IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v30y2022i10ns0218348x22402691.html
   My bibliography  Save this article

Asymptotic Analysis About The Periodogram Of A General Class Of Time Series Models With Spectral Supportson Lines Not Parallel To The Main Diagonal

Author

Listed:
  • LEI SHI

    (School of Mathematics and Statistics, Anyang Normal University, Anyang 455002, Henan, P. R. China)

  • SHILPI JAIN

    (��Department of Mathematics, Poornima College of Engineering, Jaipur, India)

  • PRAVEEN AGARWAL

    (��Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India§Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE¶Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, 117198, Moscow Russian Federation)

  • YOUSIF ALTAYED

    (��Department of Mathematics, College of Mathematics, College of Science and Arts in ArRass, Qassim University, Saudi Arabia)

  • SHAHER MOMANI

    (�Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE**Department of Mathematics, Faculty of Science, The University of Jordan, Amman, Jordan)

Abstract

The aim of this paper is to make inference about a general class of time series models including fractional Brownian motion. The spectral of these processes is supported on lines not parallel to the diagonal T1(x) = x, Tj(x) = αjx ± βj, j = 2,…,m, in spectral square [0, 2π) × [0, 2π), and this class includes stationary, cyclostationary, almost cyclostationary time series and specially fractional Brownian motions. First, the periodogram of these processes is defined and auxiliary operator is applied to explore the distribution of the periodogram. Then the asymptotical estimation for the spectral density function is proposed and asymptotical Wishart function is found. Finally, the validity of the theoretical results is studied using simulated data sets.

Suggested Citation

  • Lei Shi & Shilpi Jain & Praveen Agarwal & Yousif Altayed & Shaher Momani, 2022. "Asymptotic Analysis About The Periodogram Of A General Class Of Time Series Models With Spectral Supportson Lines Not Parallel To The Main Diagonal," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(10), pages 1-17, December.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:10:n:s0218348x22402691
    DOI: 10.1142/S0218348X22402691
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X22402691
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0218348X22402691?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:wsi:fracta:v:30:y:2022:i:10:n:s0218348x22402691. 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: Tai Tone Lim (email available below). General contact details of provider: https://www.worldscientific.com/worldscinet/fractals .

    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.