The permutation test as a non-parametric method for testing the statistical significance of power spectrum estimation in cyclostratigraphic research

A computer-intensive significance test for estimated power spectra of cyclic sedimentary successions is presented. This simple method requires no more than a few minutes in computer time for a PC-486, and does not require distributional assumptions. It is suitable for all the spectral analysis approaches used in practice. Moreover, good performance is achieved with relatively short stratigraphical series. The method is similar to a permutation test that has been successfully applied to other statistical problems. In the proposed application of the permutation test to the spectral analysis of time series, the data of a stratigraphic sequence are ordered at random (random permutation) and the power spectrum is estimated by the given approach. The process is repeated many times (e.g. 1000 times) and thus it is possible to assess the statistical significance of the power spectrum of the original sequence for each frequency. Simulation results and the application to real data are shown in order to discuss the performance of the method.