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

Bianchi, Alessandra ; Bregni, Stefano ; Crimaldi, Irene ; Ferrari, Marco (2012) Analysis of a Hurst parameter estimator based on the modified Allan variance. [Preprint]
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Abstract

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.

Abstract
Document type
Preprint
Creators
CreatorsAffiliationORCID
Bianchi, Alessandra
Bregni, Stefano
Crimaldi, Irene
Ferrari, Marco
Keywords
Hurst parameter, long-range dependence, self-similarity, modified Allan variance, parameter estimation, wavelets, fractional Brownian motion.
Subjects
DOI
Deposit date
10 Feb 2012 14:20
Last modified
17 Feb 2012 11:24
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