Estimating the Hurst Exponent of Fractional Levy Motion by the Fractional Moments Method

Model of fractional Levy motion has been studied. As it was shown, conventional methods for estimating the Hurst exponent are based on second-order statistics, so are inapplicable to the processes with heavy tails. Applying the method of fractional moments, makes it possible to estimate Hurst exponent both for heavy-tailed processes and for processes with long-range dependence. The proposed method is very simple in software implementation, which is its undoubted advantage. Numerical simulations were made and numerical results are in accordance with analytic ones.