Variance Bound of ACF Estimation of One Block of fGn with LRD. (27th January 2010)

• Record Type: Journal Article
• Authors: Li, Ming; Zhao, Wei
• Other Names: Cattani Carlo Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2010(2010)
• Publication Date: 2010-01-27
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2010/560429
• Languages: English
• ISSNs: 1024-123X

Abstract

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 (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.