Dependence matrices for spatial extreme events

C. Fonseca, A. P. Martins, L. Pereira and H. Ferreira

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 21, 6321-6341

Abstract: If a spatial process {Xi}i∈Z2$\lbrace X_{\mathbf {i}}\rbrace _{\mathbf {i} \in \mathbb {Z}^2}$ is isotropic then the usual pairwise extremal dependence measures depend only on the distance ‖i − j‖ between the locations i and j. Nevertheless, in general, we need to evaluate the spatial dependence in different directions of Z2$\mathbb {Z}^2$. In this paper, we consider matrices of multivariate tail and extremal coefficients where we table the degrees of dependence for chosen pairs of sets A and B of locations. In this multidirectional approach, the well-known relation between the bivariate tail dependence λ and the extremal ε coefficients, λ = 2 − ϵ, is generalized and new properties arise. The measure matrices here defined to describe spatial dependence are used in several random fields, including a new space time ARMAX storage model and an M4 random field.

Date: 2016
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DOI: 10.1080/03610926.2013.781649

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