Title: On the significance of modulations in time series
Authors: POMME STEFAANDE HAUWERE TOTA
Citation: NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION A-ACCELERATORS SPECTROMETERS DETECTORS AND ASSOCIATED EQUIPMENT vol. 956 p. 163377
Publisher: ELSEVIER SCIENCE BV
Publication Year: 2020
JRC N°: JRC118116
ISSN: 0168-9002 (online)
URI: https://publications.jrc.ec.europa.eu/repository/handle/JRC118116
DOI: 10.1016/j.nima.2019.163377
Type: Articles in periodicals and books
Abstract: Analytical equations are derived for the uncertainty of the amplitude of cyclic modulations obtained by a least-squares fit of a sinusoidal function to a time series. A general equation is presented for a weighted fit to unevenly spaced data. A simple solution is derived for randomly distributed data with constant relative uncertainty and compared to a formerly published heuristic relationship. Different scenarios are considered in which, besides the amplitude, also the phase shift and/or an offset value are free parameters. A free fit of the phase shift parameter transforms the normal probability distribution of the amplitude into a Rayleigh distribution. The additional fit of an offset value increases the width due to the change in degrees of freedom. A time series analysis is applied to the residuals of an exponential fit to experimental decay curves of various nuclides, in search of cyclic deviations to the exponential decay law. The statistical significance of the modulations is discussed.
JRC Directorate:Nuclear Safety and Security

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