Estimation and testing of the Hurst parameter using p-variation

Progress in measurement tools and numerical simulations has led to an increase in attention towards complex systems. Recently developed methods based on the so-called p-variation appeared to be very effective in researching the stochastic origin of such phenomena, in particular in fitting the widely used fractional Brownian motion model. In this paper, we propose an estimator based on the p-variation which allows us to determine the Hurst parameter of a single fractional Brownian motion, other fractal-dimension Gaussian processes or a fractional Lévy stable motion trajectory. Additionally, we present a statistical test designed to validate the results. We explain thoroughly the procedure of analysing data and study its effectiveness during Monte Carlo simulations and real data applications. (paper)