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

doi:10.1587/transfun.E95.A.1506

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

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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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E95-A No.9 pp.1506-1511

Publication Date: 2012/09/01

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Online ISSN: 1745-1337

DOI: 10.1587/transfun.E95.A.1506

Type of Manuscript: PAPER

Category: Digital Signal Processing

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Yen-Ching CHANG, Liang-Hwa CHEN, Li-Chun LAI, Chun-Ming CHANG, "An Efficient Variance Estimator for the Hurst Exponent of Discrete-Time Fractional Gaussian Noise" in IEICE TRANSACTIONS on Fundamentals, vol. E95-A, no. 9, pp. 1506-1511, September 2012, doi: 10.1587/transfun.E95.A.1506.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E95.A.1506/_p

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@ARTICLE{e95-a_9_1506,
author={Yen-Ching CHANG, Liang-Hwa CHEN, Li-Chun LAI, Chun-Ming CHANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={An Efficient Variance Estimator for the Hurst Exponent of Discrete-Time Fractional Gaussian Noise},
year={2012},
volume={E95-A},
number={9},
pages={1506-1511},
abstract={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.},
keywords={},
doi={10.1587/transfun.E95.A.1506},
ISSN={1745-1337},
month={September},}

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TY - JOUR
TI - An Efficient Variance Estimator for the Hurst Exponent of Discrete-Time Fractional Gaussian Noise
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1506
EP - 1511
AU - Yen-Ching CHANG
AU - Liang-Hwa CHEN
AU - Li-Chun LAI
AU - Chun-Ming CHANG
PY - 2012
DO - 10.1587/transfun.E95.A.1506
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E95-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2012
AB - 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.
ER -