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May, 1993 Prediction of Stationary Max-Stable Processes
Richard A. Davis, Sidney I. Resnick
Ann. Appl. Probab. 3(2): 497-525 (May, 1993). DOI: 10.1214/aoap/1177005435


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.


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Richard A. Davis. Sidney I. Resnick. "Prediction of Stationary Max-Stable Processes." Ann. Appl. Probab. 3 (2) 497 - 525, May, 1993.


Published: May, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0779.60048
MathSciNet: MR1221163
Digital Object Identifier: 10.1214/aoap/1177005435

Primary: 60G70
Secondary: 60G55

Keywords: Extreme value theory , max-stable processes , Poisson processes , prediction , Stationary processes , time series

Rights: Copyright © 1993 Institute of Mathematical Statistics


Vol.3 • No. 2 • May, 1993
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