IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v10y1989i1p13-31.html
   My bibliography  Save this article

The Resolution Of Closely Adjacent Spectral Lines

Author

Listed:
  • E. J. Hannan
  • B. G. Quinn

Abstract

. The problem is that of determining the parameters in a trigonometric polynomial when it is observed with added stationary noise. The frequencies, in particular, must be determined and the situation especially considered is that where these are close together. A similar problem arises if an angular frequency is close to zero or π. The method of estimation is the maximization of the regression sum of squares as a function of the unknown frequencies. In the asymptotic theory, the closely adjacent frequencies are separated by an amount that is of the order T‐1, where T is the length of the series. Simulations show that this asymptotic treatment gives a better approximation in cases where the separation is of this magnitude than that obtained by treating the frequencies as fixed.

Suggested Citation

  • E. J. Hannan & B. G. Quinn, 1989. "The Resolution Of Closely Adjacent Spectral Lines," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(1), pages 13-31, January.
    • Handle: RePEc:bla:jtsera:v:10:y:1989:i:1:p:13-31
    DOI: 10.1111/j.1467-9892.1989.tb00012.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9892.1989.tb00012.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9892.1989.tb00012.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

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


    Cited by:

    1. A. M. Walker, 2003. "A note on estimation by least squares for harmonic component models," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(5), pages 613-629, September.

    More about this item

    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:bla:jtsera:v:10:y:1989:i:1:p:13-31. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.