IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

On the integral of the squared periodogram

  • Deo, Rohit S.
  • Chen, Willa W.
Registered author(s):

    Let X1,X2,...,Xn be a sample from a stationary Gaussian time series and let I(·) be the sample periodogram. Some researchers have either proved heuristically or claimed that under general conditions, the asymptotic behaviour of is equivalent to that of the discrete version of the integral given by , where [lambda]i are the Fourier frequencies and [phi] and [eta] are suitable possibly non-linear functions. In this paper, we prove that this asymptotic equivalence is not true when [phi] is a non-linear function. We derive the exact finite sample variance of when {Xt} is Gaussian white noise and show that it is asymptotically different from that of . The asymptotic distribution of is also obtained in this case. The result is then extended to obtain the limiting distribution of when {Xt}is a stationary Gaussian series with spectral density f(·). From these results, the limiting distribution of the integral version of a goodness-of-fit statistic proposed in the literature is obtained.

    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: http://www.sciencedirect.com/science/article/B6V1B-3Y1639J-B/2/92a1022df0f764343884445752f88a19
    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): 85 (2000)
    Issue (Month): 1 (January)
    Pages: 159-176

    as
    in new window

    Handle: RePEc:eee:spapps:v:85:y:2000:i:1:p:159-176
    Contact details of provider: Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description

    Order Information: Postal: http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
    Web: https://shop.elsevier.com/OOC/InitController?id=505572&ref=505572_01_ooc_1&version=01

    No references listed on IDEAS
    You can help add them by filling out this form.

    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:85:y:2000:i:1:p:159-176. 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: (Zhang, Lei)

    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.