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Time–Series Analysis of Paleoclimate Data

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Encyclopedia of Paleoclimatology and Ancient Environments

Part of the book series: Encyclopedia of Earth Sciences Series ((EESS))

Introduction

This article is a brief synopsis of time-series analysis methods that have proven to be useful in the analysis of paleoclimate data. Space limitations precludes all but the briefest outline of the actual mathematics involved, but references are provided. The following sections define some basic functions such as spectrum and autocorrelations, outline the basic multitaper methods that are recommended to estimate them, describe periodic components and Cramér–Rao bounds for frequency estimation, and coherence estimates. Other sections below discuss jackknife confidence limits for spectra and similar functions, spectrogram methods useful with nonstationary processes, discusses wavelets, Lomb–Scargle and Blackman–Tukey estimates which should be avoided for these applications. Finally, the last section summarizes the points made.

One should not expect the analysis of paleoclimate data to be easy. If one considers the effort that has been made over the last three or four decades...

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Notes

  1. 1.

    1The data was obtained from //delphi.esc.cam.ac.uk/coredata/v677846.html and the few gaps interpolated; see Appendix A of Thomson et al. (2001).

  2. 2.

    2The actual factor is the estimate efficiency Ξ defined in Thomson (1982) §VII.

  3. 3.

    3If the time-steps and number of samples are different one can still do the analysis as long as the total time span is the same and, obviously, one can always truncate a longer series. The frequencies used must be the same, so it may be necessary to use a “slow” Fourier transform (see e.g., Gentleman, 1969).

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Authors
  1. David J. Thomson
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Editors and Affiliations

  1. Goddard Institute for Space Studies, Columbia University, New York, USA

    Vivien Gornitz

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© 2009 Springer-Verlag

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Thomson, D.J. (2009). Time–Series Analysis of Paleoclimate Data. In: Gornitz, V. (eds) Encyclopedia of Paleoclimatology and Ancient Environments. Encyclopedia of Earth Sciences Series. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-4411-3_222

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