Source Of Multifractality Research Articles

Dynamic relationship between Japanese Yen exchange rates and market anxiety: A new perspective based on MF-DCCA

This paper investigates the dynamic relationship between Japanese Yen exchange rates and market anxiety during the period from January 5, 1998 to April 18, 2016. A quantitative technique of multifractal detrended cross-correlation analysis (MF-DCCA) is used to explore the multifractal features of the cross-correlations between USD/JPY, AUD/JPY exchange rates and the market anxiety gauge VIX. The investigation shows that the causal relationship between Japanese Yen exchange rates and VIX are bidirectional in general, and the cross-correlations between the two sets of time series are multifractal. Strong evidence suggests that the cross-correlation exponents tend to exhibit different volatility patterns in response to diverse external shocks such as financial distress and widening in interest rate spread, suggesting that the cross-correlated behavior between Japanese Yen exchange rates and VIX are susceptible to economic uncertainties and risks. In addition, the performances of two market anxiety gauges, the VIX and the TED spread, are compared and the sources of multifractality are also traced. Thus, this paper contributes to the literature by shedding light on the unique driving forces of the Yen exchange rate fluctuations in the international foreign exchange market.

Multifractality and Network Analysis of Phase Transition.

Many models and real complex systems possess critical thresholds at which the systems shift dramatically from one sate to another. The discovery of early-warnings in the vicinity of critical points are of great importance to estimate how far the systems are away from the critical states. Multifractal Detrended Fluctuation analysis (MF-DFA) and visibility graph method have been employed to investigate the multifractal and geometrical properties of the magnetization time series of the two-dimensional Ising model. Multifractality of the time series near the critical point has been uncovered from the generalized Hurst exponents and singularity spectrum. Both long-term correlation and broad probability density function are identified to be the sources of multifractality. Heterogeneous nature of the networks constructed from magnetization time series have validated the fractal properties. Evolution of the topological quantities of the visibility graph, along with the variation of multifractality, serve as new early-warnings of phase transition. Those methods and results may provide new insights about the analysis of phase transition problems and can be used as early-warnings for a variety of complex systems.

Coupling detrended fluctuation analysis of Asian stock markets

This paper uses the coupling detrended fluctuation analysis (CDFA) method to investigate the multifractal characteristics of four Asian stock markets using three stock indices: stock price returns, trading volumes and the composite index. The results show that coupled correlations exist among the four stock markets and the coupled correlations have multifractal characteristics. We then use the chi square (χ2) test to identify the sources of multifractality. For the different stock indices, the contributions of a single series to multifractality are different. In other words, the contributions of each country to coupled correlations are different. The comparative analysis shows that the research on the combine effect of stock price returns and trading volumes may be more comprehensive than on an individual index. By comparing the strength of multifractality for original data with the residual errors of the vector autoregression (VAR) model, we find that the VAR model could not be used to describe the dynamics of the coupled correlations among four financial time series.

Multifractal behavior of an air pollutant time series and the relevance to the predictability

Compared with the traditional method of detrended fluctuation analysis, which is used to characterize fractal scaling properties and long-range correlations, this research provides new insight into the multifractality and predictability of a nonstationary air pollutant time series using the methods of spectral analysis and multifractal detrended fluctuation analysis. First, the existence of a significant power-law behavior and long-range correlations for such series are verified. Then, by employing shuffling and surrogating procedures and estimating the scaling exponents, the major source of multifractality in these pollutant series is found to be the fat-tailed probability density function. Long-range correlations also partly contribute to the multifractal features. The relationship between the predictability of the pollutant time series and their multifractal nature is then investigated with extended analyses from the quantitative perspective, and it is found that the contribution of the multifractal strength of long-range correlations to the overall multifractal strength can affect the predictability of a pollutant series in a specific region to some extent. The findings of this comprehensive study can help to better understand the mechanisms governing the dynamics of air pollutant series and aid in performing better meteorological assessment and management.

NEW SUNS IN THE COSMOS. III. MULTIFRACTAL SIGNATURE ANALYSIS

ABSTRACT In the present paper, we investigate the multifractality signatures in hourly time series extracted from the CoRoTspacecraft database. Our analysis is intended to highlight the possibility that astrophysical time series can be members of a particular class of complex and dynamic processes, which require several photometric variability diagnostics to characterize their structural and topological properties. To achieve this goal, we search for contributions due to a nonlinear temporal correlation and effects caused by heavier tails than the Gaussian distribution, using a detrending moving average algorithm for one-dimensional multifractal signals (MFDMA). We observe that the correlation structure is the main source of multifractality, while heavy-tailed distribution plays a minor role in generating the multifractal effects. Our work also reveals that the rotation period of stars is inherently scaled by the degree of multifractality. As a result, analyzing the multifractal degree of the referred series, we uncover an evolution of multifractality from shorter to larger periods.

Revisiting the multifractality in stock returns and its modeling implications

Abstract In this paper, we investigate the multifractality of Chinese and the U.S. stock markets using a multifractal detrending moving average algorithm. The results show that stock returns in both markets are multifractal at a similar extent. We detect the source of multifractality and find that long-range correlations are one of the major sources of multifractality in the US market but not in the Chinese market. Fat-tailed distribution plays a crucial role in multifractality of both markets. As an innovation, we quantify the effect of extreme events on multifractality and find the strong evidence of their contribution to multifractality. Furthermore, we investigate the usefulness of popular ARFIMA-GARCH models with skew-t distribution in capturing multifractality. Our results indicate that these models can capture only a fraction of multifractality. More complex models do not necessarily perform better than simple GARCH models in describing multifractality in stock returns.

Asymmetric multifractal detrending moving average analysis in time series of PM2.5 concentration

Abstract In this paper, we propose the asymmetric multifractal detrending moving average analysis (A-MFDMA) method to explore the asymmetric correlation in non-stationary time series. The proposed method is applied to explore the asymmetric correlation of PM2.5 daily average concentration with uptrends or downtrends in China. In addition, shuffling and phase randomization procedures are applied to detect the sources of multifractality. The results show that existences of asymmetric correlations, and the asymmetric correlations are multifractal. Further, the multifractal scaling behavior in the Chinese PM2.5 is caused not only by long-range correlation but also by fat-tailed distribution, but the major source of multifractality is fat-tailed distribution.

LONG-TERM CORRELATIONS AND MULTIFRACTALITY OF TRAFFIC FLOW MEASURED BY GIS FOR CONGESTED AND FREE-FLOW ROADS

In this paper, a GIS-based method was developed to extract the real-time traffic information (RTTI) from the Google Maps system for city roads. The method can be used to quantify both congested and free-flow traffic conditions. The roadway length was defined as congested length (CL) and free-flow length (FFL). Chengdu, the capital of Sichuan Province in the southwest of China, was chosen as a case study site. The RTTI data were extracted from the Google real-time maps in May 12–17, 2013 and were used to derive the CL and FFL for the study areas. The Multifractal Detrended Fluctuation Analysis (MFDFA) was used to characterize the long-term correlations of CL and FFL time series and their corresponding multifractal properties. Analysis showed that CL and FFL had demonstrated time nonlinearity and long-term correlations and both characteristics differed significantly. A shuffling procedure and a phase randomization procedure were further integrated with multifractal detrending moving average (MFDMA) to identify the major sources of multifractality of these two time series. The results showed that a multifractal process analysis could be used to characterize complex traffic data. Traffic data collected and methods developed in this paper will help better understand the complex traffic systems.

Multifractal characterization of energy stocks in China: A multifractal detrended fluctuation analysis

In this paper, we investigate the impacts of oil price changes on energy stocks in Chinese stock market from the multifractal perspective. The well-known multifractal detrended fluctuation analysis (MF-DFA) is applied to detect the multifractality. We find that both returns and volatilities of energy industry index display apparent multifractal behavior. Oil market activity is an important source of multifractality in energy stocks index in addition to long-range correlations and fat-tail distributions.

An analysis of multifractal characteristics of API time series in Nanjing, China

This paper describes multifractal characteristics of daily air pollution index (API) records in Nanjing from 2001 to 2012. The entire daily API time series is first divided into 12 parts that serve as research objects, and the generalized Hurst exponent is calculated for each series. And then, the multifractal sources are analyzed and singularity spectra are shown. Next, based on a singularity spectrum, the multifractal-characteristics parameters (maximum exponent α0, spectrum width Δα, and asymmetry Δαas) are introduced. The results show that the fractality of daily API for each year is multifractal. The multifractal sources originate from both a broad probability density function and different long-range correlations with small and large fluctuations. The strength of the distribution multifractality is stronger than that of the correlation multifractality. The variation in the structure of API time series with increasing years is mainly related to long-range correlations. The structure of API time series in some years is richer. These findings can provide a scientific basis for further probing into the complexity of API.

Comparative Multifractal Detrended Fluctuation Analysis of Heavy Ion Interactions at a Few GeV to a Few Hundred GeV

We have studied the multifractality of pion emission process in16O-AgBr interactions at 2.1 AGeV and 60 AGeV,12C-AgBr and 24Mg-AgBr interactions at 4.5 AGeV, and32S-AgBr interactions at 200 AGeV using Multifractal Detrended Fluctuation Analysis (MFDFA) method which is capable of extracting the actual multifractal property filtering out the average trend of fluctuation. The analysis reveals that the pseudorapidity distribution of the shower particles is multifractal in nature for all the interactions; that is, pion production mechanism has inbuilt multiscale self-similarity property. We have employed MFDFA method for randomly generated events for32S-AgBr interactions at 200 AGeV. Comparison of expt. results with those obtained from randomly generated data set reveals that the source of multifractality in our data is the presence of long range correlation. Comparing the results obtained from different interactions, it may be concluded that strength of multifractality decreases with projectile mass for the same projectile energy and for a particular projectile it increases with energy. The values of ordinary Hurst exponent suggest that there is long range correlation present in our data for all the interactions.

Fractal behavior of traffic volume on urban expressway through adaptive fractal analysis

In this paper, we investigate the fractal behavior of traffic volume in urban expressway based on a newly developed adaptive fractal analysis (AFA), which has a number of advantages over traditional method of detrended fluctuation analysis (DFA). Before fractal analysis, autocorrelation function was first adopted on traffic volume data and the long-range correlation behavior was found to be existed in both on-ramp and off-ramp situations. Then AFA as well as DFA was applied to further examine the fractal behavior. The results showed that the multifractality and the long-range anti-persistent behavior existed on both on-ramp and off-ramp. Additionally, multifractal analysis on weekdays and weekends are performed respectively and the results show that the degree of multifractality on weekdays is higher than that on weekends, implying that long-range correlation behaviors were more obvious on weekdays. Finally, the source of multifractality is examined with randomly shuffled and the surrogated series. Long-range correlation behaviors are identified in both on-ramp and off-ramp situations and fat-tail distributions were found to make little in the contributions of multifractality.

Analyzing Origin of Multifractality of Surface Electromyography Signals in Dynamic Contractions

The aim of this study is to analyze the origin of multifractality of surface electromyography (sEMG) signals during dynamic contraction in nonfatigue and fatigue conditions. sEMG signals are recorded from triceps brachii muscles of 22 healthy subjects. The signals are divided into six equal segments on time scale for normalization. The first and sixth segments are considered as the nonfatigue and fatigue conditions, respectively. The source of multifractality can be due to correlation and probability distribution. The original sEMG series are transformed into shuffled and surrogate series. These three series namely, original, shuffled, and surrogate series in the nonfatigue and fatigue conditions are subjected to multifractal detrended fluctuation analysis (MFDFA) and features are extracted. The results indicate that sEMG signals exhibit multifractal behavior. Further investigation revealed that origin of multifractality is primarily due to correlation. The origin of multifractality due to correlation is quantified as 80% in nonfatigue and 86% in fatigue conditions. This method of multifractal analysis may be useful for analyzing the progressive changes in muscle contraction in varied neuromuscular studies.

Multifractal characteristics of gold grades series in the Dayingezhuang Deposit, Jiaodong Gold Province, China

In the paper, the multifractal detrended fluctuation analysis is used to investigate the multifractal characteristics of gold grades series in the Dayingezhuang gold deposit, Jiaodong province, China. Results obtained from the multifractal parameters and multifractal spectra show that the gold grades series exhibit multifractal scaling and different long-range correlations. The asymmetry of multifractal spectrum shows that the range of the right-side branches of the multifractal spectrum is larger than that of the left-side branches for the gold grades series of intensely mineralized drifts, but the gold grades series of the barely mineralized zones is on the contrary, which indicates that the shape of of multifractal spectrum may provide directions in the study of ore-forming potential. Moreover, we analyze the sources of multifractality quantifying the contributions of two factors, the long-range correlations and the broad fat-tail distributions. We find that the multifractality structure of gold grades series is due to both long-range correlation and the fat-tail probability density function, but the former is greater attributed to the latter.

Multifractal characteristic analysis of near-fault earthquake ground motions

This study aims to reveal the multi-scaling behavior and quantify the irregularity of near-fault earthquake ground motions from a new perspective of multifractal theory. Based on multifractal detrended fluctuation analysis, the multifractal characteristic parameters of acceleration time series for typical near-fault ground motions are calculated, and their correlations with two period parameters (i.e., mean period Tm and characteristic period Tc) and box-counting fractal dimensions are analyzed. Numerical results of strong nonlinear dependence of generalized Hurst exponents h(q) upon the fluctuation orders q indicate that near-fault ground motions present the multifractal properties and long-range correlation obviously. Furthermore, the scaling exponent h(2) of near-fault records has a strong correlation with their periods Tm and Tc, and strongly negative correlation with their box dimension. Moreover, h(2) can be regarded as a measure of frequency content and irregularity degree of strong earthquake ground motions. Finally, it is pointed out that the long-range correlation of small and large fluctuation is the major source of multifractality of near-fault ground motions.

Measuring efficiency of international crude oil markets: A multifractality approach

The three major international crude oil markets are treated as complex systems and their multifractal properties are explored. The study covers daily prices of Brent crude, OPEC reference basket and West Texas Intermediate (WTI) crude from January 2, 2003 to January 2, 2014. A multifractal detrended fluctuation analysis (MFDFA) is employed to extract the generalized Hurst exponents in each of the time series. The generalized Hurst exponent is used to measure the degree of multifractality which in turn is used to quantify the efficiency of the three international crude oil markets. To identify whether the source of multifractality is long-range correlations or broad fat-tail distributions, shuffled data and surrogated data corresponding to each of the time series are generated. Shuffled data are obtained by randomizing the order of the price returns data. This will destroy any long-range correlation of the time series. Surrogated data is produced using the Fourier-Detrended Fluctuation Analysis (F-DFA). This is done by randomizing the phases of the price returns data in Fourier space. This will normalize the distribution of the time series. The study found that for the three crude oil markets, there is a strong dependence of the generalized Hurst exponents with respect to the order of fluctuations. This shows that the daily price time series of the markets under study have signs of multifractality. Using the degree of multifractality as a measure of efficiency, the results show that WTI is the most efficient while OPEC is the least efficient market. This implies that OPEC has the highest likelihood to be manipulated among the three markets. This reflects the fact that Brent and WTI is a very competitive market hence, it has a higher level of complexity compared against OPEC, which has a large monopoly power. Comparing with shuffled data and surrogated data, the findings suggest that for all the three crude oil markets, the multifractality is mainly due to long-range correlations.

Multifractal Processes and Self-Organized Criticality of PM2.5 during a Typical Haze Period in Chengdu, China

Scaling and multifractal properties of the hourly PM2.5 average concentration series at the four air monitoring stations of Chengdu (southwestern China) were explored by using a multifractal detrended fluctuation analysis method, during a typical haze episode (from 1 March to 17 March, 2013). Using shuffling procedure and phase randomization procedure, the major sources of multifractality in these PM2.5 series are studied. The results show that the multifractality nature of PM2.5 series is mainly due to long-range correlation. At the same time, the non-Gaussian probability distributions also partly contribute to the multifractal behaviour. The scale-free power laws behaviours are found to govern the cumulative distributions statistics for PM2.5 concentration fluctuations. The temporal evolutions of the multifractality were investigated by the approach of a sliding window. Further, we attempt to find the answers to the following questions: how does longrange correlation and power-law distribution in PM2.5 evolution emerge? It is inviting to do it in a self-organized criticality (SOC) framework, which was specially designed to model the dynamics of complex systems. A novel PM2.5 evolution model is developed on the bases of SOC theory. The model displays robust power law behaviour in certain dynamical region. The self-organized criticality properties of PM2.5 evolution are discussed. This SOC behaviour is related to a statistically steady state that implies the presence of long-range correlation and power-law distribution in PM2.5 evolution during the haze period. It is the stability of SOC that causes the haze period to be sustained for a long time in Chengdu.

Source Of The Multifractality In Exchange Markets: Multifractal Detrended Fluctuations Analysis

In this study, we analyzed the multifractality and the source of multifractality of the returns of GBP/USD, EUR/USD, USD/JPY and USD/CHF currencies. In the examination of multifractality we performed the Multifractal Detrended Fluctuation Analysis (MF-DFA). Also, we used shuffled and surrogated data that was derived from the Statically Transformed Autoregressive Process (STAP) method to determine the source of multifractality. According to the results, GBP/USD returns have monofractal features, whereas EUR/USD, USD/JPY and USD/CHF returns have multifractal behaviours. The tests concerning the source of multifractality indicated that the reason of multifractality for EUR/USD and USD/JPY returns is fat-tails of the probability density function of returns, whereas the reason of multifractality of USD/CHF returns are both long memory and fat tails. Also we have seen that there is an ambiguous relationship between the liquidity of the currency market and multifractality.

The complexity and fractal structures of CSI300 before and after the introduction of CSI300IF

This paper employs multifractal detrended fluctuation analysis (MF-DFA) approach to analyze the complexity and fractal structures of China Securities Index 300 (CSI300), which covers the period from April 5, 2006 to May 9, 2014. Through comparing the statistic properties before and after the introduction of CSI300 index futures (CSI300IF), we find that: (1) the price return series exhibits multifractal properties for the two periods; (2) by comparing the efficient measure based on the general Hurst exponent, we find the market becomes more efficient after the introduction of CSI300IF; (3) the width of multifractal spectrum becomes narrower, which means the complexity of the market is decreased. Therefore, the introduction of CSI300IF is beneficial to reduce the risk and increase the efficiency of Chinese securities market. Furthermore, the main sources of multifractality of these time series are examined through the shuffle method, and the results show that before CSI300IF the multifractality is mainly due to the long-range correlation properties between small and large fluctuations, while after CSI300IF it is more due to fat-tailed probability distributions.

The MDF technique for the analysis of tokamak edge plasma fluctuations

Tokamak edge plasma was analyzed by applying the multifractal detrend fluctuation analysis (MF-DFA) technique. This method has found wide application in the analysis of correlations and characterization of scaling behavior of the time-series data in physiology, finance, and natural sciences. The time evolution of the ion saturation current (Is), the floating potential fluctuation (Vf), the poloidal electric field (Ep), and the radial particle flux (Γr) has been measured by using a set of Langmuir probes consisting of four tips on the probe head. The generalized Hurst exponents (h(q)), local fluctuation function (Fq(s)), the Rényi exponents (τ(q)) as well as the multifractal spectrum f(αh) have been calculated by applying the MF-DFA method to Is, Vf, and the magnetohydrodynamic (MHD) fluctuation signal. Furthermore, we perform the shuffling and the phase randomization techniques to detect the sources of multifractality. The nonlinearity shape of τ(q) reveals a multifractal behavior of the time-series data. The results show that in the presence of biasing, Is, Vf, Ep, and Γr reduce about 25%, 90%, 70%, and 50%, respectively, compared with the situation with no biasing. Also, they reduce about 15%, 90%, 35%, and 25%, respectively, after resonant helical magnetic field (RHF) application. In the presence of biasing or RHF, the amplitude of the power spectrum of Is, Vf, Γr, and MHD activity reduce remarkably in all the ranges of frequency, while their h(q) increase. The values of h(q) have been restricted between 0.6 and 0.68. These results are evidence of the existence of long-range correlations in the plasma edge turbulence. They also show the self-similar nature of the plasma edge fluctuations. Biasing or RHF reduces the amount of Fq(s). The multifractal spectrum width of Is, Vf, and MHD fluctuation amplitude reduce about 60%, 70%, and 42%, respectively, by applying biasing. In the presence of RHF, their width reduces about 60%, 85%, and 75%, respectively. It means that biasing and RHF reduce the degree of multifractality.