Strength Of Multifractality Research Articles

Analysis of Multifractals in Game Behaviors

We study the diffusive process and the multifractal property in the Baduk. We are able to ascertain the superdiffusive process that the dispersion is proportional to tɛ with the scaling exponent ɛ =1.66±0.26 for our model. After simulating the multifractal behavior, we analyze the multifractal strength of three different segments.

Multifractal characterization of water-worked gravel surfaces

This study investigates the roughness of water-worked gravel surfaces using stable gravel-beds armoured in flume and field experiments. As an alternative to traditional approaches, multifractal analysis is employed to investigate the roughness of these surfaces. Power spectra analysis is used to study scale-invariant regimes, defined by the ranges of scales where the spectra follow power laws. Then, multifractal spectra are calculated and analysed. The strength of multifractality reflecting heterogeneity of elevations is related to the development of a stable armour layer. The development of armouring processes of the gravel surfaces formed in the flume experiments is investigated using the effective grain size approach based on Gessler's model. For surfaces in the field, the two-dimensional second-order structure function is used to study the static armour surfaces due to the absence of historical hydrological data. The results of these analyses confirm the results of multifractal analyses.

Multifractal analysis of China's agricultural commodity futures markets

Abstract We investigate the multifractal characteristics of the volatility time series from China's agricultural commodity futures markets, using Multifractal Detrended Fluctuation Analysis and multifractal spectrum analysis. We find that prominent multifractal features exit in China's major agricultural commodity futures markets, including the Hard Winter Wheat (HW) futures, the Strong Gluten Wheat (SG) futures, Soy Bean (SB) futures and corn futures. Furthermore, the multifractality strength and multifractal spectrum width of HW futures are both bigger than that of SG, SB and corn futures, implying that the market risk for HW futures might be the strongest among all the four futures contracts. Finally, comparing empirical results of shuffling and surrogate data, we also find that nonlinear temporal correlations instead of non-Gaussian distribution constitute the major contributions in the formation of multifractal features in these four agricultural commodity futures markets.

Unconditional uncertainties of historical and simulated river flows subjected to climate change

► Observed and simulated river flows exhibit similar multifractal behavior. ► Multifractal characteristics have significant implications for uncertainty estimates. ► Climate Change can alter the multifractal character of river flows. ► Uncertainty due to multifractal variation is on the order of +/- 50%. ► Uncertainty due to emissions scenarios and GCM selection is on the order of +/- 20%. The objective of this study was to estimate the unconditional sample uncertainty of observed streamflows and streamflows simulated from a hydrologic model (MISBA) for the Fraser River Basin (FRB) and the Athabasca River Basin (ARB) of Canada under historic conditions and under future conditions simulated by General Circulation Models (GCMs). For each basin, the multifractal properties of 54 simulated hydrographs based on the predictions of seven GCMs and four climate scenarios over three 30-year periods of the 21st century were evaluated and used to generate extended artificial time series by the randomized generalized multifractal cascade model. Uncertainty estimates derived from this multifractal approach were compared with classical statistics, Hurst exponent, and autocorrelation methods. The multifractal approach resulted in greater departures from statistical independence, higher skewness, and a wider range of flows over a 30-year time scale than the other methods. Under climate change, the multifractal strength of streamflows of FRB increased with temperature as the snow fed character of the basin weakened, but in the colder ARB, a decrease in multifractal strength resulted under rising temperatures because of declined snow packs. The estimated unconditional sample uncertainty was compared with uncertainty associated with model and emissions scenario selection. Among four major sources of uncertainty, uncertainty associated with two different hydrologic models (MISBA and SAC-SMA) and global emission patterns in the 21st century were relatively small (20% or less) even though for the latter, the range of SRES climate scenarios may not be representative of future economy and the seven GCMs may not accurately represent actual physical processes. The uncertainties associated with multifractal variation were the largest, on the order of ±50%.

Are developed and emerging agricultural futures markets multifractal? A comparative perspective

Although there are many reports on the empirical evidence of the existence of multifractality in various financial or commodity markets in current literature, few can be found to compare the multifractal properties of emerging and developed economies, especially for agricultural futures markets in those countries (regions). We therefore chose China as the representative of the transition and emerging economies, and USA as the representative of developed ones. We attempt to find the answers to the following questions: (1) Are all those different markets multifractal? (2) What are the dynamical causes for multifractality in those markets (if any)? (3) Are the multifractality strengths in those markets of the transition and emerging economies weaker (or stronger) than those of the developed ones? To answer these questions, Multifractal Detrended Fluctuation Analysis (MF-DFA) are applied to study some of the representative agricultural futures markets in China and USA, namely, wheat, soy meal, soybean and corn. Our results suggest that all the markets of China and USA exhibit multifractal properties except US soybean market, which is much closer to mono-fractal comparing with China’s soybean market. To investigate the sources of multifractality, shuffling and phase randomization procedures are applied to destroy the temporal correlations and non-Gaussian distributions respectively. We found that multifractality can be mainly attributed to the non-Gaussian probability distribution and secondarily to the nonlinear temporal correlation mechanism for all the markets, except US soybean and soy meal, which derives from some other unknown factors. Furthermore, the average of τ ( q ) are applied to obtain the multifractal spectra of the two markets as a whole. The results show that the width of the multifractal spectrum of US agricultural futures markets is significantly narrower than that of China’s. Based on our findings, we proposed a hypothesis that the strength of multifractality in developed economies may be weaker than that in emerging and transition ones.

Multifractal properties of the Indian financial market

We investigate the multifractal properties of the logarithmic returns of the Indian financial indices (BSE & NSE) by applying the multifractal detrended fluctuation analysis. The results are compared with that of the US S&P 500 index. Numerically we find that q th-order generalized Hurst exponents h ( q ) and τ ( q ) change with the moments q . The nonlinear dependence of these scaling exponents and the singularity spectrum f ( α ) show that the returns possess multifractality. By comparing the MF-DFA results of the original series to those for the shuffled series, we find that the multifractality is due to the contributions of long-range correlations as well as the broad probability density function. The financial markets studied here are compared with the Binomial Multifractal Model (BMFM) and have a smaller multifractal strength than the BMFM.

Wavelet multiresolution based multifractal analysis of electric fields by lightning return strokes

Lightning can be seen as a large-scale cooperative phenomenon, which may evolve in a self-similar cascaded way. Using the electric field waveforms recorded by the slow antenna system, the mono- and multifractal behaviors of 115 first return strokes in negative cloud-to-ground discharges have been investigated with a wavelet multiresolution based multifractal method. The results show that the return stroke process, in term of its electric field waveform, has apparent fractality and strong degree of multifractality. The multifractal spectra obtained for the 115 cases are all well fitted to a modified version of the binomial cascade multifractal model. The width of the multifractal spectra, which measure the strength of multifractality, is 1.6 on average. The fractal dimension of the electric field waveforms ranges from 1.2 to 1.5 with an average of 1.3, a similar value to the fractal dimension of the lightning channel obtained by others. This suggests that the lightning-produced electric fields may have the same fractal dimension as its channel. The relationship between the peak current of a return stroke and the charge deposition in its channel is also discussed. The results suggest that the wavelet and scaling analysis may be a powerful tool in interpretation of the lightning-produced electric fields and therefore in understanding lightning.

Interleaving distribution of multifractal strength of 16-channel EEG signals

Multifractal characteristics of 16-channel human electroencephalogram (EEG) signals under eye-closed rest are analyzed for the first time. The result shows that the EEGs from the different sites on the scalp have different multifractal characteristics and the multifractal strength value Δα exhibits a kind of interleaving and left-right opposite distribution on scalp. This distribution rule is consistent with the localization of function and the lateralization theory in physiology. So Δα can become an effective parameter to describe the brain potential character. And such a Δα stable distribution rule on sites of the scalp means a classic cerebral cortex active state.