Spodarev}, journal={Journal of Applied Probability}, year={2021}, volume={58}, pages={569 - 593} }

Abstract We introduce a definition of long range dependence of random processes and fields on an (unbounded) index space
$T\subseteq \mathbb{R}^d$
in terms of integrability of the covariance of indicators that a random function exceeds any given level. This definition is specifically designed to cover the case of random functions with infinite variance. We show the value of this new definition and its connection to limit theorems via some examples including subordinated Gaussian as well as…

## 3 Citations

Long range dependence for stable random processes

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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…

PR ] 2 9 A ug 2 01 9 Long Range Dependence for Stable Random Processes

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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…

Detection of Long Range Dependence in the Time Domain for (In)Finite-Variance Time Series

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- 2022

Empirical detection of long range dependence (LRD) of a time series often consists of deciding whether an estimate of the memory parameter d corresponds to LRD. Surprisingly, the literature oﬀers…

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