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Self-similarity principle: the reduced description of randomness

  • Research Article
  • Published:
Central European Journal of Physics

Abstract

A new general fitting method based on the Self-Similar (SS) organization of random sequences is presented. The proposed analytical function helps to fit the response of many complex systems when their recorded data form a self-similar curve. The verified SS principle opens new possibilities for the fitting of economical, meteorological and other complex data when the mathematical model is absent but the reduced description in terms of some universal set of the fitting parameters is necessary. This fitting function is verified on economical (price of a commodity versus time) and weather (the Earth’s mean temperature surface data versus time) and for these nontrivial cases it becomes possible to receive a very good fit of initial data set. The general conditions of application of this fitting method describing the response of many complex systems and the forecast possibilities are discussed.

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References

  1. J. Kwapien, S. Drozdz, Phys. Rep. 515, 115 (2012)

    Article  MathSciNet  ADS  Google Scholar 

  2. A. Yasutomi, Physica D 82, 180 (1995)

    Article  MATH  Google Scholar 

  3. J. Duffy, J. Ochs, Am. Econ. Rev. 89, 847 (1999)

    Article  Google Scholar 

  4. P. Howlett, R. Clower, J. Econ. Behav. Organ. 41, 55 (2000)

    Article  Google Scholar 

  5. J. Feder, Fractals, Plenum Press (New York and London, 1988)

    Book  Google Scholar 

  6. H. Sheng, Y. Chen, T. Qui, Fractional Processes and Fractional-Order Signal Processing, Springer-Verlag (NY, Heidelberg, London, 2012)

    Book  Google Scholar 

  7. R. R. Nigmatullin, G. Smith, Physica A 320, 291 (2003)

    Article  ADS  MATH  Google Scholar 

  8. R. R. Nigmatullin, Commun. Nonlinear Sci. 15, 637 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. D. Sornette, Phys. Rep. 297, 239 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  10. J. Voigt, The Statistical Mechanics of the Financial Markets, 3rd edition (Springer-Verlag. Berlin-Heidelberg, 2005)

    Google Scholar 

  11. R. R. Nigmatullin, J. Appl. Magn. Reson. 14, 601 (1998)

    Article  Google Scholar 

  12. R. R. Nigmatullin, Physica A 285, 547 (2000)

    Article  ADS  MATH  Google Scholar 

  13. R. Menezes, N. B. Ferreira, D. A. Mendes, Nonlinear Dynam. 44, 359 (2006)

    Article  MATH  Google Scholar 

  14. J. T. Machado, G. M. Duarte, F. B. Duarte, Nonlinear Dynam. 63, 611 (2011)

    Article  Google Scholar 

  15. J. T. Machado, F. B. Duarte, G. M. Duarte, Commun. Nonlinear Sci. 16, 4610 (2011)

    Article  Google Scholar 

  16. J. T. Machado, G. M. Duarte, F. B. Duarte, Int. J. Bifurcat. Chaos 22, 1250249 (2012)

    Article  MathSciNet  Google Scholar 

  17. D. A. Dickey, W. A. Fuller, Econometrica 49, 1057 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  18. D. Kwiatkowski, P. Phillips, P. Schmidt, Y. Shin, J. Econometrics 54, 159 (1992)

    Article  MATH  Google Scholar 

  19. C. W. J. Granger, P. Newbold, J. Econ. 2, 111 (1974)

    Article  MATH  Google Scholar 

  20. R. R. Nigmatullin, The Journal of Applied Nonlinear Dynamics 1, 173 (2012)

    Google Scholar 

  21. R. R. Nigmatullin, The Journal of Applied Nonlinear Dynamics 1, 207 (2012)

    Google Scholar 

  22. R. R. Nigmatullin, Phys. Wave Phenom.16, 119 (2008)

    Article  ADS  Google Scholar 

  23. R. R. Nigmatullin, W. Zhang, Commun. Nonlinear Sci. 18, 547 (2013)

    Article  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Theoretical Physics Department, Institute of Physics, Kazan Federal University, Kremlevskaya str., 18, 420008, Kazan, Tatarstan, Russian Federation

    Raoul R. Nigmatullin

  2. Dept. of Electrical Engineering, Institute of Engineering of Polytechnic of Porto, Rua Dr. Antonio Bernardino de Almeida, 431, 4200-072, Porto, Portugal

    José Tenreiro Machado

  3. Dept. of Quantitative Methods, ISCTE Business School, Av. das Forças Armadas, 1649-025, Lisbon, Portugal

    Rui Menezes

Authors
  1. Raoul R. Nigmatullin
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  2. José Tenreiro Machado
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  3. Rui Menezes
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Correspondence to Raoul R. Nigmatullin.

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Nigmatullin, R.R., Machado, J.T. & Menezes, R. Self-similarity principle: the reduced description of randomness. centr.eur.j.phys. 11, 724–739 (2013). https://doi.org/10.2478/s11534-013-0181-9

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  • DOI: https://doi.org/10.2478/s11534-013-0181-9

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