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- Title
ASYMPTOTIC ANALYSIS ABOUT THE PERIODOGRAM OF A GENERAL CLASS OF TIME SERIES MODELS WITH SPECTRAL SUPPORTSON LINES NOT PARALLEL TO THE MAIN DIAGONAL.
- Authors
SHI, LEI; JAIN, SHILPI; AGARWAL, PRAVEEN; ALTAYED, YOUSIF; MOMANI, SHAHER
- 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 T 1 (x) = x , T j (x) = α j x ± β j , j = 2 , ... , m , in spectral square [ 0 , 2 π) × [ 0 , 2 π) , 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.
- Subjects
TIME series analysis; SPECTRAL lines; SIGNAL frequency estimation; BROWNIAN motion; DISCRETE Fourier transforms
- Publication
Fractals, 2022, Vol 30, Issue 10, p1
- ISSN
0218-348X
- Publication type
Article
- DOI
10.1142/S0218348X22402691