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Frequency estimation based on the cumulated Lomb–Scargle periodogram

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Listed:
  • C. Lévy‐Leduc
  • E. Moulines
  • F. Roueff

Abstract

. We consider the problem of estimating the period of an unknown periodic function observed in additive Gaussian noise sampled at irregularly spaced time instants in a semiparametric setting. To solve this problem, we propose a novel estimator based on the cumulated Lomb–Scargle periodogram. We prove that this estimator is consistent, asymptotically Gaussian and we provide an explicit expression of the asymptotic variance. Some Monte Carlo experiments are then presented to support our claims.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:29:y:2008:i:6:p:1104-1131
    DOI: 10.1111/j.1467-9892.2008.00599.x
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    References listed on IDEAS

    as
    1. 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.
    2. Lii, Keh-Shin & Masry, Elias, 1994. "Spectral estimation of continuous-time stationary processes from random sampling," Stochastic Processes and their Applications, Elsevier, vol. 52(1), pages 39-64, August.
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