- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
International Journal of Stochastic Analysis
Volume 2012 (2012), Article ID 905082, 20 pages
Asymptotic Normality of a Hurst Parameter Estimator Based on the Modified Allan Variance
1Department of Pure and Applied Mathematics, University of Padua, Via Trieste 63, 35121 Padova, Italy
2Department of Mathematics, University of Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy
3IMT Institute for Advanced Studies, Piazza S. Ponziano 6, 55100 Lucca, Italy
Received 25 July 2012; Revised 9 October 2012; Accepted 21 October 2012
Academic Editor: Hari Srivastava
Copyright © 2012 Alessandra Bianchi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. Beran, Statistics for Long-Memory Processes, vol. 61 of Monographs on Statistics and Applied Probability, Chapman and Hall, London, UK, 1994.
- B. B. Mandelbrot and J. W. Van Ness, “Fractional Brownian motions, fractional noises and applications,” SIAM Review, vol. 10, pp. 422–437, 1968.
- L. G. Bernier, “Theoretical analysis of the modified Allan variance,” in Proceedings of the 41st Annual Frequency Control Symposium, pp. 161–121, 1987.
- S. Bergni, “Characterization and modelling of clocks,” in Synchronization of Digital Telecommu-Nications Networks, John Wiley & Sons, 2002.
- S. Bregni and L. Primerano, “The modified Allan variance as time-domain analysis tool for estimating the hurst parameter of long-rangé dependent traffic,” in IEEE Global Telecommunications Conference (GLOBECOM '04), pp. 1406–1410, December 2004.
- S. Bregni and W. Erangoli, “Fractional noise in experimental measurements of IP traffic in a metropolitan area network,” in Proceedings of the IEEE Global Telecommunications Conference (GLOBECOM '05), pp. 781–785, December 2005.
- S. Bregni and L. Jmoda, “Accurate estimation of the Hurst parameter of long-range dependent traffic using modified Allan and Hadamard variances,” IEEE Transactions on Communications, vol. 56, no. 11, pp. 1900–1906, 2008.
- A. Bianchi, S. Bregni, I. Crimaldi, and M. FERRARI, “Analysis of a hurst parameter estimator based on the modified Allan variance,” in Proceedings of the IEEE Global Telecommunications Conference and Exhibition (GLOBECOM) and IEEE Xplore, 2012.
- J. F. Coeurjolly, “Simulation and identification of the fractional brownian motion: a bibliographical and comparative study,” Journal of Statistical Software, vol. 5, pp. 1–53, 2000.
- J.-F. Coeurjolly, “Estimating the parameters of a fractional Brownian motion by discrete variations of its sample paths,” Statistical Inference for Stochastic Processes, vol. 4, no. 2, pp. 199–227, 2001.
- E. Moulines, F. Roueff, and M. S. Taqqu, “Central limit theorem for the log-regression wavelet estimation of the memory parameter in the gaussian semi-parametric context,” Fractals, vol. 15, no. 4, pp. 301–313, 2007.
- E. Moulines, F. Roueff, and M. S. Taqqu, “On the spectral density of the wavelet coefficients of long-memory time series with application to the log-regression estimation of the memory parameter,” Journal of Time Series Analysis, vol. 28, no. 2, pp. 155–187, 2007.
- E. Moulines, F. Roueff, and M. S. Taqqu, “A wavelet whittle estimator of the memory parameter of a nonstationary Gaussian time series,” Annals of Statistics, vol. 36, no. 4, pp. 1925–1956, 2008.
- P. Abry and D. Veitch, “Wavelet analysis of long-range-dependent traffic patrice abry and darryl veitch,” IEEE Transactions on Information Theory, vol. 44, no. 1, pp. 2–15, 1998.
- P. Abry, P. Flandrin, M. S. Taqqu, and D. Veitch, “Wavelets for the analysis, estimation and synthesis of scaling data,” in Self-Similar Network Traffic and Performance Evaluation, K. Park and W. Willinger, Eds., pp. 39–88, Wiley, New York, NY, USA, 2000.
- T. Lindstrom, “A weighted random walk approximation to fractional Brownian motion,” Tech. Rep. 11, Department of Mathematics, University of Oslo, 2007, http://arxiv.org/abs/0708.1905.
- A. M. Yaglom, Correlation Theory of Stationary and Related Random Functions, Springer Series in Statistics, Springer, New York, NY, USA, 1987.
- F. Roueff and M. S. Taqqu, “Asymptotic normality of wavelet estimators of the memory parameter for linear processes,” Journal of Time Series Analysis, vol. 30, no. 5, pp. 534–558, 2009.
- J. Glimm and A. Jaffe, Quantum Physics. A Functional Integral Point of View, Springer, New York, NY, USA, 2nd edition, 1987.