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Journal of Applied Nonlinear Dynamics 2(2) (2013) 141--150 | DOI:10.5890/JAND.2013.04.003

Raoul R. Nigmatullin$^{1}$; J.A. Tenreiro Machado$^{2}$

$^{1}$ Theoretical Physics Department, Institute of Physics, Kazan(Volga Region) Federal University, Kremlevskaya str., 18, 420008, Kazan, Tatarstan, Russian Federation

$^{2}$ ISEP-Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, Rua Dr. Antonio Bernardino de Almeida, 431 4200-072 Porto, Portugal

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Abstract

Many random signals with clearly expressed trends can have selfsimilar properties. In order to see this self-similar property new presentation of signals is suggested. A novel algorithm for inverse solution of the scaling equation is developed. This original algorithm allows finding the scaling parameters, the corresponding power-law exponent and the unknown log-periodic function from the fitting procedure. The effectiveness of algorithm is tested in financial data revealing season fluctuations of annual, monthly and weekly prices. The general recommendations are given that allow the verification of this algorithm in general data series.

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