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Bernstein polynomial estimation of a spectral density

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  • Yoshihide Kakizawa
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    Abstract

    We 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 Info

    Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

    Volume (Year): 27 (2006)
    Issue (Month): 2 (03)
    Pages: 253-287

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    Handle: RePEc:bla:jtsera:v:27:y:2006:i:2:p:253-287

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    Cited by:
    1. Taoufik Bouezmarni & Anouar El Ghouch & Abderrahim Taamouti, 2011. "Bernstein estimator for unbounded density copula," Economics Working Papers we1143, Universidad Carlos III, Departamento de Economía.
    2. Kakizawa, Yoshihide, 2007. "Moderate deviations for quadratic forms in Gaussian stationary processes," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 98(5), pages 992-1017, May.
    3. BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen V.K. & TAAMOUTI, Abderrahim, 2008. "Asymptotic properties of the Bernstein density copula for dependent data," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2008045, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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