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Wavelet entropy of stochastic processes

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  • Zunino, L.
  • Pérez, D.G.
  • Garavaglia, M.
  • Rosso, O.A.

Abstract

We compare two different definitions for the wavelet entropy associated to stochastic processes. The first one, the normalized total wavelet entropy (NTWS) family [S. Blanco, A. Figliola, R.Q. Quiroga, O.A. Rosso, E. Serrano, Time–frequency analysis of electroencephalogram series, III. Wavelet packets and information cost function, Phys. Rev. E 57 (1998) 932–940; O.A. Rosso, S. Blanco, J. Yordanova, V. Kolev, A. Figliola, M. Schürmann, E. Başar, Wavelet entropy: a new tool for analysis of short duration brain electrical signals, J. Neurosci. Method 105 (2001) 65–75] and a second introduced by Tavares and Lucena [Physica A 357(1) (2005) 71–78]. In order to understand their advantages and disadvantages, exact results obtained for fractional Gaussian noise (-1<α<1) and fractional Brownian motion (1<α<3) are assessed. We find out that the NTWS family performs better as a characterization method for these stochastic processes.

Suggested Citation

  • Zunino, L. & Pérez, D.G. & Garavaglia, M. & Rosso, O.A., 2007. "Wavelet entropy of stochastic processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 503-512.
    • Handle: RePEc:eee:phsmap:v:379:y:2007:i:2:p:503-512
    DOI: 10.1016/j.physa.2006.12.057
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    References listed on IDEAS

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    1. Zunino, L. & Pérez, D.G. & Garavaglia, M. & Rosso, Osvaldo A., 2006. "Characterization of laser propagation through turbulent media by quantifiers based on the wavelet transform: Dynamic study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 79-86.
    2. Robert J. Elliott & John Van Der Hoek, 2003. "A General Fractional White Noise Theory And Applications To Finance," Mathematical Finance, Wiley Blackwell, vol. 13(2), pages 301-330, April.
    3. Pérez, D.G. & Zunino, L. & Garavaglia, M. & Rosso, O.A., 2006. "Wavelet entropy and fractional Brownian motion time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(2), pages 282-288.
    4. Carbone, A. & Castelli, G. & Stanley, H.E., 2004. "Time-dependent Hurst exponent in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 267-271.
    5. González, C.M. & Larrondo, H.A. & Rosso, O.A., 2005. "Statistical complexity measure of pseudorandom bit generators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 281-300.
    6. Rosso, O.A. & Hyslop, W. & Gerlach, R. & Smith, R.L.L. & Rostas, J.A.P. & Hunter, M., 2005. "Quantitative EEG analysis of the maturational changes associated with childhood absence epilepsy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 356(1), pages 184-189.
    7. Rosso, O.A & Martin, M.T & Plastino, A, 2002. "Brain electrical activity analysis using wavelet-based informational tools," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 313(3), pages 587-608.
    8. Korol, A.M. & Rasia, R.J. & Rosso, O.A., 2007. "Alterations of thalassemic erythrocytes detected by wavelet entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 257-264.
    9. Rosso, Osvaldo A & Mairal, Marı́a Liliana, 2002. "Characterization of time dynamical evolution of electroencephalographic epileptic records," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(3), pages 469-504.
    10. Tavares, D.M. & Lucena, L.S., 2005. "Entropy analysis of stochastic processes at finite resolution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 357(1), pages 71-78.
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    1. Zunino, L. & Pérez, D.G. & Kowalski, A. & Martín, M.T. & Garavaglia, M. & Plastino, A. & Rosso, O.A., 2008. "Fractional Brownian motion, fractional Gaussian noise, and Tsallis permutation entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6057-6068.
    2. Mastroeni, Loretta & Mazzoccoli, Alessandro & Vellucci, Pierluigi, 2024. "Studying the impact of fluctuations, spikes and rare events in time series through a wavelet entropy predictability measure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 641(C).
    3. He, Kaijian & Lu, Xingjing & Zou, Yingchao & Keung Lai, Kin, 2015. "Forecasting metal prices with a curvelet based multiscale methodology," Resources Policy, Elsevier, vol. 45(C), pages 144-150.

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