Estimations of uncertainties of frequencies

Abstract

AbstractDiverse variable phenomena in the Universe are periodic. Astonishingly many of the periodic signals present in stars have timescales coinciding with human ones (from minutes to years). The periods of signals often have to be deduced from time series which are irregularly sampled and sparse, furthermore correlations between the brightness measurements and their estimated uncertainties are common. The uncertainty on the frequency estimation is reviewed. We explore the astronomical and statistical literature, in both cases of regular and irregular samplings. The frequency uncertainty is depending on signal to noise ratio, the frequency, the observational timespan. The shape of the light curve should also intervene, since sharp features such as exoplanet transits, stellar eclipses, raising branches of pulsation stars give stringent constraints. We propose several procedures (parametric and nonparametric) to estimate the uncertainty on the frequency which are subsequently tested against simulated data to assess their performances.