IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/6867.html
   My bibliography  Save this paper

Stationarity and memory of ARCH models

Author

Listed:
  • Zaffaroni, Paolo

Abstract

Sufficient conditions for strict stationarity of ARCH(8) are established, without imposing covariance stationarity and for any specification of the conditional second moment coefficients. GARCH(p,q) as well as the case of hyperbolically decaying coefficients are included, such as the autoregressive coefficients of ARFIMA(p,d,q), once the non-negativity constraints are imposed. Second, we show the necessary and sufficient conditions for covariance stationarity of ARCH(8), both for the levels and the squares. These prove to be much stronger than the strict stationarity conditions. The covariance stationarity condition for the levels rules out long memory in the squares.

Suggested Citation

  • Zaffaroni, Paolo, 2000. "Stationarity and memory of ARCH models," LSE Research Online Documents on Economics 6867, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:6867
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/6867/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    Other versions of this item:

    Citations

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


    Cited by:

    1. Gilles Zumbach, 2004. "Volatility processes and volatility forecast with long memory," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 70-86.
    2. Zaffaroni, Paolo & d'Italia, Banca, 2003. "Gaussian inference on certain long-range dependent volatility models," Journal of Econometrics, Elsevier, vol. 115(2), pages 199-258, August.

    More about this item

    Keywords

    ARCH(); GARCH(p; q); nonlinear moving average representation; strict and weak stationarity; memory;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    Statistics

    Access and download statistics

    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:ehl:lserod:6867. 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: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.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.