Hurst exponent estimation from short time series

Abstract

Fractal investigation of time series is very complex for several reasons. Due to the existence of fully continuous model, on which the majority of conventional methods are based, the quality of Hurst exponent estimate is often influenced by the number of input data and its sampling rate. In this work, we present a novel approach of unbiased Hurst exponent estimate that is suitable especially for short time series. The crucial idea is deriving the discrete fractional Brownian bridge and its statistical properties that can be subsequently used for model parameter estimation. For the verification and demonstration of efficiency of the method, several generators of fractional Gaussian noise are presented and tested.