The Visibility Graph: a new method for estimating the Hurst exponent of fractional Brownian motion
arXiv:0901.0888 · doi:10.1209/0295-5075/86/30001
Abstract
Fractional Brownian motion (fBm) has been used as a theoretical framework to study real time series appearing in diverse scientific fields. Because its intrinsic non-stationarity and long range dependence, its characterization via the Hurst parameter H requires sophisticated techniques that often yield ambiguous results. In this work we show that fBm series map into a scale free visibility graph whose degree distribution is a function of H. Concretely, it is shown that the exponent of the power law degree distribution depends linearly on H. This also applies to fractional Gaussian noises (fGn) and generic f^(-b) noises. Taking advantage of these facts, we propose a brand new methodology to quantify long range dependence in these series. Its reliability is confirmed with extensive numerical simulations and analytical developments. Finally, we illustrate this method quantifying the persistent behavior of human gait dynamics.
5 pages, submitted for publication
References in corpus (5)
- Power laws, Pareto distributions and Zipf's law
- From time series to complex networks: the visibility graph
- Detrended Cross-Correlation Analysis: A New Method for Analyzing Two Non-stationary Time Series
- Algorithm to estimate the Hurst exponent of high-dimensional fractals
- Self-similar signature of the active solar corona within the inertial range of solar wind turbulence
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