Analysis of a Hurst parameter estimator based on the modified Allan variance

In order to estimate the Hurst parameter of Internet traffic data, it has been recently proposed a log-regression estimator based on the so-called modified Allan variance (MAVAR). Simulations have shown that this estimator achieves higher accuracy and better confidence when compared with an other method of common use based on wavelet analysis. Here we link it to the wavelets setting and stress why a different analysis for the two approaches is required. We then focus on the asymptotic analysis of the MAVAR log-regression estimator and provide new formulas for the related confidence intervals. By numerical evaluation, we analyze these formulas and make a comparison between three suitable choices on the regression weights, also optimizing over different choices on the data progression.