Abstract

This paper adopts the visibility graph to analyze the short time series of fractal Brownian motion (fBm), and examines this method in estimating Hurst exponents. The maximum likelihood estimation is introduced to estimate the power-law index and the statistics to judge the performance of the estimation. In the result, we found that the first minimum of the Kuiper statistic can provide an optimal estimation of the power-law index, which can be in turn translated into Hurst exponents with an adjusted equation. Our results show that an accurate estimation of Hurst exponent can be obtained by combining visibility graph, maximum likelihood estimation and Kuiper statistics.

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