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

The periodogram of an i.i.d. sequence

Listed author(s):
  • Fay, Gilles
  • Soulier, Philippe
Registered author(s):

    Periodogram ordinates of a Gaussian white-noise computed at Fourier frequencies are well known to form an i.i.d. sequence. This is no longer true in the non-Gaussian case. In this paper, we develop a full theory for weighted sums of non-linear functionals of the periodogram of an i.i.d. sequence. We prove that these sums are asymptotically Gaussian under conditions very close to those which are sufficient in the Gaussian case, and that the asymptotic variance differs from the Gaussian case by a term proportional to the fourth cumulant of the white noise. An important consequence is a functional central limit theorem for the spectral empirical measure. The technique used to obtain these results is based on the theory of Edgeworth expansions for triangular arrays.

    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: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 92 (2001)
    Issue (Month): 2 (April)
    Pages: 315-343

    in new window

    Handle: RePEc:eee:spapps:v:92:y:2001:i:2:p:315-343
    Contact details of provider: Web page:

    Order Information: Postal: http://

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    in new window

    1. Velasco, Carlos, 2000. "Non-Gaussian Log-Periodogram Regression," Econometric Theory, Cambridge University Press, vol. 16(01), pages 44-79, February.
    2. Kokoszka, Piotr & Mikosch, Thomas, 2000. "The periodogram at the Fourier frequencies," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 49-79, March.
    Full references (including those not matched with items on IDEAS)

    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:eee:spapps:v:92:y:2001:i:2:p:315-343. 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: (Dana Niculescu)

    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.