Statistical Properties of the Hurst Exponent Estimates for Fractional Levy Motion

In this paper, the model of fractional Levy motion is studied. Conventional methods for estimating the Hurst exponent are inapplicable to such processes because of the heavy tails. 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 obtained estimate is simple in software implementation and applicable according to numerical results. Studying the statistical properties of this estimate (such as consistency and unbiasedness proof, mean square error estimating) as well as finding the optimal values of fractional moment is of current interest.