Methodologies are suggested for the analysis of cyclic sediments. These include (1) linear analysis to determine whether cycles are of approximately constant duration and whether the relation between thickness and time is facies dependent and (2) multiple prolate-spheroidal windowing spectral analysis to determine whether time-series data indicate periodicities, either of the primary cycles or of higher or lower orders. The results of both methods are compared to a null hypothesis as a semiquantitative test of periodicity. Application of the methods to Newark Supergroup lacustrine cycles suggests that the primary cycles are approximately periodic and record a response to astronomical precession. The time represented by a given thickness of the different facies increases with the depositional water depth of that facies and with decreasing grain size. Precessional index cycles and long-period precessional index beats, or eccentricity, are strongly recorded in the spectra. Spectral results suggest but do not prove lengthening of the periodicities of orbital parameters since 200 Ma
