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.
Publié le : 1993-05-14
Classification:
Extreme value theory,
Poisson processes,
max-stable processes,
prediction,
time series,
stationary processes,
60G70,
60G55
@article{1177005435,
author = {Davis, Richard A. and Resnick, Sidney I.},
title = {Prediction of Stationary Max-Stable Processes},
journal = {Ann. Appl. Probab.},
volume = {3},
number = {4},
year = {1993},
pages = { 497-525},
language = {en},
url = {http://dml.mathdoc.fr/item/1177005435}
}
Davis, Richard A.; Resnick, Sidney I. Prediction of Stationary Max-Stable Processes. Ann. Appl. Probab., Tome 3 (1993) no. 4, pp. 497-525. http://gdmltest.u-ga.fr/item/1177005435/