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Empirical study of the scaling behavior of the amplitude–frequency distribution of the Hilbert–Huang transform and its application in sunspot time series analysis

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  • Zhou, Yu
  • Leung, Yee
  • Ma, Jian-Min

Abstract

Investigating long-range correlation by the Hurst exponent, H, is crucial in the study of time series. Recently, empirical-mode-decomposition-based arbitrary-order Hilbert spectral analysis (EMD-HSA) has been proposed to numerically obtain without proof a scaling relationship, generated from the amplitude–frequency distribution, related to H. We propose a formalism to empirically study EMD-HSA, to deduce its scaling exponent ξ(q) from the perspective of EMD-based arbitrary-order Hilbert marginal spectrum (EMD-HMS), and to numerically compare the results with the expected H. EMD-HSA and EMD-HMS experiments show that, by incompletely removing (quasi-)periodic trends, the sunspot series should have an H value around 0.12.

Suggested Citation

  • Zhou, Yu & Leung, Yee & Ma, Jian-Min, 2013. "Empirical study of the scaling behavior of the amplitude–frequency distribution of the Hilbert–Huang transform and its application in sunspot time series analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1336-1346.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:6:p:1336-1346
    DOI: 10.1016/j.physa.2012.11.055
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    References listed on IDEAS

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    1. Nagarajan, Radhakrishnan & Kavasseri, Rajesh G., 2005. "Minimizing the effect of periodic and quasi-periodic trends in detrended fluctuation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 777-784.
    2. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
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