We study the efficiency properties of the goodness-of-fit test based on the Qn statistic
introduced in Fortiana and Grané (2003) using the concepts of Bahadur asymptotic relative
efficiency and Bahadur asymptotic optimality. We compare the test based on this statistic with
those based on the Kolmogorov-Smirnov, the Cramér-von Mises and the Anderson-Darling
statistics. We also describe the distribution families for which the test based on Qn is
asymptotically optimal in the Bahadur sense and, as an application, we use this test to detect the
presence of hidden periodicities in a stationary time series