Frequency estimation based on the cumulated Lomb-Scargle periodogram

2007/12/30 by Céline Lévy‐Leduc, Lévy-Leduc, Céline, Moulines, Eric +2
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Advanced Statistical Process Monitoring #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.0801.0158

openalex publication_date 2007/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the problem of estimating the period of an unknown periodic function observed in additive 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.

Citations

• Least-squares frequency analysis of unequally spaced data
• Studies in astronomical time series analysis. II - Statistical aspects of spectral analysis of unevenly spaced data

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