IDEAS home Printed from https://ideas.repec.org/p/aiz/louvar/2024004.html
   My bibliography  Save this paper

Invariance properties of limiting point processes and applications to clusters of extremes

Author

Listed:
  • Janssen, Anja
  • Segers, Johan

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

Abstract

Motivated by examples from extreme value theory, but without using the theory of regularly varying time series or any assumptions about the marginal distribution, we introduce the general notion of a cluster process as a limiting point process of returns of a certain event in a time series. We explore general invariance properties of cluster processes that are implied by stationarity of the underlying time series. Of particular interest in applications are the cluster size distributions, and we derive general properties and interconnections between the size of an inspected and a typical cluster. While the extremal index commonly used in extreme value theory is often interpreted as the inverse of a “mean cluster size”, we point out that this only holds true for the expected value of the typical cluster size, caused by an effect very similar to the inspection paradox in renewal theory.

Suggested Citation

  • Janssen, Anja & Segers, Johan, 2024. "Invariance properties of limiting point processes and applications to clusters of extremes," LIDAM Reprints ISBA 2024004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2024004
    DOI: https://doi.org/10.1515/demo-2023-0109
    Note: In: Dependence Modeling, 2024, vol. 12(1), p. 20230109
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:aiz:louvar:2024004. See general information about how to correct material in RePEc.

    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.

    We have no bibliographic references for this item. You can help adding them by using 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Nadja Peiffer (email available below). General contact details of provider: https://edirc.repec.org/data/isuclbe.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.