B1570
Title: Extremal dependence of moving average processes driven by exponential-tailed Levy noise
Authors: David Bolin - King Abdullah University of Science and Technology (KAUST) (Saudi Arabia)
Sebastian Engelke - University of Geneva (Switzerland)
Raphael Huser - King Abdullah University of Science and Technology (Saudi Arabia)
Zhongwei Zhang - University of Geneva (Switzerland) [presenting]
Abstract: Moving average processes driven by exponential-tailed Levy noise are important extensions of their Gaussian counterparts in order to capture deviations from Gaussianity, more flexible dependence structures, and sample paths with jumps. Popular examples include non-Gaussian Ornstein-Uhlenbeck processes and type G Matern stochastic partial differential equation random fields. The focus is on the open problem of determining their extremal dependence structure. The fact that such processes admit approximations on grids or triangulations that are used in practice for efficient simulations and inference is leveraged. These approximations can be expressed as special cases of a class of linear transformations of independent, exponential-tailed random variables that bridge asymptotic dependence and independence in a novel, tractable way. The new fundamental result allows for showing that the integral approximation of general moving average processes with exponential-tailed Levy noise is asymptotically independent when the mesh is fine enough. Under mild assumptions on the kernel function, the limiting residual tail dependence function is also derived. For the popular exponential-tailed Ornstein-Uhlenbeck process, it is proven that it is asymptotically independent but with a different residual tail dependence function than its Gaussian counterpart.
