• Fourier analysis;
  • Milankovitch theory;
  • astronomical forcing;
  • red noise;
  • spectral analysis;
  • time series analysis

[1] We discuss the detection of cyclic signals in stratigraphic ‘time series’ using spectral methods. The dominant source of variance in the stratigraphic record is red noise, which greatly complicates the process of searching for weak periodic signals. We highlight two issues that are more significant than generally appreciated. The first is the lack of a correction for ‘multiple tests’ – many independent frequencies are examined for periods but using a significance test appropriate for examination of a single frequency. The second problem is the poor choice of null hypothesis used to model the spectrum of non-periodic variations. Stratigraphers commonly assume the noise is a first-order autoregressive process – the AR(1) model – which in practice often gives a very poor match to real data; a fact that goes largely unnoticed because model checking is rarely performed. These problems have the effect of raising the number of false positives far above the expected rate, to the extent that the literature on spatial stratigraphic cycles is dominated by false positives. In turn these will distort the construction of astronomically calibrated timescales, lead to inflated estimates of the physical significance of deterministic forcing of the climate and depositional processes in the pre-Neogene, and may even bias models of solar system dynamics on very long timescales. We make suggestions for controlling the false positive rate, and emphasize the value of Monte Carlo simulations to validate and calibrate analysis methods.