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23 pages, 546 KB  
Article
Some Asymptotic Properties of a Kernel Bispectum Estimate with Different Multitapers
by Mahmoud El-Morshedy, Abd El-Moneim A. M. Teamah, Mohammed H. El-Menshawy, Rashad M. EL-Sagheer, Hasnaa M. Faied, Afrah Al-Bossly and Mohamed S. Eliwa
Mathematics 2022, 10(18), 3284; https://doi.org/10.3390/math10183284 - 9 Sep 2022
Viewed by 1550
Abstract
Assume X1,X2,,XN are realizations of N observations from a real-valued discrete parameter third-order stationary process Xt,t=0±1,±2,, with bispectrum [...] Read more.
Assume X1,X2,,XN are realizations of N observations from a real-valued discrete parameter third-order stationary process Xt,t=0±1,±2,, with bispectrum fXXX(λ1,λ2) where “πλ1,λ2π”. Based on the previous assumption, L different multitapered biperiodograms IXXX(mt)j(λ1,λ2);j=1,2,,L on overlapped segments (Xt(j);1t<N) 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 (Wβ(j)(α1,α2), where “πα1,α2π” andβ is the bandwidth) and IXXX(mt)j(λ1,λ2), the bispectrum fXXX(λ1,λ2) 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. Full article
(This article belongs to the Section D1: Probability and Statistics)
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