The visibility graph: A new method for estimating the Hurst exponent of fractional Brownian motion

Fractional Brownian motion (fBm) has been used as a theoretical framework to study real-time series appearing in diverse scientific fields. Because of its intrinsic nonstationarity 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 −β 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.