This article presents an experiment in time series analysis, specifically the Rayleigh Test, applied to the ancient Egyptian calendars of lucky and unlucky days recorded in papyri P. Cairo 86637, P. BM 10474 and P. Sallier IV. The Rayleigh Test is used to determine whether the lucky and unlucky days are distributed randomly within the year, or whether they exhibit periodicity. The results of the analysis show beyond doubt that some of the lucky days were distributed according to a lunar calendar. The cycles of the moon thus played an important role in the religious thinking of the Egyptians. Other periods found using the Rayleigh Test are connected to the civil calendar, the mythological symbolism of the twelfth hour of the day and possibly the period of variation of the star Algol.