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

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  • Ming Li
  • Wei Zhao

Abstract

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.

Suggested Citation

  • Ming Li & Wei Zhao, 2010. "Variance Bound of ACF Estimation of One Block of fGn with LRD," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-14, January.
    • Handle: RePEc:hin:jnlmpe:560429
    DOI: 10.1155/2010/560429
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