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Joint multifractal analysis based on wavelet leaders |
Zhi-Qiang Jiang1,2,3( ),Yan-Hong Yang1,2,3,Gang-Jin Wang3,4(),Wei-Xing Zhou1,2,5() |
1. School of Business, East China University of Science and Technology, Shanghai 200237, China
2. Research Center for Econophysics, East China University of Science and Technology, Shanghai 200237, China
3. Department of Physics and Center for Polymer Studies, Boston University, Boston, MA 02215, USA
4. Business School and Center of Finance and Investment Management, Hunan University, Changsha 410082, China
5. Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China |
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Abstract Mutually interacting components form complex systems and these components usually have longrange cross-correlated outputs. Using wavelet leaders, we propose a method for characterizing the joint multifractal nature of these long-range cross correlations; we call this method joint multifractal analysis based on wavelet leaders (MF-X-WL). We test the validity of the MF-X-WL method by performing extensive numerical experiments on dual binomial measures with multifractal cross correlations and bivariate fractional Brownian motions (bFBMs) with monofractal cross correlations. Both experiments indicate that MF-X-WL is capable of detecting cross correlations in synthetic data with acceptable estimating errors. We also apply the MF-X-WL method to pairs of series from financial markets (returns and volatilities) and online worlds (online numbers of different genders and different societies) and determine intriguing joint multifractal behavior.
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| Keywords
joint multifractal analysis
wavelet leader
binomial measure
bivariate fractional Brownian motion
econophysics
online world
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Corresponding Author(s):
Zhi-Qiang Jiang,Gang-Jin Wang,Wei-Xing Zhou
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Issue Date: 17 March 2017
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