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

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

Author(s) -

Ming Li,

Wei Zhao

Publication year - 2010

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2010/560429

Subject(s) - statistics , block (permutation group theory) , variance (accounting) , mathematics , autocorrelation , estimation , upper and lower bounds , point estimation , value (mathematics) , hurst exponent , econometrics , combinatorics , engineering , economics , mathematical analysis , accounting , systems engineering

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

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