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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
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