Estimation of the Hurst exponent in the mixed traffic models

In this paper we consider the problem of the Hurst parameter estimation for the input flow generated by the composition of independent fractal browian motion and $\alpha$-stable Lévy motion. We use the time-frequency decomposition of the process by Haar wavelet and apply the weighted least square regression to the sum of logarithms of the wavelet-coefficients absolute values. Proposed method does't require any additional corrections neither dependent variable nor octave's number $j$ (factor variable) and provides an asymptotically efficient estimation. Several simulated examples are used for its illustration.