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An Efficient Variance Estimator for the Hurst Exponent of DiscreteTime Fractional Gaussian Noise
YenChing CHANG LiangHwa CHEN LiChun LAI ChunMing CHANG
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E95A
No.9
pp.15061511 Publication Date: 2012/09/01
Online ISSN: 17451337
DOI: 10.1587/transfun.E95.A.1506
Print ISSN: 09168508 Type of Manuscript: PAPER Category: Digital Signal Processing Keyword: discretetime fractional Brownian motion, discretetime fractional Gaussian noise, Hurst exponent, variance estimator,
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Summary:
DiscreteTime fractional Brownian motion (DFBM) and its increment process, called discretetime fractional Gaussian noise (DFGN), are usually used to describe natural and biomedical phenomena. These two processes are dominated by one parameter, called the Hurst exponent, which needs to be estimated in order to capture the characteristics of physical signals. In the previous work, a variance estimator for estimating the Hurst exponent directly via DFBM was provided, and it didn't consider point selection for linear regression. Since physical signals often appear to be DFGNtype, not DFBMtype, it is imperative to first transform DFGN into DFBM in real applications. In this paper, we show that the variance estimator possesses another form, which can be estimated directly via the autocorrelation functions of DFGN. The above extra procedure of transforming DFGN into DFBM can thus be avoided. On the other hand, the point selection for linear regression is also considered. Experimental results show that 4point linear regression is almost optimal in most cases. Therefore, our proposed variance estimator is more efficient and accurate than the original one mentioned above. Besides, it is also superior to AR and MA methods in speed and accuracy.

