Joint multifractal analysis based on wavelet leaders

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 anal...

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Bibliographic Details
Published in:Frontiers of physics 2017-12, Vol.12 (6), p.127-137, Article 128907
Main Authors: Jiang, Zhi-Qiang, Yang, Yan-Hong, Wang, Gang-Jin, Zhou, Wei-Xing
Format: Article
Language:English
Subjects:
Astronomy
Astrophysics and Cosmology
Atomic
binomial measure
Bivariate analysis
bivariate fractional Brownian motion
Complex systems
Condensed Matter Physics
Correlation analysis
Cross correlation
econophysics
Fractal analysis
Fractals
joint multifractal analysis
Methods
Molecular
online world
Optical and Plasma Physics
Particle and Nuclear Physics
Physics
Physics and Astronomy
Research Article
Securities markets
Soft-Matter Physics and Complex Systems
Synthetic data
wavelet leader
Wavelet transforms
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Summary: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 tile 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.
ISSN:2095-0462
2095-0470
DOI:10.1007/s11467-017-0674-x