Maximum entropy spectral analysis of uneven time series in the geosciences

Abstract

Time series with a non-constant sampling interval (i.e., uneven time series) are ubiquitous in the geosciences. This is due to random sampling, gaps in sampling, missing data, hiatuses, or the transformation between a spatial scale and a temporal scale when, for example, the sedimentation rate is not constant. The preferred approach in the spectral analyses of these uneven sequences are interpolation-free spectral methods, and the Lomb-Scargle periodogram is a popular choice. In the work presented here, the maximum entropy spectral estimator, modified to deal with uneven time series, is proposed as an alternative to the periodogram. The appeal of this approach is that the maximum entropy spectral estimator is a high resolution estimator. The proposed methodology uses the equivalence between the maximum entropy and the autoregressive spectral estimator. The permutation test is used to assess the statistical confidence of the estimated power spectrum and real and simulated time series are used to illustrate the performance of the proposed methodology. This study shows that the maximum entropy spectral estimation of uneven time series avoids the side lobe problem that plagues the Lomb-Scargle periodogram whilst maintaining its high resolution for short time series. The maximum spectral estimator works well in cases where large proportions of the data are randomly missing, when there are gaps in the data, where there is one or more significant hiatus in the process that generates the data, and for time series with random sampling.