Tracking performance and robustness analysis of Hurst estimators for multifractional processes

H. Sheng; Y.Q. Chen; T.S. Qiu

Tracking performance and robustness analysis of Hurst estimators for multifractional processes

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Tracking performance and robustness analysis of Hurst estimators for multifractional processes

Author(s): H. Sheng ; Y.Q. Chen ; T.S. Qiu
DOI: 10.1049/iet-spr.2010.0170

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Author(s): H. Sheng ^{1, 2} ; Y.Q. Chen ² ; T.S. Qiu ³
- Affiliations: 1: School of Electrical and Information, Dalian Jiaotong University, Dalian, People's Republic of China
  2: CSOIS, Electrical and Computer Engineering Department, Utah State University, Logan, USA
  3: Department of Electronic Engineering, Dalian University of Technology, Dalian, People's Republic of China
Source: Volume 6, Issue 3, May 2012, p. 213 – 226
DOI: 10.1049/iet-spr.2010.0170 , Print ISSN 1751-9675, Online ISSN 1751-9683

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In this study, the authors focus on the tracking performance and the robustness of 12 sliding-windowed Hurst estimators for multifractional processes with linear trend local Hölder exponent, noisy multifractional processes and multifractional processes with infinite second-order statistics. Four types of multifractional processes are synthesised to test the tracking performance and robustness of these 12 sliding-windowed Hurst estimators. They are (i) noise-free multifractional process; (ii) multifractional process corrupted by 30-dB signal-to-noise ratio (SNR) white Gaussian noise; (iii) multifractional process corrupted by 30-dB SNR impulse noise; and (iv) multifractional stable process, which has no finite second-order statistics. Furthermore, the standard error of different sliding-windowed Hurst estimators are calculated in order to quantify the accuracy and robustness. This study provides a guideline and principle in the selection of Hurst estimators for noise-free multifractional process, noise-corrupted multifractional process and multifractional process with infinite second-order statistics. The results of this analysis show that the sliding-windowed Kettani and Gubner's method provides the best-tracking performance for multifractional processes with linear trend local Hölder exponent and good robustness to noise.

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Tracking performance and robustness analysis of Hurst estimators for multifractional processes

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