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Zbl 1191.94042
Li, Ming; Zhao, Wei
Variance bound of ACF estimation of one block of fGn with LRD. (English)
[J] Math. Probl. Eng. 2010, Article ID 560429, 14 p. (2010). ISSN 1024-123X; ISSN 1563-5147/e

Summary: 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 ($H$) 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 $H$ 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.

MSC 2000:: *94A12 Signal theory

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Zentralblatt MATH Berlin [Germany]