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.
[1] J. Kwapien, S. Drozdz, Phys. Rep. 515, 115 (2012) http://dx.doi.org/10.1016/j.physrep.2012.01.00710.1016/j.physrep.2012.01.007Search in Google Scholar
[2] A. Yasutomi, Physica D 82, 180 (1995) http://dx.doi.org/10.1016/0167-2789(94)00234-H10.1016/0167-2789(94)00234-HSearch in Google Scholar
[3] J. Duffy, J. Ochs, Am. Econ. Rev. 89, 847 (1999) http://dx.doi.org/10.1257/aer.89.4.84710.1257/aer.89.4.847Search in Google Scholar
[4] P. Howlett, R. Clower, J. Econ. Behav. Organ. 41, 55 (2000) http://dx.doi.org/10.1016/S0167-2681(99)00087-610.1016/S0167-2681(99)00087-6Search in Google Scholar
[5] J. Feder, Fractals, Plenum Press (New York and London, 1988) http://dx.doi.org/10.1007/978-1-4899-2124-610.1007/978-1-4899-2124-6Search in Google Scholar
[6] H. Sheng, Y. Chen, T. Qui, Fractional Processes and Fractional-Order Signal Processing, Springer-Verlag (NY, Heidelberg, London, 2012) http://dx.doi.org/10.1007/978-1-4471-2233-310.1007/978-1-4471-2233-3Search in Google Scholar
[7] R. R. Nigmatullin, G. Smith, Physica A 320, 291 (2003) http://dx.doi.org/10.1016/S0378-4371(02)01600-X10.1016/S0378-4371(02)01600-XSearch in Google Scholar
[8] R. R. Nigmatullin, Commun. Nonlinear Sci. 15, 637 (2010) http://dx.doi.org/10.1016/j.cnsns.2009.05.01910.1016/j.cnsns.2009.05.019Search in Google Scholar
[9] D. Sornette, Phys. Rep. 297, 239 (1998) http://dx.doi.org/10.1016/S0370-1573(97)00076-810.1016/S0370-1573(97)00076-8Search in Google Scholar
[10] J. Voigt, The Statistical Mechanics of the Financial Markets, 3rd edition (Springer-Verlag. Berlin-Heidelberg, 2005) Search in Google Scholar
[11] R. R. Nigmatullin, J. Appl. Magn. Reson. 14, 601 (1998) http://dx.doi.org/10.1007/BF0316186510.1007/BF03161865Search in Google Scholar
[12] R. R. Nigmatullin, Physica A 285, 547 (2000) http://dx.doi.org/10.1016/S0378-4371(00)00237-510.1016/S0378-4371(00)00237-5Search in Google Scholar
[13] R. Menezes, N. B. Ferreira, D. A. Mendes, Nonlinear Dynam. 44, 359 (2006) http://dx.doi.org/10.1007/s11071-006-2020-710.1007/s11071-006-2020-7Search in Google Scholar
[14] J. T. Machado, G. M. Duarte, F. B. Duarte, Nonlinear Dynam. 63, 611 (2011) http://dx.doi.org/10.1007/s11071-010-9823-210.1007/s11071-010-9823-2Search in Google Scholar
[15] J. T. Machado, F. B. Duarte, G. M. Duarte, Commun. Nonlinear Sci. 16, 4610 (2011) http://dx.doi.org/10.1016/j.cnsns.2011.04.02710.1016/j.cnsns.2011.04.027Search in Google Scholar
[16] J. T. Machado, G. M. Duarte, F. B. Duarte, Int. J. Bifurcat. Chaos 22, 1250249 (2012) http://dx.doi.org/10.1142/S021812741250249510.1142/S0218127412502495Search in Google Scholar
[17] D. A. Dickey, W. A. Fuller, Econometrica 49, 1057 (1981) http://dx.doi.org/10.2307/191251710.2307/1912517Search in Google Scholar
[18] D. Kwiatkowski, P. Phillips, P. Schmidt, Y. Shin, J. Econometrics 54, 159 (1992) http://dx.doi.org/10.1016/0304-4076(92)90104-Y10.1016/0304-4076(92)90104-YSearch in Google Scholar
[19] C. W. J. Granger, P. Newbold, J. Econ. 2, 111 (1974) http://dx.doi.org/10.1016/0304-4076(74)90034-710.1016/0304-4076(74)90034-7Search in Google Scholar
[20] R. R. Nigmatullin, The Journal of Applied Nonlinear Dynamics 1, 173 (2012) 10.5890/JAND.2012.05.005Search in Google Scholar
[21] R. R. Nigmatullin, The Journal of Applied Nonlinear Dynamics 1, 207 (2012) 10.5890/JAND.2012.06.001Search in Google Scholar
[22] R. R. Nigmatullin, Phys. Wave Phenom.16, 119 (2008) http://dx.doi.org/10.3103/S1541308X0802006410.3103/S1541308X08020064Search in Google Scholar
[23] R. R. Nigmatullin, W. Zhang, Commun. Nonlinear Sci. 18, 547 (2013) http://dx.doi.org/10.1016/j.cnsns.2012.07.00810.1016/j.cnsns.2012.07.008Search in Google Scholar
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