Astronomical time-series analysis - III. The role of the observational errors in the minimum entropy method

In two recent papers a new method for searching for periodicity in time ser ies was introduced. It takes advantage of the Shannon entropy to compute th e amount of information contained in the light curve of a given signal as a function of a supposed period p. The basic result is that, if the signal i s T-periodic, the entropy is then minimum when p = T. Also, there is theore tical and numerical evidence that the minimum entropy method is more sensit ive to the presence of periodicity and has a higher resolution power than o ther classical techniques. In the present work the discussion is focused on the way in which the observational errors have to be included in the metho d. The application of the resulting modified algorithm to real data and a p erformance comparison with the former algorithm are presented. The dependen ce of both periodograms on the size of the partition is also investigated. Analytical estimates are given only for the limiting case of small errors. The numerical results show that the new algorithm leads to a smoother perio dogram and provides a higher significance for the minimum than the former a lgorithm.