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Bernstein polynomial estimation of a spectral density

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  • Yoshihide Kakizawa

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.

Suggested Citation

  • Yoshihide Kakizawa, 2006. "Bernstein polynomial estimation of a spectral density," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(2), pages 253-287, March.
  • Handle: RePEc:bla:jtsera:v:27:y:2006:i:2:p:253-287
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    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9892.2005.00465.x
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    Cited by:

    1. Lu, Lu, 2015. "On the uniform consistency of the Bernstein density estimator," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 52-61.
    2. Bouezmarni, Taoufik & Rombouts, Jeroen V.K. & Taamouti, Abderrahim, 2010. "Asymptotic properties of the Bernstein density copula estimator for [alpha]-mixing data," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 1-10, January.
    3. Taamouti, Abderrahim & Bouezmarni, Taoufik & Rombouts, Jeroen V. K., 2008. "Asymptotic properties of the Bernstein density copula for dependent data," UC3M Working papers. Economics we083619, Universidad Carlos III de Madrid. Departamento de Economía.
    4. Taamouti, Abderrahim & Bouezmarni, Taoufik & El Ghouch, Anouar, 2011. "Bernstein estimator for unbounded density copula," UC3M Working papers. Economics we1143, Universidad Carlos III de Madrid. Departamento de Economía.
    5. Kakizawa, Yoshihide, 2007. "Moderate deviations for quadratic forms in Gaussian stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 992-1017, May.
    6. Bouezmarni Taoufik & Ghouch El & Taamouti Abderrahim, 2013. "Bernstein estimator for unbounded copula densities," Statistics & Risk Modeling, De Gruyter, vol. 30(4), pages 343-360, December.

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