Title: Comparing significance criteria for cyclic modulations in time series
Authors: POMME STEFAAN
Citation: NUCLEAR INSTRUMENTS \& METHODS IN PHYSICS RESEARCH SECTION A-ACCELERATORS SPECTROMETERS DETECTORS AND ASSOCIATED EQUIPMENT vol. 968 p. 163933
Publisher: ELSEVIER SCIENCE BV
Publication Year: 2020
JRC N°: JRC120184
ISSN: 0168-9002 (online)
URI: https://publications.jrc.ec.europa.eu/repository/handle/JRC120184
DOI: 10.1016/j.nima.2020.163933
Type: Articles in periodicals and books
Abstract: General solutions are derived for least-squares fits of amplitude, phase shift and baseline shift of sinusoidal modulations to normally distributed time series. Four cases are compared: weighted and unweighted fit, with and without a baseline shift. Computer simulations have been performed of the statistical distribution of the amplitude resulting from fits to white noise. A normalised amplitude is defined which follows exactly a Rayleigh distribution, even for small, uneven-sampled data sets. Equations are provided for the width of the distribution and the cumulative probability function. A simple criterion for the statistical significance of the fitted amplitude to a time series is derived and compared for equivalence with the Lomb-Scargle criterion based on a power function.
JRC Directorate:Nuclear Safety and Security

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