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Multifractal detrended fluctuation analysis of analog random multiplicative processes

Author

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  • Silva, L.B.M.
  • Vermelho, M.V.D.
  • Lyra, M.L.
  • Viswanathan, G.M.

Abstract

We investigate non-Gaussian statistical properties of stationary stochastic signals generated by an analog circuit that simulates a random multiplicative process with weak additive noise. The random noises are originated by thermal shot noise and avalanche processes, while the multiplicative process is generated by a fully analog circuit. The resulting signal describes stochastic time series of current interest in several areas such as turbulence, finance, biology and environment, which exhibit power-law distributions. Specifically, we study the correlation properties of the signal by employing a detrended fluctuation analysis and explore its multifractal nature. The singularity spectrum is obtained and analyzed as a function of the control circuit parameter that tunes the asymptotic power-law form of the probability distribution function.

Suggested Citation

  • Silva, L.B.M. & Vermelho, M.V.D. & Lyra, M.L. & Viswanathan, G.M., 2009. "Multifractal detrended fluctuation analysis of analog random multiplicative processes," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2806-2811.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:5:p:2806-2811
    DOI: 10.1016/j.chaos.2008.10.027
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    References listed on IDEAS

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    1. da Silva Jr., M.P. & Lyra, M.L. & Vermelho, M.V.D., 2005. "Analog study of the first passage time problem driven by power-law distributed noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 348(C), pages 85-96.
    2. Iovane, G., 2006. "Cantorian spacetime and Hilbert space: Part I—Foundations," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 857-878.
    3. Solomon, Sorin & Richmond, Peter, 2001. "Power laws of wealth, market order volumes and market returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 188-197.
    4. C. Anteneodo & R. Riera, 2005. "Additive-multiplicative stochastic models of financial mean-reverting processes," Papers physics/0502119, arXiv.org.
    5. Miliou, A.N. & Valaristos, A.P. & Stavrinides, S.G. & Kyritsi, K. & Anagnostopoulos, A.N., 2007. "Characterization of a non-autonomous second-order non-linear circuit for secure data transmission," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1248-1255.
    6. Duarte, J.R.R. & Vermelho, M.V.D. & Lyra, M.L., 2008. "Stochastic resonance of a periodically driven neuron under non-Gaussian noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(7), pages 1446-1454.
    7. Iovane, G., 2006. "Cantorian space–time and Hilbert space: Part II—Relevant consequences," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 1-22.
    8. Ruiz, P. & Gutiérrez, J.M. & Güémez, J., 2008. "Experimental mastering of nonlinear dynamics in circuits by sporadic pulses," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 635-645.
    9. Oya, Takahide & Asai, Tetsuya & Amemiya, Yoshihito, 2007. "Stochastic resonance in an ensemble of single-electron neuromorphic devices and its application to competitive neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 855-861.
    10. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    11. Serva, M. & Fulco, U.L. & Gléria, I.M. & Lyra, M.L. & Petroni, F. & Viswanathan, G.M., 2006. "A Markov model of financial returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 393-403.
    12. Shang, Pengjian & Lu, Yongbo & Kamae, Santi, 2008. "Detecting long-range correlations of traffic time series with multifractal detrended fluctuation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 82-90.
    13. Kaushik Matia & Yosef Ashkenazy & H. Eugene Stanley, 2003. "Multifractal Properties of Price Fluctuations of Stocks and Commodities," Papers cond-mat/0308012, arXiv.org.
    14. de Oliveira, I.N. & Lyra, M.L. & Albuquerque, E.L., 2004. "Specific heat anomalies of non-interacting fermions with multifractal energy spectra," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 424-432.
    15. Sornette, Didier, 1998. "Linear stochastic dynamics with nonlinear fractal properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 250(1), pages 295-314.
    16. Lim, Gyuchang & Kim, SooYong & Lee, Hyoung & Kim, Kyungsik & Lee, Dong-In, 2007. "Multifractal detrended fluctuation analysis of derivative and spot markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 259-266.
    17. Moshe Levy & Sorin Solomon, 1996. "Power Laws Are Logarithmic Boltzmann Laws," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 595-601.
    18. Iovane, G. & Chinnici, M. & Tortoriello, F.S., 2008. "Multifractals and El Naschie E-infinity Cantorian space–time," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 645-658.
    19. Lima, Rodrigo P.A & Lyra, Marcelo L & Cressoni, José C, 2001. "Multifractality of one electron eigen states in 1D disordered long range models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(1), pages 154-157.
    20. Li, Xuewei & Shang, Pengjian, 2007. "Multifractal classification of road traffic flows," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1089-1094.
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