Wavelet-Tsallis Entropy Detection and Location of Mean Level-Shifts in Long-Memory fGn Signals
Abstract
:1. Introduction
2. Long-Memory fGn Signals
2.1. Wavelet Analysis of Long-Memory Signals
2.2. Estimators of the Long-Memory Parameter
3. Wavelet-Tsallis q-Entropy
3.1. The Analysis of fGn Signals with Level-Shifts via Wavelet-Tsallis q-Entropy
4. A Technique Based on Wavelet-Tsallis q-Entropy for Level-Shift Detection and Location
- (1)
- Compute the wavelet-Tsallis q-entropy as a function of time to signal to obtain .
- (2)
- Perform a transformation and a baseline correction to obtain positive peaks.
- (3)
- Detect and locate peaks in the baseline-corrected wavelet-Tsallis signal using a standard peak detection and location methodology.
5. Results and Discussion
5.1. Detection of Single Level-Shifts in Short-Length fGn Signals
5.2. Detection of Single and Multiple Mean Breaks in Long fGn Signals
5.3. Detection of Single Level-Shifts in the Presence of Gaussian Noise
5.4. Location of Single Mean Breaks in fGn Signals
Atheoretical regression (ART) results | Tsallis q-entropy results | |||||||
Statistics | Nominal H | Nominal H | ||||||
0.6 | 0.7 | 0.8 | 0.9 | 0.6 | 0.7 | 0.8 | 0.9 | |
Length | ||||||||
BIAS | 5.00 | 26.00 | -67.00 | 28 | -7.00 | 136 | 30 | -11 |
σ | 91 | 437 | 584 | 447 | 649 | 935 | 871 | 937 |
91 | 436 | 585 | 446 | 646 | 940 | 867 | 932 | |
μ | 2042 | 2021 | 2114 | 2019 | 2054 | 1911 | 2017 | 2058 |
Length | ||||||||
BIAS | 4.000 | 14.00 | 243 | 489 | 0.000 | -114 | 431 | 419 |
σ | 43.00 | 479 | 1795 | 2141 | 0.000 | 1654 | 3866 | 4075 |
43.00 | 477 | 1803 | 2186 | 0.000 | 1649 | 3870 | 4075 | |
μ | 8187 | 8177 | 7948 | 7702 | 8192 | 8305 | 7760 | 7772 |
5.5. Computation Times
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Ramírez-Pacheco, J.C.; Rizo-Domínguez, L.; Cortez-González, J. Wavelet-Tsallis Entropy Detection and Location of Mean Level-Shifts in Long-Memory fGn Signals. Entropy 2015, 17, 7979-7995. https://doi.org/10.3390/e17127856
Ramírez-Pacheco JC, Rizo-Domínguez L, Cortez-González J. Wavelet-Tsallis Entropy Detection and Location of Mean Level-Shifts in Long-Memory fGn Signals. Entropy. 2015; 17(12):7979-7995. https://doi.org/10.3390/e17127856
Chicago/Turabian StyleRamírez-Pacheco, Julio César, Luis Rizo-Domínguez, and Joaquin Cortez-González. 2015. "Wavelet-Tsallis Entropy Detection and Location of Mean Level-Shifts in Long-Memory fGn Signals" Entropy 17, no. 12: 7979-7995. https://doi.org/10.3390/e17127856
APA StyleRamírez-Pacheco, J. C., Rizo-Domínguez, L., & Cortez-González, J. (2015). Wavelet-Tsallis Entropy Detection and Location of Mean Level-Shifts in Long-Memory fGn Signals. Entropy, 17(12), 7979-7995. https://doi.org/10.3390/e17127856