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|Title:||Comparing significance criteria for cyclic modulations in time series|
|Citation:||NUCLEAR INSTRUMENTS \& METHODS IN PHYSICS RESEARCH SECTION A-ACCELERATORS SPECTROMETERS DETECTORS AND ASSOCIATED EQUIPMENT vol. 968 p. 163933|
|Publisher:||ELSEVIER SCIENCE BV|
|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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