Advanced Search
MyIDEAS: Login

A Note on the Asymptotic Normality of Sample Autocorrelations for a Linear Stationary Sequence


Author Info

  • He, Shuyuan
Registered author(s):


    We consider a stationary time series {Xt} given byXt=[summation operator][infinity]k=-[infinity] [psi]kZt-k, where {Zt} is a strictly stationary martingale difference white noise. Under assumptions that the spectral densityf([lambda]) of {Xt} is squared integrable andm[tau] [summation operator]k[greater-or-equal, slanted]m [psi]2k-->0 for some[tau]>1/2, the asymptotic normality of the sample autocorrelations is shown. For a stationary long memoryARIMA(p, d, q) sequence, the conditionm[tau] [summation operator]k[greater-or-equal, slanted]m [psi]2k-->0 for some[tau]>1/2 is equivalent to the squared integrability off([lambda]). This result extends Theorem 4.2 of Cavazos-Cadena [5], which were derived under the conditionm [summation operator]k[greater-or-equal, slanted]m [psi]2k-->0.

    Download Info

    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.

    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 58 (1996)
    Issue (Month): 2 (August)
    Pages: 182-188

    as in new window
    Handle: RePEc:eee:jmvana:v:58:y:1996:i:2:p:182-188

    Contact details of provider:
    Web page:

    Order Information:

    Related research

    Keywords: autocorrelation central limit theorem martingale difference ARIMA model;


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


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

    Cited by:
    1. Biao Wu, Wei & Min, Wanli, 2005. "On linear processes with dependent innovations," Stochastic Processes and their Applications, Elsevier, vol. 115(6), pages 939-958, June.


    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.


    Access and download statistics


    When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:58:y:1996:i:2:p:182-188. 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.