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Assessing characteristic scales using wavelets

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  • Michael J. Keim
  • Donald B. Percival

Abstract

type="main" xml:id="rssc12079-abs-0001"> Characteristic scale is a notion that pervades the geophysical sciences, but it has no widely accepted precise definition. Motivated by the facts that the wavelet transform decomposes a time series into coefficients that are associated with different scales and that the variance of these coefficients (the so-called wavelet variance) decomposes the variance of the time series across scales, the paper proposes a definition for characteristic scale in terms of peaks in plots of the wavelet variance versus scale. After presenting basic theory for wavelet-based characteristic scales, a natural estimator for these scales is considered. Large sample theory for this estimator permits the construction of confidence intervals for a true unknown characteristic scale. Computer experiments are presented that demonstrate the efficacy of the large sample theory for finite sample sizes. Characteristic scale estimates are calculated for medium multiyear Arctic sea ice, global temperature records, coherent structures in river flows and the Madden–Julian oscillation in an atmospheric time series.

Suggested Citation

  • Michael J. Keim & Donald B. Percival, 2015. "Assessing characteristic scales using wavelets," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 64(2), pages 377-393, February.
    • Handle: RePEc:bla:jorssc:v:64:y:2015:i:2:p:377-393
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    File URL: http://hdl.handle.net/10.1111/rssc.2015.64.issue-2
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    Cited by:

    1. Marco Gallegati, 2018. "A systematic wavelet-based exploratory analysis of climatic variables," Climatic Change, Springer, vol. 148(1), pages 325-338, May.
    2. Ijaz Younis & Cheng Longsheng & Muhammad Farhan Basheer & Ahmed Shafique Joyo, 2020. "Stock market comovements among Asian emerging economies: A wavelet-based approach," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-23, October.
    3. Fredy Gamboa-Estrada, 2023. "The Role of Foreign Investors and Local Agents in the Derivatives Market and their Impact on the Exchange Rate in Colombia: A Wavelet Analysis," IHEID Working Papers 12-2023, Economics Section, The Graduate Institute of International Studies.

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