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

• Autor(a) principal: Campanharo, Andriana S. L. O. [UNESP]
• Data de Publicação: 2016
• Outros Autores: Ramos, Fernando M.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1016/j.physa.2015.09.094; http://hdl.handle.net/11449/161065
• topic: Self-affine time series; Hurst exponent; Complex networks; Quantile graphs

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. (C) 2015 Elsevier B.V. All rights reserved.