The standard approach to the application of spectral analysis in the search for orbitally forced cycles in stratigraphic data series involves comparing the power spectrum of the data with that of a statistical model representing (random) background noise. The discrimination of a (candidate) periodic cycle from random noise requires estimation of the statistical confidence that power at a given frequency in the spectrum is unlikely to be part of the noise. Andrews et al. (2016) made spectral analyses of natural gamma-ray (GR) data from onshore and offshore sections through the lacustrine Caithness Flags (Middle Devonian, Scotland), the offshore section comprising 807 m of strata in the UK Continental Shelf (UKCS) well 11/25-2 ST1. They generated periodograms using Thomson's multi-taper method (MTM), followed by the Matlab function Redconf (Husson et al. 2014) to model the noise in the data and to derive their statistical confidence levels. As is the convention in cyclostratigraphic analysis, Redconf uses a first-order autocorrelation (AR(1)) process to model the random noise inherent in the data. The resulting periodograms for the total dataset and for subgroup-level subsets (fig. 9a–e of Andrews et al. 2016) appear to show the presence of substantial numbers of cycles significant at the statistical 90% confidence level (CL).

This standard approach to the estimation of confidence levels in cyclostratigraphy was criticized by Vaughan et al. (2011). They found two sources of high false positive rates of cycle identification: (1) failure to correct the probabilistic CLs for the inevitably multiple nature of the significance tests; (2) universal reliance on AR(1) for modelling the noise. We show here that almost all of the cycles identified by Andrews et al. …