Full-text resources of PSJD and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl

PL EN


Preferences help
enabled [disable] Abstract
Number of results

Journal

2013 | 11 | 6 | 724-739

Article title

Self-similarity principle: the reduced description of randomness

Content

Title variants

Languages of publication

EN

Abstracts

EN
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.

Publisher

Journal

Year

Volume

11

Issue

6

Pages

724-739

Physical description

Dates

published
1 - 6 - 2013
online
9 - 10 - 2013

Contributors

  • Theoretical Physics Department, Institute of Physics, Kazan Federal University, Kremlevskaya str., 18, 420008, Kazan, Tatarstan, Russian Federation
author
  • Dept. of Electrical Engineering, Institute of Engineering of Polytechnic of Porto, Rua Dr. Antonio Bernardino de Almeida, 431, 4200-072, Porto, Portugal
author
  • Dept. of Quantitative Methods, ISCTE Business School, Av. das Forças Armadas, 1649-025, Lisbon, Portugal

References

  • [1] J. Kwapien, S. Drozdz, Phys. Rep. 515, 115 (2012) http://dx.doi.org/10.1016/j.physrep.2012.01.007[Crossref]
  • [2] A. Yasutomi, Physica D 82, 180 (1995) http://dx.doi.org/10.1016/0167-2789(94)00234-H[Crossref]
  • [3] J. Duffy, J. Ochs, Am. Econ. Rev. 89, 847 (1999) http://dx.doi.org/10.1257/aer.89.4.847[Crossref]
  • [4] P. Howlett, R. Clower, J. Econ. Behav. Organ. 41, 55 (2000) http://dx.doi.org/10.1016/S0167-2681(99)00087-6[Crossref]
  • [5] J. Feder, Fractals, Plenum Press (New York and London, 1988) http://dx.doi.org/10.1007/978-1-4899-2124-6[Crossref]
  • [6] H. Sheng, Y. Chen, T. Qui, Fractional Processes and Fractional-Order Signal Processing, Springer-Verlag (NY, Heidelberg, London, 2012) http://dx.doi.org/10.1007/978-1-4471-2233-3[Crossref]
  • [7] R. R. Nigmatullin, G. Smith, Physica A 320, 291 (2003) http://dx.doi.org/10.1016/S0378-4371(02)01600-X[Crossref]
  • [8] R. R. Nigmatullin, Commun. Nonlinear Sci. 15, 637 (2010) http://dx.doi.org/10.1016/j.cnsns.2009.05.019[Crossref]
  • [9] D. Sornette, Phys. Rep. 297, 239 (1998) http://dx.doi.org/10.1016/S0370-1573(97)00076-8[Crossref]
  • [10] J. Voigt, The Statistical Mechanics of the Financial Markets, 3rd edition (Springer-Verlag. Berlin-Heidelberg, 2005)
  • [11] R. R. Nigmatullin, J. Appl. Magn. Reson. 14, 601 (1998) http://dx.doi.org/10.1007/BF03161865[Crossref]
  • [12] R. R. Nigmatullin, Physica A 285, 547 (2000) http://dx.doi.org/10.1016/S0378-4371(00)00237-5[Crossref]
  • [13] R. Menezes, N. B. Ferreira, D. A. Mendes, Nonlinear Dynam. 44, 359 (2006) http://dx.doi.org/10.1007/s11071-006-2020-7[Crossref]
  • [14] J. T. Machado, G. M. Duarte, F. B. Duarte, Nonlinear Dynam. 63, 611 (2011) http://dx.doi.org/10.1007/s11071-010-9823-2[Crossref]
  • [15] J. T. Machado, F. B. Duarte, G. M. Duarte, Commun. Nonlinear Sci. 16, 4610 (2011) http://dx.doi.org/10.1016/j.cnsns.2011.04.027[Crossref]
  • [16] J. T. Machado, G. M. Duarte, F. B. Duarte, Int. J. Bifurcat. Chaos 22, 1250249 (2012) http://dx.doi.org/10.1142/S0218127412502495[Crossref]
  • [17] D. A. Dickey, W. A. Fuller, Econometrica 49, 1057 (1981) http://dx.doi.org/10.2307/1912517[Crossref]
  • [18] D. Kwiatkowski, P. Phillips, P. Schmidt, Y. Shin, J. Econometrics 54, 159 (1992) http://dx.doi.org/10.1016/0304-4076(92)90104-Y[Crossref]
  • [19] C. W. J. Granger, P. Newbold, J. Econ. 2, 111 (1974) http://dx.doi.org/10.1016/0304-4076(74)90034-7[Crossref]
  • [20] R. R. Nigmatullin, The Journal of Applied Nonlinear Dynamics 1, 173 (2012)
  • [21] R. R. Nigmatullin, The Journal of Applied Nonlinear Dynamics 1, 207 (2012)
  • [22] R. R. Nigmatullin, Phys. Wave Phenom.16, 119 (2008) http://dx.doi.org/10.3103/S1541308X08020064[Crossref]
  • [23] R. R. Nigmatullin, W. Zhang, Commun. Nonlinear Sci. 18, 547 (2013) http://dx.doi.org/10.1016/j.cnsns.2012.07.008[Crossref]

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.-psjd-doi-10_2478_s11534-013-0181-9
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.