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

Bianchi, Alessandra and Bregni, Stefano and Crimaldi, Irene and Ferrari, Marco Analysis of a Hurst parameter estimator based on the modified Allan variance. Technical Report (Submitted)

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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 other methods of common use. Here we link it to the wavelets setting and provide an asymptotic analysis in the case the signal process is a fractional Brownian motion. In particular we show that the MAVAR log-regression estimator is consistent and asymptotically normal, providing the related confidence intervals for a suitable choice on the regression weights. Finally, we show some numerical examples.

Item Type: Working Paper (Technical Report)
Identification Number: 3214
Additional Information: Electronic preprint, University of Bologna, ISSN 2038-7954
Uncontrolled Keywords: Hurst parameter, long-range dependence, self-similarity, modified Allan variance, parameter estimation, wavelets, fractional Brownian motion
Subjects: H Social Sciences > HA Statistics
Q Science > QA Mathematics
Research Area: Economics and Institutional Change
Depositing User: Irene Crimaldi
Date Deposited: 20 Feb 2012 09:03
Last Modified: 07 Jan 2013 12:05
URI: http://eprints.imtlucca.it/id/eprint/1132

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