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

Andriana S.L.O. Campanharo and Fernando M. Ramos

Physica A: Statistical Mechanics and its Applications, 2016, vol. 444, issue C, 43-48

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.

Keywords: Self-affine time series; Hurst exponent; Complex networks; Quantile graphs (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:444:y:2016:i:c:p:43-48

DOI: 10.1016/j.physa.2015.09.094

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