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

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概要

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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.

著者

• CHANG Yen-Ching

  School of Applied Information Sciences, Chung Shan Medical University and Department of Medical Imaging, Chung Shan Medical University Hospital

• LAI Li-Chun

  Department of Electrical Engineering and Energy Technology, Chung Chou University of Science and Technology

• CHEN Liang-Hwa

  Department of Computer Information and Network Engineering, Lunghwa University of Science and Technology

• CHANG Chun-Ming

  Department of Applied Informatics and Multimedia, Asia University

関連論文

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

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