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Efficient Semiparametric Estimation of the Periods in a Superposition of Periodic Functions with Unknown Shape

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  • Elisabeth Gassiat
  • Céline Lévy‐Leduc

Abstract

. We consider the estimation of the periods of periodic functions when their shape is unknown and they are corrupted by Gaussian white noise. In the case of a single periodic function, we propose a consistent and asymptotically efficient semiparametric estimator of the period. We then study the case of a sum of two periodic functions of unknown shape with different periods and propose semiparametric estimators of their periods that are consistent and asymptotically Gaussian.

Suggested Citation

  • Elisabeth Gassiat & Céline Lévy‐Leduc, 2006. "Efficient Semiparametric Estimation of the Periods in a Superposition of Periodic Functions with Unknown Shape," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 877-910, November.
    • Handle: RePEc:bla:jtsera:v:27:y:2006:i:6:p:877-910
    DOI: 10.1111/j.1467-9892.2006.00493.x
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    References listed on IDEAS

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    1. Franses, Philip Hans, 1996. "Periodicity and Stochastic Trends in Economic Time Series," OUP Catalogue, Oxford University Press, number 9780198774549, Decembrie.
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    Cited by:

    1. Oliver Linton & Michael Vogt, 2012. "Nonparametric estimation of a periodic sequence in the presence of a smooth trend," CeMMAP working papers 23/12, Institute for Fiscal Studies.
    2. Michael Vogt & Oliver Linton, 2014. "Nonparametric estimation of a periodic sequence in the presence of a smooth trend," Biometrika, Biometrika Trust, vol. 101(1), pages 121-140.
    3. C. Lévy‐Leduc & E. Moulines & F. Roueff, 2008. "Frequency estimation based on the cumulated Lomb–Scargle periodogram," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 1104-1131, November.

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