EPL, 81 (2008) 18002
DOI: 10.1209/0295-5075/81/18002

Multifractality and heteroscedastic dynamics: An application to time series analysis

C. M. Nascimento¹, H. B. N. Júnior¹, H. D. Jennings², M. Serva³, Iram Gleria¹ and G. M. Viswanathan<sup>1

1</sup>  Instituto de Física, Universidade Federal de Alagoas - 57072-970, Maceió-AL, Brazil
²  Instituto de Ciências Humanas, Comunicação e Artes, Universidade Federal de Alagoas 57072-970, Maceió-AL, Brazil
³  Dipartimento di Matematica and INFM, Università dell'Aquila - I-67010 L'Aquila, Italy

received 26 July 2007; accepted in final form 30 October 2007; published January 2008
published online 3 December 2007

Abstract
An increasingly important problem in physics concerns scale invariance symmetry in diverse complex systems, often characterized by heteroscedastic dynamics. We investigate the nature of the relationship between the heteroscedastic and fractal aspects of the dynamics of complex systems, by analyzing the sensitivity to heteroscedasticity of the scaling properties of weakly nonstationary time series. By using multifractal detrended fluctuation analysis, we study the singularity spectra of currency exchange rate fluctuations, after partially or completely eliminating n-point correlations via data shuffling techniques. We conclude that heteroscedasticity can significantly increase multifractality and interpret these findings in the context of self-organizing and adaptive complex systems.

PACS
89.65.Gh - Economics; econophysics, financial markets, business and management.
89.20.-a - Interdisciplinary applications of physics.
02.50.-r - Probability theory, stochastic processes, and statistics.

© EPLA 2008