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

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  • Alessandra Bianchi
  • Massimo Campanino
  • Irene Crimaldi

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.

Suggested Citation

  • Alessandra Bianchi & Massimo Campanino & Irene Crimaldi, 2012. "Asymptotic Normality of a Hurst Parameter Estimator Based on the Modified Allan Variance," International Journal of Stochastic Analysis, Hindawi, vol. 2012, pages 1-20, November.
    • Handle: RePEc:hin:jnijsa:905082
    DOI: 10.1155/2012/905082
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