IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v90y2000i1p157-174.html
   My bibliography  Save this article

Convergence of weighted sums of random variables with long-range dependence

Author

Listed:
  • Pipiras, Vladas
  • Taqqu, Murad S.

Abstract

Suppose that f is a deterministic function, is a sequence of random variables with long-range dependence and BH is a fractional Brownian motion (fBm) with index . In this work, we provide sufficient conditions for the convergencein distribution, as m-->[infinity]. We also consider two examples. In contrast to the case when the [xi]n's are i.i.d. with finite variance, the limit is not fBm if f is the kernel of the Weierstrass-Mandelbrot process. If however, f is the kernel function from the "moving average" representation of a fBm with index H', then the limit is a fBm with index .

Suggested Citation

  • Pipiras, Vladas & Taqqu, Murad S., 2000. "Convergence of weighted sums of random variables with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 90(1), pages 157-174, November.
    • Handle: RePEc:eee:spapps:v:90:y:2000:i:1:p:157-174
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(00)00040-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Kris Brabanter & Farzad Sabzikar, 2021. "Asymptotic theory for regression models with fractional local to unity root errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(7), pages 997-1024, October.

    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:spapps:v:90:y:2000:i:1:p:157-174. 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.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.