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Asymptotic Normality of a Hurst Parameter Estimator Based on the Modified Allan Variance

Bianchi, Alessandra and Campanino, Massimo and Crimaldi, Irene Asymptotic Normality of a Hurst Parameter Estimator Based on the Modified Allan Variance. International Journal of Stochastic Analysis, 2012. pp. 1-20. ISSN 2090-3332 (2012)

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Abstract

In order to estimate the memory 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. In this paper we present a rigorous study of the MAVAR log-regression estimator. In particular, under the assumption that the signal process is a fractional Brownian motion, we prove that it is consistent and asymptotically normally distributed. Finally, we discuss its connection with the wavelets estimators.

Item Type: Article
Identification Number: 10.1155/2012/905082
Uncontrolled Keywords: modified Allan variance, log-regression estimator, fractional Brownian motion, long-range dependence, self-similarity
Subjects: H Social Sciences > HA Statistics
Q Science > QA Mathematics
Research Area: Economics and Institutional Change
Depositing User: Irene Crimaldi
Date Deposited: 28 Nov 2012 13:24
Last Modified: 29 Nov 2012 13:17
URI: http://eprints.imtlucca.it/id/eprint/1434

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