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

Alessandra Bianchi, Massimo Campanino and Irene Crimaldi

International Journal of Stochastic Analysis, 2012, vol. 2012, 1-20

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:905082

DOI: 10.1155/2012/905082

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