Comparison of the Performance of Two Advanced Spectral Methods for the Analysis of Times Series in Paleoceanography

Eulogio Pardo-Igúzquiza,Francisco Rodríguez-Tovar

doi:10.3390/jmse3030957

Eulogio Pardo-Igúzquiza, Francisco Rodríguez-Tovar

Open Access

https://doi.org/10.3390/jmse3030957

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Abstract

Many studies have revealed the cyclicity of past ocean/atmosphere dynamics at a wide range of time scales (from decadal to millennial time scales), based on the spectral analysis of time series of climate proxies obtained from deep sea sediment cores. Among the many techniques available for spectral analysis, the maximum entropy method and the Thomson multitaper approach have frequently been used because of their good statistical properties and high resolution with short time series. The novelty of the present study is that we compared the two methods by according to the performance of their statistical tests to assess the statistical significance of their power spectrum estimates. The statistical significance of maximum entropy estimates was assessed by a random permutation test (Pardo-Igúzquiza and Rodríguez-Tovar, 2000), while the statistical significance of the Thomson multitaper method was assessed by an F-test (Thomson, 1982). We compared the results obtained in a case study using simulated data where the spectral content of the time series was known and in a case study with real data. In both cases the results are similar: while the cycles identified as significant by maximum entropy and the permutation test have a clear physical interpretation, the F-test with the Thomson multitaper estimator tends to find as no significant the peaks in the low frequencies and tends to give as significant more spurious peaks in the middle and high frequencies. Nevertheless, the best strategy is to use both techniques and to use the advantages of each of them.

Highlights

In many paleoceanographic and engineering studies, spectral analysis of time series is employed to detect signals embedded in noise
Many of these spectral analysis studies are carried out on cores obtained from deep sea drilling programs, and the information obtained can be used to infer past ocean/atmosphere dynamics, which is closely related to paleoclimatological research
The purpose of this paper is to compare the performance of the two previous advanced spectral estimation methods, the maximum entropy spectral estimator and the Thomson multitaper estimator, according to the statistical significance of the estimated spectra in two selected case studies: a simulated time series where spectral content is known and a real time series that has been well studied in the scientific literature

Summary

Introduction

In many paleoceanographic and engineering studies, spectral analysis of time series is employed to detect signals embedded in noise. Those signals are generally cyclic components that in harmonic analysis are represented by sinusoids. In cyclostratigraphy (Weedon, 2003, [1]), time series of geological variables are analyzed to detect periodicities that are related to past climatic conditions on. Many of these spectral analysis studies are carried out on cores obtained from deep sea drilling programs, and the information obtained can be used to infer past ocean/atmosphere dynamics, which is closely related to paleoclimatological research. Each methodology has its own parametric statistical test, such as the chi-square test for the Blackman-Tukey and periodogram estimators (Chatfield, 1991, [2]), the F-test for the Thomson multitaper estimator (Thomson, 1982, [3]), and more complex tests for the maximum entropy estimator (Burshtein and Weinstein, 1987, [4]), among others

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