Geodesic
Estimation of the Hurst exponent in the mixed traffic models
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2019), pp. 20-39

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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.
Keywords: long-range dependence, heavy-tailed distributions, fractal brownian noise, Hurst parameter, weighted least square regression.
Mots-clés : $\alpha$-stable Lévy motion 
O. I. Sidorova; Yu. S. Khokhlov. Estimation of the Hurst exponent in the mixed traffic models. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2019), pp. 20-39. http://geodesic.mathdoc.fr/item/VTPMK_2019_3_a1/
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