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Spectral covariance and limit theorems for random fields with infinite variance

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  • Damarackas, Julius
  • Paulauskas, Vygantas

Abstract

In the paper, we continue to investigate measures of dependence for random variables with infinite variance. For random variables with regularly varying tails, we introduce a general class of such measures, which includes the codifference and the spectral covariance. In particular, we investigate the α-spectral covariance, a new measure from this general class, for linear random fields with infinite second moment. Under some conditions on the filter of a linear random field, we investigate asymptotic properties of the α-spectral covariance for linear random fields with infinite variance. We also provide an application of spectral covariances for limit theorems for stationary and associated random fields with infinite variance.

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  • Damarackas, Julius & Paulauskas, Vygantas, 2017. "Spectral covariance and limit theorems for random fields with infinite variance," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 156-175.
    • Handle: RePEc:eee:jmvana:v:153:y:2017:i:c:p:156-175
    DOI: 10.1016/j.jmva.2016.09.013
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    Cited by:

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    2. Surgailis, Donatas, 2020. "Scaling transition and edge effects for negatively dependent linear random fields on Z2," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7518-7546.
    3. Karling, Maicon J. & Lopes, Sílvia R.C. & de Souza, Roberto M., 2023. "Multivariate α-stable distributions: VAR(1) processes, measures of dependence and their estimations," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    4. Peligrad, Magda & Sang, Hailin & Xiao, Yimin & Yang, Guangyu, 2022. "Limit theorems for linear random fields with innovations in the domain of attraction of a stable law," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 596-621.

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