| Time series analysis |
Spectral analysis
| Typical application | Assumptions | Data needed |
| Finding periodicities in counted or measured data | Time series long enough to contain at least four cycles | One or two columns of counted or measured data |
Since palaeontological data are often unevenly sampled, the FFT algorithm can be difficult to use. PAST therefore includes the Lomb periodogram algorithm for unevenly sampled data (Press et al. 1992), with time values given in the first column and dependent values in the second column. If only one column is selected, an even spacing of one unit between data points is assumed. The Lomb periodogram should then give similar results as the FFT.
The frequency axis is in units of 1/(x unit). If for example, your x values are given in millions of years, a frequency of 0.1 corresponds to a period of 10 million years. The power axis is in units proportional to the square of the amplitudes of the sinusoids present in the data.
Also note that the frequency axis extends to very high values. If your data are evenly sampled, the upper half of the spectrum is a mirror image of the lower half, and is of little use. If some of your regions are closely sampled, the algorithm may be able to find useful information even above the half-point (Nyquist frequency).
The highest peak in the spectrum is presented with its frequency and power value, together with a probability that the peak could occur from random data.
Autocorrelation
| Typical application | Assumptions | Data needed |
| Finding periodicities in counted or measured data | Time series long enough to contain at least two cycles. Even spacing of data points. | One column of counted or measured data |
Autocorrelation (Davis 1986)is carried out on separate column(s) of evenly sampled temporal/stratigraphic data. Lag times up to N/2, where N is the number of values in the vector, are shown along the x axis (positive lag times only - the autocorrelation function is symmetrical around zero). A predominantly zero autocorrelation signifies random data - periodicities turn up as peaks.