Joint multifractal analysis based on the partition function approach: analytical analysis, numerical simulation and empirical application

Xie, Wen-Jie; Jiang, Zhi‐Qiang; Gu, Gao-Feng; Xiong, Xiong; Zhou, Wei‐Xing

doi:10.1088/1367-2630/17/10/103020

Cited by 77 publications

(50 citation statements)

References 80 publications

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“…The quality of such fit determines in turn the extent of the error bar on τ q . The τ q vs q curve (middle panel) does not present a single linear behaviour, but a typically multifractal behaviour with two different slopes for the two q < 0 and q > 0 regimes, and a non-linear behaviour in the transition zone (cf., e.g., Movahed et al 2011;Xie et al 2015). Similarly, the obtained D q vs q curve (right panel) is far from being constant (cf., e.g., Halsey et al 1986;Meneveau & Sreenivasan 1987), confirming that the analysed image presents a multifractal rather than a simple mono-fractal character.…”

Section: Practical Derivation Of Multifractal Parametersmentioning

confidence: 94%

Multifractal analysis of the interstellar medium: first application to Hi-GAL observations

Elia

Strafella

Dib

et al. 2018

Monthly Notices of the Royal Astronomical Society

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The multifractal geometry remains an under-exploited approach to describe and quantify the large-scale structure of interstellar clouds. In this paper, the typical tools of multifractal analysis are applied to Herschel far-infrared (70-500 µm) dust continuum maps, which represent an ideal case of study. This dust component is a relatively optically thin tracer at these wavelengths and the size in pixel of the maps is well suitable for this statistical analysis. We investigate the so-called multifractal spectrum and generalised fractal dimension of six Hi-GAL regions in the third Galactic quadrant. We measure systematic variations of the spectrum at increasing wavelength, which generally correspond to an increasing complexity of the image, and we observe peculiar behaviours of the investigated fields, strictly related to the presence of highemission regions, which in turn are connected to star formation activity. The same analysis is applied to synthetic column density maps, generated from numerical turbulent molecular cloud models and from fractal Brownian motion (fBm), allowing for the confrontation of the observations with models with well controlled physical parameters. This comparison shows that, in terms of multifractal descriptors of the structure, fBm images exhibit a very different, quite unrealistic behaviour when compared with Hi-GAL observations, whereas the numerical simulations appear in some cases (depending on the specific model) more similar to the observations. Finally, the link between mono-fractal parameters (commonly found in the literature) and multifractal indicators is investigated: the former appear to be only partially connected with the latter, with the multifractal analysis offering a more extended and complete characterization of the cloud structure.

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Section: Practical Derivation Of Multifractal Parametersmentioning

confidence: 94%

Multifractal analysis of the interstellar medium: first application to Hi-GAL observations

Elia

Strafella

Dib

et al. 2018

Monthly Notices of the Royal Astronomical Society

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“…Multifractals is ubiquitous in natural and social sciences [23]. Many different methods have been applied to characterize the hidden multifractal behavior of different social variables, such as the fluctuation scaling analysis [24,25], the structure function method [26][27][28][29], the multifractal detrended fluctuation analysis (MF-DFA) [30][31][32], the multifractal detrending moving average analysis (MF-DMA) [33], the partition function method [34][35][36][37][38], the multiplier method [39][40][41], the wavelet transform approaches [42,43], and the microcanonical multifractal analysis [44,45], some of which are borrowed from the multifractal analysis of turbulence data. We apply the partition function approach to the absolute fluctuation time series of 1min online user number to uncover the multifractal nature of the records in the present study.…”

Section: Introductionmentioning

confidence: 99%

Statistical properties of user activity fluctuations in virtual worlds

Yang

Xie

et al. 2017

Chaos, Solitons & Fractals

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User activity fluctuations reflect the performance of online society. We investigate the statistical properties of 1-min user activity time series of simultaneously online users inhabited in 95 independent virtual worlds. The number of online users exhibits clear intraday and weekly patterns due to human's circadian rhythms and week cycles. Statistical analysis shows that the distribution of absolute activity fluctuations has a power-law tail for 44 virtual worlds with an average tail exponent close to 2.15. The partition function approach unveils that the absolute activity fluctuations possess multifractal features for all the 95 virtual worlds. For the sample of 44 virtual worlds with power-law tailed distributions of the absolute activity fluctuations, the width of singularity ∆α is negatively correlated with the maximum activity (p-value=0.070) and the time to the maximum activity (p-value=0.010). The negative correlations are not observed for neither the other 51 virtual worlds nor the whole sample of the 95 virtual worlds. In addition, numerical experiments indicate that both temporal structure and large fluctuations have influence on the multifractal spectrum. We also find that the temporal structure has stronger impact on the singularity width than large fluctuations. [Chaos, Solitons & Fractals 105, 271-278 (2017)]

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“…For future developments we are planning to study the consequences of these considerations on the scaling in the physical time, which, making the time series synchronous, would give us a natural setting in order to extend our approach to the study of the multivariate multifractality [65,66].…”

Section: Discussionmentioning

confidence: 99%

Asymptotic scaling properties and estimation of the generalized Hurst exponents in financial data

2017

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We propose a method to measure the Hurst exponents of financial time series. The scaling of the absolute moments against the aggregation horizon of real financial processes and of both uniscaling and multiscaling synthetic processes converges asymptotically towards linearity in log-log scale. In light of this we found appropriate a modification of the usual scaling equation via the introduction of a filter function. We devised a measurement procedure which takes into account the presence of the filter function without the need of directly estimating it. We verified that the method is unbiased within the errors by applying it to synthetic time series with known scaling properties. Finally we show an application to empirical financial time series where we fit the measured scaling exponents via a second or a fourth degree polynomial, which, because of theoretical constraints, have respectively only one and two degrees of freedom. We found that on our data set there is not clear preference between the second or fourth degree polynomial. Moreover the study of the filter functions of each time series shows common patterns of convergence depending on the momentum degree.

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Joint multifractal analysis based on the partition function approach: analytical analysis, numerical simulation and empirical application

Cited by 77 publications

References 80 publications

Multifractal analysis of the interstellar medium: first application to Hi-GAL observations

Multifractal analysis of the interstellar medium: first application to Hi-GAL observations

Statistical properties of user activity fluctuations in virtual worlds

Asymptotic scaling properties and estimation of the generalized Hurst exponents in financial data

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