Issue
EPL
Volume 88, Number 2, October 2009
Article Number 28004
Number of page(s) 6
Section Interdisciplinary Physics and Related Areas of Science and Technology
DOI http://dx.doi.org/10.1209/0295-5075/88/28004
Published online 29 October 2009
EPL, 88 (2009) 28004
DOI: 10.1209/0295-5075/88/28004

The components of empirical multifractality in financial returns

Wei-Xing Zhou1, 2, 3, 4

1  School of Business, East China University of Science and Technology - Shanghai 200237, China,
2  School of Science, East China University of Science and Technology - Shanghai 200237, China
3  Research Center for Econophysics, East China University of Science and Technology - Shanghai 200237, China
4  Research Center on Fictitious Economics & Data Science, Chinese Academy of Sciences - Beijing 100080, China

wxzhou@ecust.edu.cn

received 7 August 2009; accepted in final form 1 October 2009; published October 2009
published online 29 October 2009

Abstract
We perform a systematic investigation on the components of the empirical multifractality of financial returns using the daily data of Dow Jones Industrial Average from 26 May 1896 to 27 April 2007 as an example. The temporal structure and fat-tailed distribution of the returns are considered as possible influence factors. The multifractal spectrum of the original return series is compared with those of four kinds of surrogate data: 1) shuffled data that contain no temporal correlation but have the same distribution, 2) surrogate data in which any nonlinear correlation is removed but the distribution and linear correlation are preserved, 3) surrogate data in which large positive and negative returns are replaced with small values, and 4) surrogate data generated from alternative fat-tailed distributions with the temporal correlation preserved. We find that all these factors have influence on the multifractal spectrum. We also find that the temporal structure (linear or nonlinear) has minor impact on the singularity width $\Delta \alpha $ of the multifractal spectrum while the fat tails have major impact on $\Delta \alpha $, which confirms the earlier results. In addition, the linear correlation is found to have only a horizontal translation effect on the multifractal spectrum in which the distance is approximately equal to the difference between its DFA scaling exponent and 0.5. Our method can also be applied to other financial or physical variables and other multifractal formalisms.

PACS
89.65.Gh - Economics; econophysics, financial markets, business and management.
89.75.Da - Systems obeying scaling laws.
05.45.Df - Fractals.

© EPLA 2009