IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v344y2004i3p619-625.html
   My bibliography  Save this article

On the connection between ARCH time series and non-extensive statistical mechanics

Author

Listed:
  • Duarte Queirós, Sı́lvio M.

Abstract

The ARCH(1) is a generator of stochastic discrete time series, {εt}, widely used in finance and characterised by conditional time-varying (and correlated) second-order moment. It involves a parameter, β and a noise, η. In this work one presents, through an analytical result, that ARCH(1) stationary distributions are well approached by the distributions that maximise the entropy, Sq=1−∫[p(x)]qdx1−q. Using the generalised Kullback–Leibler relative entropy, Iq, one also quantifies the degree of dependence between variables εt and εt′ and shows that the degree of dependence increases with parameter β.

Suggested Citation

  • Duarte Queirós, Sı́lvio M., 2004. "On the connection between ARCH time series and non-extensive statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(3), pages 619-625.
    • Handle: RePEc:eee:phsmap:v:344:y:2004:i:3:p:619-625
    DOI: 10.1016/j.physa.2004.06.041
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437104008064
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2004.06.041?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. S. M. Duarte Queiros, 2005. "On non-Gaussianity and dependence in financial time series: a nonextensive approach," Quantitative Finance, Taylor & Francis Journals, vol. 5(5), pages 475-487.

    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:eee:phsmap:v:344:y:2004:i:3:p:619-625. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.