Whittle estimation based on the extremal spectral density of a heavy-tailed random field

Ewa Damek, Thomas Mikosch, Yuwei Zhao and Jacek Zienkiewicz

Stochastic Processes and their Applications, 2023, vol. 155, issue C, 232-267

Abstract: We consider a strictly stationary random field on the two-dimensional integer lattice with regularly varying marginal and finite-dimensional distributions. Exploiting the regular variation, we define the spatial extremogram which takes into account only the largest values in the random field. This extremogram is a spatial autocovariance function. We define the corresponding extremal spectral density and its estimator, the extremal periodogram. Based on the extremal periodogram, we consider the Whittle estimator for suitable classes of parametric random fields including the Brown–Resnick random field and regularly varying max-moving averages.

Keywords: Extreme value theory; Whittle estimation; Brown-Resnick random field; Max-moving averages; Spectral analysis (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:155:y:2023:i:c:p:232-267

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DOI: 10.1016/j.spa.2022.10.004

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