Assessing the statistical significance of periodogram peaks

The least-squares (or Lomb-Scargle) periodogram is a powerful tool that is routinely used in many branches of astronomy to search for periodicities in observational data. The problem of assessing the statistical significance of candidate periodicities for a number of periodograms is considered. Based on results in extreme value theory, improved analytic estimations of false alarm probabilities are given. These include an upper limit to the false alarm probability (or a lower limit to the significance). The estimations are tested numerically in order to establish regions of their practical applicability.