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Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 560429, 14 pages
Research Article

Variance Bound of ACF Estimation of One Block of fGn with LRD

1School of Information Science & Technology, East China Normal University, No. 500, Dong-Chuan Road, Shanghai 200241, China
2University of Macau, Avenue Padre Tomás Pereira, Taipa, Macau, China

Received 19 September 2009; Accepted 4 November 2009

Academic Editor: Carlo Cattani

Copyright © 2010 Ming Li and Wei Zhao. 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.


This paper discusses the estimation of autocorrelation function (ACF) of fractional Gaussian noise (fGn) with long-range dependence (LRD). A variance bound of ACF estimation of one block of fGn with LRD for a given value of the Hurst parameter () is given. The present bound provides a guideline to require the block size to guarantee that the variance of ACF estimation of one block of fGn with LRD for a given value does not exceed the predetermined variance bound regardless of the start point of the block. In addition, the present result implies that the error of ACF estimation of a block of fGn with LRD depends only on the number of data points within the sample and not on the actual sample length in time. For a given block size, the error is found to be larger for fGn with stronger LRD than that with weaker LRD.