Abstract:
The fast Fourier transform, maximum entropy method, Lomb's method of spectral analysis and rescaled range analysis are applied to the study of extinction patterns. Using a database of marine families from mid-Permian to Pleistocene, it is shown that a long-range correlation is present. Since the data record is non-stationary and unevenly spaced, linear interpolation is carried out for obtaining evenly spaced data. The data are also de-trended from their mean to obtain a stationary time series. Scaling behavior is observed in both interpolated and detrended unevenly spaced data. Application of the randomization test on both interpolated and de-trended data revealed that the interpolated data lost the randomness of the original record due to a smoothing effect, while the de-trended data retained the randomness property and hence are reliable for drawing information. The most popular method, the fast Fourier transform spectral method based on stationarity assumption, yields a contradictory result, and is independent of the interpolation technique used to fill gaps in the discontinuous fossil record.