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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.

Document type:Preprint
Uncontrolled Keywords:Hurst parameter, long-range dependence, self-similarity, modified Allan variance, parameter estimation, wavelets, fractional Brownian motion.
Subjects:Area 01 - Scienze matematiche e informatiche > MAT/06 Probabilità e statistica matematica
DOI:10.6092/unibo/amsacta/3214
Depositato da:Alessandra Bianchi
Depositato il:10 Feb 2012 15:20
Last modified:17 Feb 2012 12:24

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