Some Results for Extreme Value Processes in Analogy to the Gaussian Spectral Representation
AbstractThe extremal coefficient function has been discussed as an analog of the autocovariance function for extreme values. However, as to the behavior of valid extremal coefficient functions little is known apart from their positive definite type. In particular, the reconstruction of valid processes from given extremal coefficient functions has not been considered before. We show, for the one-dimensional case, the equivalence of the set correlation functions and the extremal coefficient functions with finite range on a grid, and study an analogy to Bochner’s theorem, namely that any such extremal coefficient function is representable as a convex combination of a finite set of positive definite functions. This allows for the construction of simple max-stable processes complying with a given extremal coefficient function and, in addition, highlights further properties of the latter. We will include an application of this approach and discuss several examples. As to processes with infinite range we will consider a natural extension of the term “long memory” that is well-known in the Gaussian framework to max-stable processes.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Courant Research Centre PEG in its series Courant Research Centre: Poverty, Equity and Growth - Discussion Papers with number 30.
Date of creation: 25 May 2010
Date of revision:
Contact details of provider:
Postal: Platz der Goettinger Sieben 3; D-37073 Goettingen, GERMANY
Phone: +49 551 39 14066
Fax: + 49 551 39 14059
Web page: http://www.uni-goettingen.de/en/82144.html
Extreme value theory; max-stable process; extremal dependence; extremal coefficient function; set covariance function; set correlation function; homometric; long memory; summability;
This paper has been announced in the following NEP Reports:
You can help add them by filling out this form.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dominik Noe).
If references are entirely missing, you can add them using this form.