  Our paper presents new methods for finding and testing of weak periodic
variability of stellar objects developed for the purpose of detecting expected
regular light variations of magnetic chemically peculiar (mCP) candidates in
the Large Magellanic Cloud. We introduce two new periodograms of the mCP star,
BS Cir (HD 125630), appropriate for rotating spotted variables and compare the
results with those obtained by the well-known Lomb-Scargle periodogram. The
usage of periodograms and the testing of the significance of the found period
candidates are demonstrated with two examples: the observed and simulated
observations of the magnetic field of the mCP star CQ UMa (HD 119213) and the
mCP candidate OGLE LMC136.7 16501. Three newly developed tests of the periodic
variability - the shuffling, bootstrap and subsidiary ones, are presented. We
demonstrate that the found periodic variations known with Signal-to-Noise ratio
larger than 6 can be approved as real.
