IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

Some Results for Extreme Value Processes in Analogy to the Gaussian Spectral Representation

Listed author(s):
  • Andree Ehlert

    (Georg-August-University Göttingen)

  • Martin Schlather

    (Georg-August-University Göttingen)

Registered author(s):

    The 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.

    If 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.

    File URL:
    Download Restriction: no

    Paper provided by Courant Research Centre PEG in its series Courant Research Centre: Poverty, Equity and Growth - Discussion Papers with number 30.

    in new window

    Date of creation: 25 May 2010
    Handle: RePEc:got:gotcrc:030
    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:

    No references listed on IDEAS
    You can help add them by filling out this form.

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:got:gotcrc:030. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dominik Noe)

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.