2004/12/30 by S. Vaughan · 374 citations
Earth and Planetary Sciences · Environmental Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Artificial intelligence #Astrophysics #Computer science #Galaxy #Mathematics #Monte Carlo method #Noise (video) #Physics #Plant Water Relations and Carbon Dynamics #Series (stratigraphy) #Simple (philosophy) #Spectral density #Spurious relationship #Statistical and numerical algorithms #Statistical physics #Statistics #Tree-ring climate responses #astro-ph
paper · pdf · doi:10.1051/0004-6361:20041453
published in Astronomy and Astrophysics 431(1), 391-403 (EDP Sciences) · 13 pages. 12 figures. Accepted for publication in A&A
arxiv created 2004/12/30 · openalex publication_date 2005/02/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We demonstrate a simple method for testing the significance of peaks in the periodogram of red noise data. The procedure was designed to test for spurious periodicities in X-ray light curves of active galaxies, but can be used quite generally to test for periodic components against a background noise spectrum assumed to have a power law shape. The method provides a simple and fast test of the significance of candidate periodic signals in short, well-sampled time series such as those obtained from XMM-Newton observations of Seyfert galaxies, without the need for Monte Carlo simulations. A full account is made of the number of trials and the uncertainties inherent to the model fitting. Ignoring these subtle effects can lead to substantially overestimated significances. These difficulties motivate us to demand high standards of detection (minimum per cent confidence) for periodicities in sources that normally show red noise spectra. The method also provides a simple means to estimate the power spectral index, which may be an interesting parameter itself, regardless of the presence/absence of periodicities.