An Efficient Variance Estimator for the Hurst Exponent of Discrete-Time Fractional Gaussian Noise

Yen-Ching CHANG  Liang-Hwa CHEN  Li-Chun LAI  Chun-Ming CHANG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E95-A   No.9   pp.1506-1511
Publication Date: 2012/09/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E95.A.1506
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
discrete-time fractional Brownian motion,  discrete-time fractional Gaussian noise,  Hurst exponent,  variance estimator,  

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Discrete-Time fractional Brownian motion (DFBM) and its increment process, called discrete-time 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 DFGN-type, not DFBM-type, 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 4-point 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.