Joint multifractal analysis based on wavelet leaders |
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| Authors: | Zhi-Qiang Jiang Yan-Hong Yang Gang-Jin Wang Wei-Xing Zhou |
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| Affiliation: | 1.School of Business,East China University of Science and Technology,Shanghai,China;2.Research Center for Econophysics,East China University of Science and Technology,Shanghai,China;3.Department of Physics and Center for Polymer Studies,Boston University,Boston,USA;4.Business School and Center of Finance and Investment Management,Hunan University,Changsha,China;5.Department of Mathematics,East China University of Science and Technology,Shanghai,China |
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| Abstract: | Mutually interacting components form complex systems and these components usually have long-range 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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