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Fractal analysis of the short time series in a visibility graph method

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  • Li, Ruixue
  • Wang, Jiang
  • Yu, Haitao
  • Deng, Bin
  • Wei, Xile
  • Chen, Yingyuan

Abstract

The aim of this study is to evaluate the performance of the visibility graph (VG) method on short fractal time series. In this paper, the time series of Fractional Brownian motions (fBm), characterized by different Hurst exponent H, are simulated and then mapped into a scale-free visibility graph, of which the degree distributions show the power-law form. The maximum likelihood estimation (MLE) is applied to estimate power-law indexes of degree distribution, and in this progress, the Kolmogorov–Smirnov (KS) statistic is used to test the performance of estimation of power-law index, aiming to avoid the influence of droop head and heavy tail in degree distribution. As a result, we find that the MLE gives an optimal estimation of power-law index when KS statistic reaches its first local minimum. Based on the results from KS statistic, the relationship between the power-law index and the Hurst exponent is reexamined and then amended to meet short time series. Thus, a method combining VG, MLE and KS statistics is proposed to estimate Hurst exponents from short time series. Lastly, this paper also offers an exemplification to verify the effectiveness of the combined method. In addition, the corresponding results show that the VG can provide a reliable estimation of Hurst exponents.

Suggested Citation

  • Li, Ruixue & Wang, Jiang & Yu, Haitao & Deng, Bin & Wei, Xile & Chen, Yingyuan, 2016. "Fractal analysis of the short time series in a visibility graph method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 531-540.
    • Handle: RePEc:eee:phsmap:v:450:y:2016:i:c:p:531-540
    DOI: 10.1016/j.physa.2015.12.071
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    Cited by:

    1. Shastitko. Andrey (Шаститко, Андрей) & Komkova, Anastasia Andreevna (Комкова, Анастасия Андреевна) & Kurdin, Alexander (Курдин, Александр) & Shastitko, Anastasia (Шаститко, Анастасия), 2016. "Competition Policy and Incentives for Innovation [Конкурентная Политика И Стимулы К Инновационной Деятельности]," Working Papers 1447, Russian Presidential Academy of National Economy and Public Administration.

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