ASYMPTOTIC ANALYSIS ABOUT THE PERIODOGRAM OF A GENERAL CLASS OF TIME SERIES MODELS WITH SPECTRAL SUPPORTSON LINES NOT PARALLEL TO THE MAIN DIAGONAL

Lei Shi (), Shilpi Jain (), Praveen Agarwal, Yousif Altayed () and Shaher Momani
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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

FRACTALS (fractals), 2022, vol. 30, issue 10, 1-17

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.

Keywords: Time Series; Fractional Brownian Motion; Spectral Analysis; Discrete Fourier Transform; Periodogram (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22402691

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