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Hurst exponent estimation of self-affine time series using quantile graphs

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  • Campanharo, Andriana S.L.O.
  • Ramos, Fernando M.

Abstract

In the context of dynamical systems, time series analysis is frequently used to identify the underlying nature of a phenomenon of interest from a sequence of observations. For signals with a self-affine structure, like fractional Brownian motions (fBm), the Hurst exponent H is one of the key parameters. Here, the use of quantile graphs (QGs) for the estimation of H is proposed. A QG is generated by mapping the quantiles of a time series into nodes of a graph. H is then computed directly as the power-law scaling exponent of the mean jump length performed by a random walker on the QG, for different time differences between the time series data points. The QG method for estimating the Hurst exponent was applied to fBm with different H values. Comparison with the exact H values used to generate the motions showed an excellent agreement. For a given time series length, estimation error depends basically on the statistical framework used for determining the exponent of the power-law model. The QG method is numerically simple and has only one free parameter, Q, the number of quantiles/nodes. With a simple modification, it can be extended to the analysis of fractional Gaussian noises.

Suggested Citation

  • Campanharo, Andriana S.L.O. & Ramos, Fernando M., 2016. "Hurst exponent estimation of self-affine time series using quantile graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 43-48.
  • Handle: RePEc:eee:phsmap:v:444:y:2016:i:c:p:43-48
    DOI: 10.1016/j.physa.2015.09.094
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    References listed on IDEAS

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    1. Andriana S L O Campanharo & M Irmak Sirer & R Dean Malmgren & Fernando M Ramos & Luís A Nunes Amaral, 2011. "Duality between Time Series and Networks," PLOS ONE, Public Library of Science, vol. 6(8), pages 1-13, August.
    2. Li, Ping & Wang, Bing-Hong, 2007. "Extracting hidden fluctuation patterns of Hang Seng stock index from network topologies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(2), pages 519-526.
    3. Yang, Yue & Yang, Huijie, 2008. "Complex network-based time series analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1381-1386.
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    Cited by:

    1. Serinaldi, Francesco & Kilsby, Chris G., 2016. "Irreversibility and complex network behavior of stream flow fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 585-600.

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