Spectral and cross-spectral analysis of uneven time series with the smoothed Lomb–Scargle periodogram and Monte Carlo evaluation of statistical significance

Many spectral analysis techniques have been designed assuming sequences taken with a constant sampling interval. However, there are empirical time series in the geosciences (sediment cores, fossil abundance data, isotope analysis, y) that do not follow regular sampling because of missing data, gapped data, random sampling or incomplete sequences, among other reasons. In general, interpolating an uneven series in order to obtain a succession with a constant sampling interval alters the spectral content of the series. In such cases it is preferable to follow an approach that works with the uneven data directly, avoiding the need for an explicit interpolation step. The Lomb-Scargle periodogram is a popular choice in such circumstances, as there are programs available in the public domain for its computation. One new computer program for spectral analysis improves the standard Lomb-Scargle periodogram approach in two ways: (1) It explicitly adjusts the statistical significance to any bias introduced by variance reduction smoothing, and (2) it uses a permutation test to evaluate confidence levels, which is better suited than parametric methods when neighbouring frequencies are highly correlated.