Significance levels of common frequencies extracted from multiple data sets

Abstract

ABSTRACT Large monitoring campaigns, particularly those using multiple filters, have produced replicated time series of observations for literally millions of stars. The search for periodicities in such replicated data can be facilitated by comparing the periodograms of the various time series. In particular, frequency spectra can be searched for common peaks. The sensitivity of this procedure to various parameters (e.g. the time base of the data, length of the frequency interval searched, number of replicate series, etc.) is explored. Two additional statistics that could sharpen results are also discussed: the closeness (in frequency) of peaks identified as common to all data sets, and the sum of the ranks of the peaks. Analytical expressions for the distributions of these two statistics are presented. The method is illustrated by showing that a ‘dubious’ periodicity in an 'Asteroid Terrestrial-impact Last Alert System' data set is highly significant.