IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v21y2000i1p95-109.html
   My bibliography  Save this article

Some Results Concerning the Asymptotic Distribution of Sample Fourier Transforms and Periodograms for a Discrete‐time Stationary Process with a Continuous Spectrum

Author

Listed:
  • A. M. Walker

Abstract

We consider a stationary process (Xt, t = 0, ±1, ...) with a continuous spectrum. Denote by Dn(λ) a tapered Fourier transform of (X0, X1, ..., Xn−1) at (angular) frequency λ. We obtain the asymptotic distribution of Dn(λ) and the joint asymptotic distribution of {Dn(λj), 1 ≤j≤k} with continuity of the spectral density f(.) at the relevant frequencies as the only assumption concerning the second‐order structure of (Xt); all other assumptions required are easily stated. The results are extended to processes for which f(.) is continuous except at λ = 0, with limλ←0f(λ)λ2d = K, a constant, where 0

Suggested Citation

  • A. M. Walker, 2000. "Some Results Concerning the Asymptotic Distribution of Sample Fourier Transforms and Periodograms for a Discrete‐time Stationary Process with a Continuous Spectrum," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(1), pages 95-109, January.
    • Handle: RePEc:bla:jtsera:v:21:y:2000:i:1:p:95-109
    DOI: 10.1111/1467-9892.00175
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9892.00175
    Download Restriction: no
    File URL: https://libkey.io/10.1111/1467-9892.00175?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. McCoy, E. J. & Stephens, D. A., 2004. "Bayesian time series analysis of periodic behaviour and spectral structure," International Journal of Forecasting, Elsevier, vol. 20(4), pages 713-730.
    2. Hsieh, Meng-Chen & Hurvich, Clifford M. & Soulier, Philippe, 2007. "Asymptotics for duration-driven long range dependent processes," Journal of Econometrics, Elsevier, vol. 141(2), pages 913-949, December.

    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:21:y:2000:i:1:p:95-109. 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.