TY - JOUR
T1 - Some Asymptotic Properties of a Kernel Bispectum Estimate with Different Multitapers
AU - El-Morshedy, Mahmoud
AU - Teamah, Abd El Moneim A.M.
AU - El-Menshawy, Mohammed H.
AU - EL-Sagheer, Rashad M.
AU - Faied, Hasnaa M.
AU - Al-Bossly, Afrah
AU - Eliwa, Mohamed S.
N1 - Publisher Copyright:
© 2022 by the authors.
PY - 2022/9
Y1 - 2022/9
N2 - Assume (Formula presented.) are realizations of N observations from a real-valued discrete parameter third-order stationary process (Formula presented.), with bispectrum (Formula presented.) where “ (Formula presented.) ”. Based on the previous assumption, L different multitapered biperiodograms (Formula presented.) on overlapped segments ((Formula presented.)) can be constructed. Further, the mean and variance of the average of these different multitapered biperiodograms can be expressed as asymptotic expressions. According to different bispectral windows/kernels ((Formula presented.), where “ (Formula presented.) ” and (Formula presented.) is the bandwidth) and (Formula presented.), the bispectrum (Formula presented.) can be estimated. The asymptotic expressions of the first- and second-ordered moments as well as the integrated relative mean squared error (IMSE) of this estimate are derived. Finally, some estimation results based on numerically generated data from the selected process “DCGINAR(1)” are presented and discussed in detail.
AB - Assume (Formula presented.) are realizations of N observations from a real-valued discrete parameter third-order stationary process (Formula presented.), with bispectrum (Formula presented.) where “ (Formula presented.) ”. Based on the previous assumption, L different multitapered biperiodograms (Formula presented.) on overlapped segments ((Formula presented.)) can be constructed. Further, the mean and variance of the average of these different multitapered biperiodograms can be expressed as asymptotic expressions. According to different bispectral windows/kernels ((Formula presented.), where “ (Formula presented.) ” and (Formula presented.) is the bandwidth) and (Formula presented.), the bispectrum (Formula presented.) can be estimated. The asymptotic expressions of the first- and second-ordered moments as well as the integrated relative mean squared error (IMSE) of this estimate are derived. Finally, some estimation results based on numerically generated data from the selected process “DCGINAR(1)” are presented and discussed in detail.
KW - DCGINAR(1) process
KW - bandwidth
KW - bispectrum estimate
KW - kernels
KW - multitapering
KW - overlapping segments
KW - stationary time series
UR - http://www.scopus.com/inward/record.url?scp=85138624570&partnerID=8YFLogxK
U2 - 10.3390/math10183284
DO - 10.3390/math10183284
M3 - Article
AN - SCOPUS:85138624570
SN - 2227-7390
VL - 10
JO - Mathematics
JF - Mathematics
IS - 18
M1 - 3284
ER -