The extremogram is a widely common measure to assess extremal dependence for random processes and is applicable throughout different fields in extreme value theory. For example, the tail dependence coefficient, which is often considered in the finance industry, is one of its special cases. We investigate the asymptotic properties of the empirical version of the extremogram, which is based on a kernel estimator, and assume that the observations of the random process come from a multidimensional Poisson process inducing a so-called irregular grid. We present the proof of a central limit theorem for the empirical spatial extremogram in full detail. In particular, we show that this central limit theorem holds when the underlying distribution of the random process is that of a Brown-Resnick process with an isotropic dependence function. Moreover, in this case, we give a new bias corrected version of the empirical extremogram to obtain better convergence rates for the asymptotic normality. The results are then applied to real precipitation data. We compare the empirical extremogram with its bias corrected version under different kernel functions and apply a transformation of the observation space to justify the assumption of isotropic data.     «

The extremogram is a widely common measure to assess extremal dependence for random processes and is applicable throughout different fields in extreme value theory. For example, the tail dependence coefficient, which is often considered in the finance industry, is one of its special cases. We investigate the asymptotic properties of the empirical version of the extremogram, which is based on a kernel estimator, and assume that the observations of the random process come from a multidimensional P...     »