Variance Bound of ACF Estimation of One Block of fGn with LRD
نویسندگان
چکیده
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.
منابع مشابه
Generalized Cauchy Type
Self-similar process with long-range dependence LRD , that is, fractional Gaussian noise fGn with LRD is a widely used model of Internet traffic. It is indexed by its Hurst parameterHfGn that linearly relates to its fractal dimensionDfGn. Note that, on the one hand, the fractal dimensionD of traffic measures local self-similarity. On the other hand, LRD is a global property of traffic, which is...
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