Hilbert–Huang Transform based multifractal analysis of China stock market

Li, Muyi; Huang, Yongxiang

doi:10.1016/j.physa.2014.03.047

Cited by 29 publications

(16 citation statements)

References 28 publications

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“…where H is the Hurst number, and µ is the intermittency parameter [20]. Note that the lognormal model is firstly introduced by Kolmogorov [13] …”

Section: Resultsmentioning

confidence: 99%

“…Several theoretical models have been put forward to describe the intermittent property of the energy dissipation field, for instance, the lognormal model [13], log-Poisson model [14,15], log-stable model [16,17], to list a few. Multifractality has also been recognized as a common feature of complex dynamic systems, such as financial activities [18][19][20], wind energy [21], geosciences [22,23], to name a few.…”

Section: Introductionmentioning

confidence: 99%

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Intermittency measurement in two-dimensional bacterial turbulence

et al. 2016

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In this paper, an experimental velocity database of a bacterial collective motion , e.g., B. subtilis, in turbulent phase with volume filling fraction 84% provided by Professor Goldstein at the Cambridge University UK, was analyzed to emphasize the scaling behavior of this active turbulence system. This was accomplished by performing a Hilbert-based methodology analysis to retrieve the scaling property without the β−limitation. A dual-power-law behavior separated by the viscosity scale ℓ ν was observed for the qth-order Hilbert moment L q (k). This dual-power-law belongs to an inverse-cascade since the scaling range is above the injection scale R, e.g., the bacterial body length.The measured scaling exponents ζ(q) of both the small-scale (resp. k > k ν ) and large-scale (resp. k < k ν ) motions are convex, showing the multifractality. A lognormal formula was put forward to characterize the multifractal intensity. The measured intermittency parameters are µ S = 0.26 and µ L = 0.17 respectively for the small-and large-scale motions. It implies that the former cascade is more intermittent than the latter one, which is also confirmed by the corresponding singularity spectrum f (α) vs α. Comparison with the conventional two-dimensional Ekman-Navier-Stokes equation, a continuum model indicates that the origin of the multifractality could be a result of some additional nonlinear interaction terms, which deservers a more careful investigation. *

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“…where H is the Hurst number, and µ is the intermittency parameter [20]. Note that the lognormal model is firstly introduced by Kolmogorov [13] …”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Intermittency measurement in two-dimensional bacterial turbulence

et al. 2016

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“…To characterize this multiscale interaction, structure function analysis is used to retrieve the 8 scale invariance for high Reynolds turbulent flows (Kolmogorov, 1941). It is then widely used in a variety of fields, including financial activity (Schmitt et al, 1999;Ghashghaie et al, 1996;Li and Huang, 2014), crack of rock surfaces (Schmittbuhl et al, 1995), rainfall patterns (Tessier et al, 1996), etc., to retrieve the scale invariant parameters. 9 To characterize the interaction between different scales, the qth-order structure function is defined as follows:…”

Section: Structure Function Analysismentioning

confidence: 99%

Spatial statistics of atmospheric particulate matter in China

Gao

Wang

Huang

et al. 2016

Atmospheric Environment

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In this paper, the spatial dynamics of the atmospheric particulate matters (resp. PM 10 and PM 2.5 ) are studied using turbulence methodologies. It is found experimentally that the spatial correlation function ρ(r) shows a log-law on the mesoscale range, i.e., 50 ≤ r ≤ 500 km, with an experimental scaling exponent β = 0.45. The spatial structure function shows a powerlaw behavior on the mesoscale range 90 ≤ r ≤ 500 km. The experimental scaling exponent ζ(q) is convex, showing that the intermittent correction is relevant in characterizing the spatial dynamic of particulate matter. The measured singularity spectrum f (α) also shows its multifractal nature. Experimentally, the particulate matter is more intermittent than the passive scalar, which could be partially due to the mesoscale movements of the atmosphere, and also due to local sources, such as local industry activities.

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“…Turbulence or turbulence-like phenomena are ubiquitous in the nature, which is often characterized by scale invariance in both spatial and temporal domains. It ranges from the evolution of the universe [17], movement of atmosphere and ocean [18,19], the painting by Leonardo da Vinci [20] or van Gogh [21], collective motion of bacteria [22,23], the Bose-Einstein condensate [24], financial activity [25][26][27][28][29], etc. Note that turbulence is usually recognized by its main features that a broad range of spatial and temporal scales or many degrees of freedom are excited in the dynamical system [30,31].…”

Section: Introductionmentioning

confidence: 99%

Turbulent lithosphere deformation in the Tibetan Plateau

et al. 2019

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In this work, we show that the Tibetan Plateau deformation demonstrates a turbulence-like statistics, e.g., spatial invariance cross continuous scales. A dual-power-law behavior is evident to show the existence of two possible conversation laws for the enstrophy-like cascade on the range 500 r 2, 000 km and kinetic-energy-like cascade on the range 50 r 500 km. The measured second-order structure-function scaling exponents ζ(2) are similar with the counterpart of the Fourier scaling exponents observed in the atmosphere, where in the latter case the earth rotation is relevant. The turbulent statistics observed here for nearly zero Reynolds number flow is favor to be interpreted by the geostrophic turbulence theory. Moreover, the intermittency correction is recognized with an intensity to be close to the one of the hydrodynamic turbulence of high Reynolds number turbulent flows, implying a universal scaling feature of very different turbulent flows. Our results not only shed new light on the debate regarding the mechanism of the Tibetan Plateau deformation, but also lead to new challenge for the geodynamic modelling using Newton or non-Newtonian model that the observed turbulence-like features have to be taken into account. *

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Hilbert–Huang Transform based multifractal analysis of China stock market

Cited by 29 publications

References 28 publications

Intermittency measurement in two-dimensional bacterial turbulence

Intermittency measurement in two-dimensional bacterial turbulence

Spatial statistics of atmospheric particulate matter in China

Turbulent lithosphere deformation in the Tibetan Plateau

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