Hilbert-Huang Transform based multifractal analysis of China stock market

In this paper, we employ the Hilbert–Huang Transform to investigate the multifractal character of Chinese stock market based on CSI 300 index. The measured Hilbert moment Lq(ω) shows a power-law behavior on the range 0.01<ω<0.1min−1, equivalent to a time scale range 10<τ<100min. The measured scaling exponents ζ(q) is convex with q and deviates from the value q/2, implying that the property of self-similarity is broken. Moreover, ζ(q) and the corresponding singularity spectrum D(h) can be described by a lognormal model with a Hurst number H=0.50 and an intermittency parameter μ=0.12. Our results suggest that the Chinese stock fluctuation might be captured well by a multifractal random walk model with a proper intermittency parameter.

[1]  Laurent E. Calvet,et al.  A Multifractal Model of Asset Returns , 1997 .

[2]  Norden E. Huang,et al.  On the Filtering Properties of the Empirical Mode Decomposition , 2010, Adv. Data Sci. Adapt. Anal..

[3]  Emmanuel Bacry,et al.  Modelling financial time series using multifractal random walks , 2001 .

[4]  F. Schmitt,et al.  Multifractal description of wind power fluctuations using arbitrary order Hilbert spectral analysis , 2013 .

[5]  François G. Schmitt,et al.  Multifractal analysis of the dollar–yuan and euro–yuan exchange rates before and after the reform of the peg , 2011 .

[6]  J. Peinke,et al.  Turbulent cascades in foreign exchange markets , 1996, Nature.

[7]  Zhi-Qiang Jiang,et al.  Multifractality in stock indexes: Fact or Fiction? , 2007, 0706.2140.

[8]  Y. X. Huang,et al.  Second-order structure function in fully developed turbulence. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  P. Davidson,et al.  Identifying turbulent energy distributions in real, rather than fourier, space. , 2005, Physical review letters.

[10]  Wei-Xing Zhou,et al.  Long-term correlations and multifractal nature in the intertrade durations of a liquid Chinese stock and its warrant , 2010, 1008.0160.

[11]  K. Lai,et al.  A new approach for crude oil price analysis based on Empirical Mode Decomposition , 2008 .

[12]  F. Toschi,et al.  Lagrangian single-particle turbulent statistics through the Hilbert-Huang transform. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  S. S. Shen,et al.  Applications of Hilbert–Huang transform to non‐stationary financial time series analysis , 2003 .

[14]  Ying Yuan,et al.  Multifractal description of stock price index fluctuation using a quadratic function fitting , 2008 .

[15]  Zhi-Qiang Jiang,et al.  Multifractal analysis of Chinese stock volatilities based on the partition function approach , 2008, 0801.1710.

[16]  Norden E. Huang,et al.  On Instantaneous Frequency , 2009, Adv. Data Sci. Adapt. Anal..

[17]  Feng Ma,et al.  Multifractal detrended cross-correlation analysis between the Chinese stock market and surrounding stock markets , 2013 .

[18]  Paulo Gonçalves,et al.  Empirical Mode Decompositions as Data-Driven Wavelet-like Expansions , 2004, Int. J. Wavelets Multiresolution Inf. Process..

[19]  K. Lai,et al.  Forecasting crude oil price with an EMD-based neural network ensemble learning paradigm , 2008 .

[20]  Rosario N. Mantegna,et al.  Turbulence and financial markets , 1996, Nature.

[21]  Y. X. Huang,et al.  An amplitude-frequency study of turbulent scaling intermittency using Empirical Mode Decomposition and Hilbert Spectral Analysis , 2008, 1401.4211.

[22]  Guangxi Cao,et al.  Asymmetric multifractal scaling behavior in the Chinese stock market: Based on asymmetric MF-DFA , 2013 .

[23]  Guangxi Cao,et al.  Multifractal detrended cross-correlations between the Chinese exchange market and stock market , 2012 .

[24]  R. Mantegna,et al.  Scaling behaviour in the dynamics of an economic index , 1995, Nature.

[25]  Rongbao Gu,et al.  Analysis of efficiency for Shenzhen stock market based on multifractal detrended fluctuation analysis , 2009 .

[26]  Y. X. Huang,et al.  Arbitrary-order Hilbert spectral analysis for time series possessing scaling statistics: comparison study with detrended fluctuation analysis and wavelet leaders. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  N. Huang,et al.  A study of the characteristics of white noise using the empirical mode decomposition method , 2004, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[28]  Gbadebo Oladosu,et al.  Identifying the oil price-macroeconomy relationship: An empirical mode decomposition analysis of US data , 2009 .

[29]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.