Bernstein polynomial estimation of a spectral density
AbstractWe consider an application of Bernstein polynomials for estimating a spectral density of a stationary process. The resulting estimator can be interpreted as a convex combination of the (Daniell) kernel spectral density estimators at m points, the coefficients of which are probabilities of the binomial distribution bin(m - 1, |lambda|/pi), lambda is an element of pi == [ - pi, pi] being the frequency where the spectral density estimation is made. Several asymptotic properties are investigated under conditions of the degree m. We also discuss methods of data-driven choice of the degree m. For a comparison with the ordinary kernel method, a Monte Carlo simulation illustrates our methodology and examines its performance in small sample. Copyright 2005 Blackwell Publishing Ltd.
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Bibliographic InfoArticle provided by Wiley Blackwell in its journal Journal of Time Series Analysis.
Volume (Year): 27 (2006)
Issue (Month): 2 (03)
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Web page: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782
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- Bouezmarni, Taoufik & Rombouts, Jeroen V. K. & Taamouti, Abderrahim, .
"Asymptotic properties of the Bernstein density copula for dependent data,"
Open Access publications from Universidad Carlos III de Madrid
info:hdl:10016/2733, Universidad Carlos III de Madrid.
- BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen V.K. & TAAMOUTI, Abderrahim, 2008. "Asymptotic properties of the Bernstein density copula for dependent data," CORE Discussion Papers 2008045, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Taoufik Bouezmarni & Jeroen V. K. Rombouts & Abderrahim Taamouti, 2008. "Asymptotic properties of the Bernstein density copula for dependent data," Economics Working Papers we083619, Universidad Carlos III, Departamento de Economía.
- Kakizawa, Yoshihide, 2007. "Moderate deviations for quadratic forms in Gaussian stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 992-1017, May.
- Taoufik Bouezmarni & Anouar El Ghouch & Abderrahim Taamouti, 2011. "Bernstein estimator for unbounded density copula," Economics Working Papers we1143, Universidad Carlos III, Departamento de Economía.
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