Self-similarity principle: the reduced description of randomness

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]  Raoul R. Nigmatullin,et al.  Is it Possible to Replace the Probability Distribution Function Describing a Random Process by the Prony’s Spectrum? (I) , 2012 .

[2]  C. Granger,et al.  Spurious regressions in econometrics , 1974 .

[3]  J. Kwapień,et al.  Physical approach to complex systems , 2012 .

[4]  Y. Chen,et al.  Fractional Processes and Fractional-Order Signal Processing , 2012 .

[5]  R. Nigmatullin,et al.  Fluctuation-noise spectroscopy and a “universal” fitting function of amplitudes of random sequences , 2003 .

[6]  R. Lourie,et al.  The Statistical Mechanics of Financial Markets , 2002 .

[7]  Ayumu Yasutomi.  The emergence and collapse of money , 1995 .

[8]  P. Howitt,et al.  The Emergence of Economic Organization , 2000 .

[9]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[10]  Raoul R. Nigmatullin,et al.  NAFASS in action: How to control randomness? , 2013, Commun. Nonlinear Sci. Numer. Simul..

[11]  J. A. Tenreiro Machado,et al.  Identifying economic periods and crisis with the multidimensional scaling , 2011 .

[12]  Raoul R. Nigmatullin,et al.  Universal distribution function for the strongly-correlated fluctuations: General way for description of different random sequences , 2010 .

[13]  J. A. Tenreiro Machado,et al.  Analysis of stock market indices through multidimensional scaling , 2011 .

[14]  R. Nigmatullin.  Eigen-coordinates: New method of analytical functions identification in experimental measurements , 1998 .

[15]  José António Tenreiro Machado,et al.  Fractional Dynamics in Financial Indices , 2012, Int. J. Bifurc. Chaos.

[16]  Co-Movements and Asymmetric Volatility in the Portuguese and U.S. Stock Markets , 2006 .

[17]  Raoul R. Nigmatullin,et al.  Strongly correlated variables and existence of a universal distribution function for relative fluctuations , 2008 .

[18]  P. Phillips,et al.  Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? , 1992 .

[19]  J. Duffy,et al.  Emergence of money as a medium of exchange: An experimental study , 1999 .

[20]  Raoul R. Nigmatullin,et al.  Recognition of nonextensive statistical distributions by the eigencoordinates method , 2000 .

[21]  Raoul R. Nigmatullin,et al.  Fluctuation Metrology Based on the Prony's Spectroscopy (II) , 2012 .

[22]  P. Steerenberg,et al.  Targeting pathophysiological rhythms: prednisone chronotherapy shows sustained efficacy in rheumatoid arthritis. , 2010, Annals of the rheumatic diseases.

[23]  W. Fuller,et al.  LIKELIHOOD RATIO STATISTICS FOR AUTOREGRESSIVE TIME SERIES WITH A UNIT ROOT , 1981 .

[24]  D. Sornette.  Discrete scale invariance and complex dimensions , 1997, cond-mat/9707012.