@Article{CampanharoRamo:2016:HuExEs,
author = "Campanharo, Adriana S. L. O. and Ramos, Fernando Manuel",
affiliation = "{Universidade Estadual Paulista (UNESP)} and {Instituto Nacional
de Pesquisas Espaciais (INPE)}",
title = "Hurst exponent estimation of self-affine time series using
quantile graphs",
journal = "Physica A: Statistical Mechanics and its Applications",
year = "2016",
volume = "444",
pages = "43--48",
month = "Feb.",
keywords = "Self-affine time series, Hurst exponent, Complex networks,
Quantile graphs.",
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.",
doi = "10.1016/j.physa.2015.09.094",
url = "http://dx.doi.org/10.1016/j.physa.2015.09.094",
issn = "0378-4371",
language = "en",
targetfile = "campanharo_hurst.pdf",
urlaccessdate = "27 nov. 2020"
}