Strength Of Multifractality Research Articles

Inner Multifractal Dynamics in the Jumps of Cryptocurrency and Forex Markets

Jump dynamics in financial markets exhibit significant complexity, often resulting in increased probabilities of subsequent jumps, akin to earthquake aftershocks. This study aims to understand these complexities within a multifractal framework. To do this, we employed the high-frequency intraday data from six major cryptocurrencies (Bitcoin, Ethereum, Litecoin, Dashcoin, EOS, and Ripple) and six major forex markets (Euro, British pound, Canadian dollar, Australian dollar, Swiss franc, and Japanese yen) between 4 August 2019 and 4 October 2023, at 5 min intervals. We began by extracting daily jumps from realized volatility using a MinRV-based approach and then applying Multifractal Detrended Fluctuation Analysis (MFDFA) to those jumps to explore their multifractal characteristics. The results of the MFDFA—especially the fluctuation function, the varying Hurst exponent, and the Renyi exponent—confirm that all of these jump series exhibit significant multifractal properties. However, the range of the Hurst exponent values indicates that Dashcoin has the highest and Litecoin has the lowest multifractal strength. Moreover, all of the jump series show significant persistent behavior and a positive autocorrelation, indicating a higher probability of a positive/negative jump being followed by another positive/negative jump. Additionally, the findings of rolling-window MFDFA with a window length of 250 days reveal persistent behavior most of the time. These findings are useful for market participants, investors, and policymakers in developing portfolio diversification strategies and making important investment decisions, and they could enhance market efficiency and stability.

Investigation on vibration characteristics induced by gas–liquid two-phase flows in a horizontal pipe

The intrinsic characteristics of multiphase flow inevitably result in vibrations within the pipe structure. The evolution of vibration characteristics is crucial for monitoring the stability of the multiphase flow pipelines. However, under high liquid velocity condition, the influence of flow pattern on the gas–liquid two-phase flow-induced vibration (GTFIV) of the pipe remains unclear. In this paper, the vibration signals in the horizontal pipe under different flow patterns at high liquid velocity are measured by a vibration test system. Synchronously, images inside the pipe are captured to illustrate the flow mechanism. The results show that the α stable distribution model holds higher fitting accuracy than the standard normal distribution for the GTFIV. The random behavior of small-scale bubbles determines the structural richness of the GTFIV. The multifractal characteristics of the GTFIV are strongly dependent on the flow pattern. The formation of the gas plug leads to significant unevenness in the fractal structure of the GTFIV. The multifractal strength of the GTFIV gradually increases as the flow pattern transforms from dispersed bubble flow to slug flow. Some multifractal spectrum parameters of the vibration signal can be applied for the identification of flow patterns in the pipe.

Multifractal Analysis of International Energy and Agricultural Markets Under the Influence of Russia–Ukraine Conflict

Taking six representative futures in the international energy and agricultural markets as the research objects, we use multifractal analysis methods to study the fluctuation characteristics, market risks and cross-correlations within and between these markets before and after the outbreak of the Russia–Ukraine conflict in this paper. The empirical results show that both the auto-correlations and cross-correlations have obvious multifractal features. It is confirmed that the multifractal strength and market risks of the international energy markets have weakened, while those of the international agricultural markets have enhanced after the Russia–Ukraine conflict broke out. In addition, the Russia–Ukraine conflict has intensified the strength of the multifractality and the degree of fluctuation complexity between these two classes of international markets. Further, the intrinsic multifractal natures of cross-correlations are tested, and the apparent and intrinsic multifractality before and after the conflict are revealed. Finally, some policy suggestions are put forward based on the empirical results.

Unravelling the Fractal Complexity of Temperature Datasets across Indian Mainland

Studying atmospheric temperature characteristics is crucial under climate change, as it helps us to understand the changing patterns in temperature that have significant implications for the environment, ecosystems, and human well-being. This study presents the comprehensive analysis of the spatiotemporal variability of scaling behavior of daily temperature series across the whole Indian mainland, using a Multifractal Detrended Fluctuation Analysis (MFDFA). The analysis considered 1° × 1° datasets of maximum temperature (Tmax), minimum temperature (Tmin), mean temperature (Tmean), and diurnal temperature range (DTR) (TDTR = Tmax − Tmin) from 1951 to 2016 to compare their scaling behavior for the first time. Our results indicate that the Tmin series exhibits the highest persistence (with the Hurst exponent ranging from 0.849 to unity, and a mean of 0.971), and all four-temperature series display long-term persistence and multifractal characteristics. The variability of the multifractal characteristics is less significant in North–Central India, while it is highest along the western coast of India. Moreover, the assessment of multifractal characteristics of different temperature series during the pre- and post-1976–1977 period of the Pacific climate shift reveals a notable decrease in multifractal strength and persistence in the post-1976–1977 series across all regions. Moreover, for the detection of climate change and its dominant driver, we propose a new rolling window multifractal (RWM) framework by evaluating the temporal evolution of the spectral exponents and the Hurst exponent. This study successfully captured the regime shifts during the periods of 1976–1977 and 1997–1998. Interestingly, the earlier climatic shift primarily mitigated the persistence of the Tmax series, whereas the latter shift significantly influenced the persistence of the Tmean series in the majority of temperature-homogeneous regions in India.

Multifractal characterization of nystagmus eye movements.

In this work, we investigate the multifractal properties of eye movement dynamics of children with infantile nystagmus, particularly the fluctuations of its velocity. The eye movements of three children and one adult with infantile nystagmus were evaluated in a simple task in comparison with 28 children with no ocular pathologies. Four indices emerge from the analysis: the classical Hurst exponent, the singularity strength corresponding to the maximum of the singularity spectrum, the asymmetry of the singularity spectrum, and the multifractal strength, each of which characterizes a particular aspect of eye movement dynamics. Our findings indicate that, when compared to children with no ocular pathologies, patients with infantile nystagmus present lower values of all indices. Except for the multifractal strength, the difference in the remaining indices is statistically significant. To test whether the characterization of patients with infantile nystagmus in terms of multifractality indices allows them to be distinguished from children without ocular pathologies, we performed an unsupervised clustering analysis and classified the subjects using supervised clustering techniques. The results indicate that these indices do, indeed, distinctively characterize the eye movements of patients with infantile nystagmus.

Multifractal and chaotic characteristics of geomagnetic inter-storm interval over eight solar cycles

The structure and characteristics of geomagnetic inter-storm intervals, the sequence of time differences between two successive storm events, can provide information about the origin and drivers of the storms compared to analyzing the entire data set. In this study, the inter-storm event was investigated using the Kp index over 8 solar cycles (17–24). Three nonlinear approaches were considered: burstiness, multifractal detrended fluctuation analysis, and chaos analysis. The burstiness analysis reveals that the inter-storm intervals are heterogeneous events with irregular time intervals. The multifractal strength of inter-storm intervals ranges from 0.23 to 0.65 for each of the solar cycles, compared to 0.38 for the entire period. Long-range correlations largely drove the multifractality across most solar cycles. Chaos analysis confirmed the low predictability of inter-storm intervals across each solar cycle. The results will be relevant to the prediction and understanding of drivers of storm events across different solar cycles.

Surge prediction in a gas-liquid mixed-flow pump based on multifractal detrended fluctuation analysis

Surge causes a sudden drop in pressure increase and possibly results in severe vibration in a multiphase pump once inlet gas volume fraction (IGVF) exceeds a critical value. In this study, a synchronous test system including a high-speed camera, a laser Doppler vibrometer and high-frequency pressure fluctuation sensors is constructed to measure shaft vibration and pressure fluctuation in a gas–liquid mixed-flow pump at different IGVFs. The multifractal characteristics of the collected signals obtained by using the multifractal detrended fluctuation analysis method have been analysed and compared in detail. Results show that pressure surge occurs once the flow pattern transforms from bubbly flow to gas pocket flow in the pump. The multifractal characteristics of the vibration and pressure fluctuations depend strongly on the IGVF. Before the surge, the multifractal strength of vibration and pressure fluctuation increase with the increment of IGVF. After the surge, they decrease rapidly as the bubble coalescence into a mass of gas pockets. Furthermore, the local fluctuation of the vibration is insensitive to the variation of the IGVF and the multifractal spectrum has a right tail at each IGVF. The local fluctuation of the pressure fluctuation become severe with the coalescence of bubbles and the multifractal spectrum has a left tail after the surge. The incipient surge state can be effectively predicted by characteristics parameters extracted from the multifractal spectrum of the shaft vibration and the pressure fluctuation in the pump. This study provides an effective method for surge state prediction in multiphase pumps.

Cavitation identification in a hydraulic bulb turbine based on vibration and pressure fluctuation measurements

Cavitation can lead to reduced efficiency, increased vibration and noise in hydraulic turbines. Accurate and rapid identification of cavitation states in a turbine is important. In this work, a test system has been constructed for a hydraulic bulb turbine, to synchronously obtain cavitation images on runner blades, vibrations on both the runner hub and the runner chamber, and pressure fluctuations on the draft tube of the turbine at different cavitation conditions. The multifractal characteristics of the collected signals obtained by using the multifractal detrended fluctuation analysis method have been analysed and compared in detail. It is found that the multifractal characteristics of the vibrations and pressure fluctuations depend strongly on the cavitation state. The multifractal strength of the pressure fluctuations in the draft tube is stronger than that of the vibrations on the runner, induced by cavitation. Furthermore, some multifractal parameters of vibrations and pressure fluctuations have been extracted and used for cavitation state identification in the turbine, which is important for safe operation of a turbine.

Multifractal Analysis of Chinese Industry and Stock Markets Fluctuation Under the COVID-19 Pandemic

Researchers and authorities have become increasingly interested in how the COVID-19 pandemic has profoundly impacted the real economy and financial markets around the world since its outbreak in late 2019. Applying the methods of multifractal analysis, this paper investigates the fluctuation characteristics and market risks of Chinese industry and stock markets under the COVID-19 pandemic, and reveals the whole dynamics of industry and stock markets from the perspective of system theory. The empirical results show that the multifractal strength of the industry market has significantly increased during the pandemic with elevated systematic risk, while the situation is different for the stock market. Specifically, the Hurst surfaces generated using the multiscale technique intuitively visualize the dynamical behaviors of the systematic fluctuation of the Chinese industry and stock markets at various scales under the COVID-19 pandemic. Furthermore, it is found that the sources of multifractality of the two types of markets include long-range correlation and fat-tailed distribution, with the contribution of fat-tailed distribution being greater. The chi-square test is promoted in this paper to measure the contribution of the internal components of the multivariate system to the multifractality sources of the whole system, revealing that the real estate industry has a greater impact on the multifractality of the whole industry system, while the Shanghai Composite Index has a stronger influence on the whole stock system.

The dynamics of market efficiency of major cryptocurrencies

The exponential growth of Fintech innovation has increased the interest in cryptocurrency market informational efficiency given that cryptocurrencies and their underlying blockchain technology represent a profound yet ambiguous facet of Fintech. In this context, this paper examines the dynamic changes in the market efficiency of six major cryptocurrencies using the multifractal detrended fluctuation analysis (MFDFA) approach. The empirical findings confirm a varying degree of multifractal strength in the cryptocurrencies under consideration, which could be related to market inefficiency and fractal market hypothesis verification. Based on the multifractal indices, Bitcoin and Litecoin are the two most inefficient cryptocurrencies, whereas Cardano and Binance Coin exhibit the least inefficiency. Ripple and Ethereum remain in the middle. Overall, the cryptocurrencies exhibit persistence behaviour but show a significant change over time. Finally, we perform a rolling-window analysis and confirm the presence of multifractality, which seems to vary over time, suggesting that market (in)efficiency is an evolving process that can be shaped by market conditions. We argue that these findings could be related to herding behaviour, especially during crisis periods. The findings have policy implications, including the possibility of using active trading for profit-making strategies.

MULTIFRACTAL ANALYSIS OF EMG FOR CLASSIFICATION AND PROGRESSIVE ASSESSMENT OF BICEPS BRACHII MUSCLE STRENGTH

The proposed research demonstrates an attempt to introduce a systematic procedure for studying the multifractal dynamics of biceps brachii muscle actions during light exercises. The intrinsic patterns in the Surface Electromyogram (sEMG) signals were extracted by fruitfully exploiting the Multifractal features of the signal. The Multifractal features are derived from the multifractal singularity spectrum of the EMG signals. This multifractal feature vector could be utilized for signal characterization, which was successfully extended for the classification of EMG signals. Experimental verification has been done to validate the feature extraction and classification algorithm proposed in this article. A pilot study was conducted on signals from the Physionet database, which was then extended to a medium database developed with biceps brachii EMG signals of 32 healthy male subjects. From this study, we could validate that the Multifractal features fit as a differentiating multi-feature set and also for the progressive assessment of EMG signals of different classes. The observations of the proposed method revealed that the strength of multifractality and area under the spectrum increase as a result of fast movements of the forearm or increases in muscle fatigue. The classification is performed using well-recognized supervised classification algorithms such as k-Nearest Neighbor and Support Vector Machine (SVM) Classifiers. The performance analysis of the classifiers are studied on various measures such as Accuracy, Precision, Recall, F1 score. The statistical significance analysis of the feature vector was carried out by one-way ANOVA test.

Complex roughening dynamics and wettability mechanism in MoS2 thin films — A system theoretic approach

We utilized fractal geometry to advance insights into the complex roughening and its facilitated wettability mechanism of sputtered MoS2 film surfaces with varying thickness are studied. Fractal parameters indicate the dominance of shadowing at lower thickness while enhancement in vertical growth rate and variation in local irregularities are observed at higher thicknesses along with anomalous roughening up to thickness of 200 nm. In addition, anti-persistent trend of surface heights was observed to be independent of thickness. Multifractal analysis exposed the non-linear variation in multifractality strength and vertical complexities of surface heights. The results corroborates the stereometric analysis revealing the 3D surface topography of analyzed films. The wettability was observed to increase with thickness. In consideration, the roughening expedited wetting trend is defined in light of stereometric parameters and multifractility strength suggesting increases the penetration of water droplets into the surface voids with decline in the surface complexities. The mechanism for increase in contact angle is realized from the augmentation in curvature pressure indicating the existence of large air pressure within the void lying lower than the water droplets as compared to the pressure from the meniscus sides of the droplets. In addition, principal component analysis is utilized to reveal the significance of fractal parameters in probing the surface roughening. The results hold prospects in surface engineering of MoS2 thin films as a function of thickness for enhanced catalytic activity in electrochemical splitting of water for hydrogen evolution reactions.

Multifractal analysis of malaria cases in India in a global warming scenario

Abstract An effort is made to evaluate the multifractal properties of malaria cases in India from 1980 to 2014. The possible changes in these properties in a global warming scenario (during 2015–2049) are also quantified. The malaria cases for this purpose are derived from the VECTRI dynamical malaria model, which uses rainfall and temperature data of Coupled Model Intercomparison Project Phase 6 models for the historical and SSP5–8.5 projection scenario, respectively. It is found that the generalized Hurst exponent h (q) and multifractal spectrum width Δα are strongly nonlinear decreasing functions of order q, thus confirming the multifractal nature (and heterogeneous distribution) of the malaria cases in India. The multifractal spectrum of the malaria cases exhibits right-tailed nature along with high inter-model variability, suggesting that the time series under consideration are fine scale and highly complex in nature. The multifractal spectrum width and change in singularity dimension are used to quantify the strength of multifractality for the historical and future projection scenario. It is demonstrated that the strength of multifractality of malaria cases is likely to decrease with an increase in greenhouse gas concentration, which may be happening due to a persistent increase in malaria cases in India as a result of global warming.

Islamic vs. Conventional Equity Markets: A Multifractal Cross-Correlation Analysis with Economic Policy Uncertainty

There is ample evidence that Islamic stock markets perform differently from conventional stock markets, particularly when economic policy uncertainty (EPU) or any other uncertainty such as geopolitical uncertainty is present. Considering this context, this paper examines the US EPU’s cross-correlation with both conventional and Islamic stock markets from the perspective of multifractality. Daily stock market prices of five main countries are considered: US, Thailand, Indonesia, Pakistan, and India. Using the multifractal detrended cross-correlation analysis (MF-DCCA), we validate the existence of long-range cross-correlation between US EPU and all the stock markets considered, demonstrating that all pairs of US EPU have strong power law and multifractal characteristics. Furthermore, all pairs display varying levels of multifractal strength, with the US EPU and US conventional stock market exhibiting the strongest multifractal patterns. Additionally, a cross-correlation between US EPU and the different stock markets is found to be persistent. The results of this study are pertinent to the various market participants in both conventional and Islamic markets, particularly investors, who may be able to draw useful conclusions from them for purposes such as portfolio diversification.

ANALYSIS OF TRANSMISSION DYNAMICS OF SARS-COV-2 UNDER SEASONAL CHANGE

In this paper, we explore whether the activity of SARS-CoV-2 was associated with seasonality. MF-DFA model is utilized to calculate multifractal strength and multifractal complexity to evaluate the change state of SARS-CoV-2 activity. We select 10 countries with serious epidemic in the world, which are distributed in different latitudes of the northern and southern hemispheres. The study utilized the time series data of daily new cases and daily new deaths recorded in these countries. We regard May to October as the “high temperature season” for countries in the northern hemisphere, November to April as the “low temperature season”, and the southern hemisphere is just the opposite. By comparing the multifractal intensity [Formula: see text] and multifractal complexity [Formula: see text] of the two time series in the two seasons, we draw a conclusion that, for both the sequence of the daily newly diagnosed persons and the daily newly increased number of deaths, in the countries of both the northern and southern hemispheres, [Formula: see text] and [Formula: see text] are weaker in the “low temperature season”. That is, in the low temperature environment, SARS-CoV-2 can survive for a long time and be more infectious. In addition, we also observe that in the northern hemisphere, Iran is at a lower latitude, and although the SARS-CoV-2 activity in the low temperature season is higher than that in the high temperature season, the difference is not significant. Therefore, the lower latitude may resist this phenomenon. However, most of the countries in the southern hemisphere are within 30° of south latitude, with low latitude, and other meteorological characteristics such as humidity in the countries in the southern hemisphere are also relatively unique. Although SARS-CoV-2 is characterized by high activity in low temperature seasons, no direct evidence related to the characteristics of latitude distribution has been found.

Scale-Free Functional Brain Networks Exhibit Increased Connectivity, Are More Integrated and Less Segregated in Patients with Parkinson's Disease following Dopaminergic Treatment.

Dopaminergic treatment (DT), the standard therapy for Parkinson's disease (PD), alters the dynamics of functional brain networks at specific time scales. Here, we explore the scale-free functional connectivity (FC) in the PD population and how it is affected by DT. We analyzed the electroencephalogram of: (i) 15 PD patients during DT (ON) and after DT washout (OFF) and (ii) 16 healthy control individuals (HC). We estimated FC using bivariate focus-based multifractal analysis, which evaluated the long-term memory and multifractal strength of the connections. Subsequent analysis yielded network metrics (node degree, clustering coefficient and path length) based on FC estimated by or . Cognitive performance was assessed by the Mini Mental State Examination (MMSE) and the North American Adult Reading Test (NAART). The node degrees of the networks were significantly higher in ON, compared to OFF and HC, while clustering coefficient and path length significantly decreased. No alterations were observed in the networks. Significant positive correlations were also found between the metrics of networks and NAART scores in the HC group. These results demonstrate that DT alters the multifractal coupled dynamics in the brain, warranting the investigation of scale-free FC in clinical and pharmacological studies.

The footprints of Russia–Ukraine war on the intraday (in)efficiency of energy markets: a multifractal analysis

PurposeThis paper examines the impact of Russian invasion of Ukraine on the intraday efficiency of four major energy markets, namely, diesel oil, Brent oil, light oil and natural gas.Design/methodology/approachThis study applies the multifractal detrended fluctuation analysis (MFDFA) to high-frequency returns (30-min intervals) for the period from October 21, 2021, to May 20, 2022. The data sample of 5,141 observations is divided into two sub-samples, before and after the invasion of 24th February 2022. Additionally, the magnitude of long memory index is employed to investigate the presence of herding behavior around the invasion period.FindingsResults confirm the presence of multifractality in energy markets and reveal significant changes of multifractal strength due to the invasion, indicating a decline of intraday efficiency for oil markets. Surprisingly, the natural gas market, being the least efficient before the invasion, turns out to be more efficient after the invasion. The findings also suggest that investors in these energy markets are likely to show herding, more prominently after the invasion.Practical implicationsThe multifractal patterns, in particular the long memory property of energy markets, can help investors develop profitable investment strategies. Furthermore, the improved efficiency observed in the natural gas market, after the invasion, highlights its unique traits and underlying complexity.Originality/valueThis study is the first attempt to assess the impact of the Russia–Ukraine war on the efficiency of global commodity markets. This is quite important because the adverse effects of the war on financial markets may potentially cause destabilizing outcomes and negative effects on social welfare on a global scale.

Multifractal Characteristics on Temporal Maximum of Air Pollution Series

Presenting and describing a temporal series of air pollution data with longer time lengths provides more concise information and is, in fact, one of the simplest techniques of data reduction in a time series. However, this process can result in the loss of important information related to data features. Thus, the purpose of this study is to determine the type of data characteristics that might be lost when describing data with different time lengths corresponding to a process of data reduction. In parallel, this study proposes the application of a multifractal technique to investigate the properties on an air pollution series with different time lengths. A case study has been carried out using an air pollution index data in Klang, Malaysia. Results show that hourly air pollution series contain the most informative knowledge regarding the behaviors and characteristics of air pollution, particularly in terms of the strength of multifractality, long-term persistent correlations, and heterogeneity of variations. On the other hand, the statistical findings found that data reduction corresponding to a longer time length will change the multifractal properties of the original data.

Evaluation of non-linear heart rate variability using multi-scale multi-fractal detrended fluctuation analysis in mice: Roles of the autonomic nervous system and sinoatrial node.

Nonlinear analyses of heart rate variability (HRV) can be used to quantify the unpredictability, fractal properties and complexity of heart rate. Fractality and its analysis provides valuable information about cardiovascular health. Multi-Scale Multi-Fractal Detrended Fluctuation Analysis (MSMFDFA) is a complexity-based algorithm that can be used to quantify the multi-fractal dynamics of the HRV time series through investigating characteristic exponents at different time scales. This method is applicable to short time series and it is robust to noise and nonstationarity. We have used MSMFDFA, which enables assessment of HRV in the frequency ranges encompassing the very-low frequency and ultra-low frequency bands, to jointly assess multi-scale and multi-fractal dynamics of HRV signals obtained from telemetric ECG recordings in wildtype mice at baseline and after autonomic nervous system (ANS) blockade, from electrograms recorded from isolated atrial preparations and from spontaneous action potential recordings in isolated sinoatrial node myocytes. Data demonstrate that the fractal profile of the intrinsic heart rate is significantly different from the baseline heart rate in vivo, and it is also altered after ANS blockade at specific scales and fractal order domains. For beating rate in isolated atrial preparations and intrinsic heart rate in vivo, the average fractal structure of the HRV increased and multi-fractality strength decreased. These data demonstrate that fractal properties of the HRV depend on both ANS activity and intrinsic sinoatrial node function and that assessing multi-fractality at different time scales is an effective approach for HRV assessment.

Characterizing stroke-induced changes in the variability of lower limb kinematics using multifractal detrended fluctuation analysis.

Movement variability reflects the adaptation of the neuromuscular control system to internal or external perturbations, but its relationship to stroke-induced injury is still unclear. In this study, the multifractal detrended fluctuation analysis was used to explore the stroke-induced changes in movement variability by analyzing the joint angles in a treadmill-walking task. Eight healthy subjects and ten patients after stroke participated in the experiment, performing a treadmill-walking task at a comfortable speed. The kinematics data of the lower limbs were collected by the motion-capture system, and two indicators, the degree of multifractality (α) and degree of correlation [h(2)], were used to investigate the mechanisms underlying neuromuscular control. The results showed that the knee and ankle joint angles were multifractal and persistent at various scales, and there was a significant difference in the degree of multifractality and the degree of correlation at the knee and ankle joint angles among the three groups, with the values being ranked in the following order: healthy subjects < non-paretic limb < paretic limb. These observations highlighted increased movement variability and multifractal strength in patients after stroke due to neuromotor defects. This study provided evidence that multifractal detrended analysis of the angles of the knee and ankle joints is useful to investigate the changes in movement variability and multifractal after stroke. Further research is needed to verify and promote the clinical applications.