Dependence matrices for spatial extreme events

If a spatial process {X-i}(i is an element of Z2) is isotropic then the usual pairwise extremal dependence measures depend only on the distance parallel to i - j parallel to between the locations i and j. Nevertheless, in general, we need to evaluate the spatial dependence in different directions of 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 and the extremal epsilon coefficients, lambda = 2 - is an element of, 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.