Prediction of Stationary Max-Stable Processes

Abstract

We consider prediction of stationary max-stable processes. The usual metric between max-stable variables can be defined in terms of the $L_1$ distance between spectral functions and in terms of this metric a kind of projection can be defined. It is convenient to project onto max-stable spaces; that is, spaces of extreme value distributed random variables that are closed under scalar multiplication and the taking of finite maxima. Some explicit calculations of max-stable spaces generated by processes of interest are given. The concepts of deterministic and purely nondeterministic stationary max-stable processes are defined and illustrated. Differences between linear and nonlinear prediction are highlighted and some characterizations of max-moving averages and max-permutation processes are given.