Geodesic
Some asymptotic properties of a kernel spectrum estimate with different multitapers
Vladikavkazskij matematičeskij žurnal, Tome 9 (2007) no. 1, pp. 56-61 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $X(t)$, $t=0,\pm 1,\ldots,$ be a zero mean real-valued stationary time series with spectrum $f_{XX}(\lambda )$, $-\pi\le\lambda\le\pi$. Given the realization $X(1),X(2),\dots,X(N)$, we construct $L$ different multitapered periodograms $I_{XX}^{(mt)_{j}}(\lambda)$, $j=1,2,\dots,L$, on non-overlapped and overlapped segments $X^{(j)}(t)$, $1\le t. Also, we give asymptotic expressions of the mean and variance of the average of these different multitapered periodograms. We obtain an estimate of $f_{XX}(\lambda)$ via $I_{XX}^{(mt)_{j}}(\lambda )$ and different kernels $W_{\beta}^{(j)}(\alpha)$, $j=1,2,\dots,L$; $-\pi<\alpha\le\pi$; $\beta$ is a bandwidth. We find asymptotic expressions of the first and second-order moments of this estimate. Moreover, we propose a choice of the considered bandwidth. An asymptotic expression of the integrated relative mean squared error (IMSE) of the estimate is formulated. 
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A. A. M. Teamah; H. S. Bakouch. Some asymptotic properties of a kernel spectrum estimate with different multitapers. Vladikavkazskij matematičeskij žurnal, Tome 9 (2007) no. 1, pp. 56-61. http://geodesic.mathdoc.fr/item/VMJ_2007_9_1_a5/

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