Degree Of Multifractality Research Articles

Multifractal Analysis of the Impact of Fuel Cell Introduction in the Korean Electricity Market

This study employs multifractal detrended fluctuation analysis to investigate the impact of fuel cell introduction in the Korean electricity market via the lens of multifractal scaling behavior. Using multifractal analysis, the research delineates discrepancies between peak and off-peak hours, accounting for the daily cyclicity of the electricity market, and proposes a crossover point detection method based on the Chow test. Furthermore, the impacts of fuel cell introduction are evidenced through various methods that encompass multifractal spectra and market efficiency. The findings initially indicate a higher degree of multifractality during off-peak hours relative to peak hours. In particular, the crossover points emerged solely during off-peak hours, unveiling short- and long-term dynamics predicated on a near-annual cycle. Additionally, the average Hurst exponent for the short-term was 0.542, while the average for the long-term was 0.098, representing a notable discrepancy. The introduction of fuel cells attenuated the heterogeneity in the scaling behavior, which is potentially attributable to the decreased volatility in both the supply and demand spectra. Remarkably, after the introduction of fuel cells, there was a discernible decrease in the influence of long-range correlation within multifractality, and the market exhibited an increased propensity toward random-walk behavior. This phenomenon was also detected in the market deficiency measure, from an average of 0.536, prior to the introduction, to an average of 0.267, following the introduction, signifying an improvement in market efficiency. This implies that the introduction of fuel cells into the market engendered increased supply stability and a consistent increase in demand, mitigating volatility on both the supply and demand sides, thus increasing market efficiency.

Multifractal signatures of light-driven self-organization in acrylated epoxidized soybean oil polymers

Multifractal properties of acrylated epoxidized soybean oil with and without a photoinitiator have been investigated. Using multifractal detrended fluctuation analysis, the photopolymerization process is analyzed by varying illumination duration and intensity. The research is conducted in two stages: the results concerning temperature fluctuations of the entire photoirradiation process are initially presented followed by a sliding window procedure to monitor system complexity during light cycling. Various multifractal mea-sures including the generalized Hurst exponent h(q), the multifractal Rényi exponent τ(q), the generalized fractal dimensions D(q) with the left and right side curvature (ΔDL, ΔDR), the multifractal singularity exponents α, the multifractal spectrum f (α), and the multifractal heat capacity C(q) with its integrated characteristic Carea are examined for both initial and shuffled series. The empirical results demonstrate that the moments of switching on and switching off photoirradiation are characterized by an instantaneous increase in the degree of multifractality of the system. It is hypothesized that the observed increase in multi-fractality at the light-switching-on/off stages is indicative of a quasi-phase transition, which may be associated with the transformation of orientational defects in the polymer network.

Multifractal properties of Covid-19 data

Multifractal detrended moving average analysis (MFDFA) has been performed on time series of three different epidemiological indices, namely daily number of new cases per million population, reproduction rate and positive rate, recorded during the Covid-19 pandemic. We consider India, Japan, USA and UK for this study. For all the series the scaling behavior of MFDMA fluctuation functions has been examined, and the multifractal variables like the generalised Hurst exponent spectra and singularity spectra have been calculated. It is found that the time series of the Covid-19 indices are of multifractal nature. The degree of multifractality of the reproduction rate series is significantly weaker than the other two series for all the countries. To find out the source(s) of multifractality, we generate a set of one hundred shuffled series and Amplitude-Adjusted Fourier Transform surrogate series for each of the original series. Comparing the results obtained from the original series with those from the shuffled and surrogate series we understand that the main source of multifractality in Covid-19 data is long-range temporal correlation among the series values.

Detection of Gate Valve Leaks through the Analysis Fractal Characteristics of Acoustic Signal

This paper considers the possibility of using monofractal and multifractal analysis of acoustic signals to detect water leaks through gate valves. Detrended fluctuation analysis (DFA) and multifractal detrended fluctuation analysis (MF-DFA) were used. Experimental studies were conducted on a ½-inch nominal diameter wedge valve, which was fitted to a ¾-inch nominal diameter steel pipeline. The water leak was simulated by opening the valve. The resulting leakage rates for different valve opening conditions were 5.3, 10.5, 14, 16.8, and 20 L per minute (L/min). The Hurst exponent for acoustic signals in a hermetically sealed valve is at the same level as a deterministic signal, while the width of the multifractal spectrum closely matches that of a monofractal process. When a leak occurs, turbulent flow pulsations appear, and with small leak sizes, the acoustic signals become anticorrelated with a high degree of multifractality. As the leakage increases, the Hurst exponent also increases and the width of the multifractal spectrum decreases. The main contributor to the multifractal structure of leak signals is small, noise-like fluctuations. The analysis of acoustic signals using the DFA and MF-DFA methods enables determining the extent of water leakage through a non-sealed gate valve. The results of the experimental studies are in agreement with the numerical simulations. Using the Ansys Fluent software (v. 19.2), the frequencies of flow vortices at different positions of gate valve were calculated. The k-ω SST turbulence model was employed for calculations. The calculations were conducted in a transient formulation of the problem. It was found that as the leakage decreases, the areas with a higher turbulence eddy frequency increase. An increase in the frequency of turbulent fluctuations leads to enhanced energy dissipation. Some of the energy from ordered processes is converted into the energy of disordered processes.

Dynamic multifractal characteristics of acoustic emission about composite samples with different stress loading and unloading conditions

Studying the failure characteristics of the common composite strata structure in western China is essential for evaluating stope stability and predicting coal mine dynamic disasters. To investigate the influence of different stress loading and unloading conditions on the instability characteristics of composite samples, three triaxial loading and unloading test schemes simulating different in-situ mining depths were designed. Complex triaxial tests were conducted on 12 sets of composite samples, and the bearing capacity, acoustic emission (AE) parameters and dynamic multifractal characteristics of the samples under different stress loading or unloading conditions were analyzed. The results indicate that samples tested by stress schemes simulating greater mining depths exhibit less damage, and the failure mode is a tensile-shear mixed failure, but the tensile failure is the main failure mode. The multifractal spectral parameters Δα\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta \\alpha$$\\end{document} of AE time series during the failure of composite samples tested with triaxial loading and unloading schemes simulating different mining depths show a decreasing trend in Δα\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta \\alpha$$\\end{document} values with increasing mining depth, while the change rules of Δfα\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta f\\left( \\alpha \\right)$$\\end{document} values are the opposite. The multifractal parameter changes degree in four-layer rock structure composite samples under different stress conditions are lower than those in three-layer rock structure composite samples, indicating that the microcrack propagation process in the three-layer composite sample is more complex, resulting in higher levels of damage. The dynamic change of multifractal parameters Δα\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta \\alpha$$\\end{document} and Δfα\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta f\\left( \\alpha \\right)$$\\end{document} during different stress loading and unloading stages reflects the influence of axial pressure or confining pressure changes on crack propagation in composite samples. Compared to the initial stress stage, the non-uniformity of AE signals increases in the residual stress stage, and the proportion of large signals becomes more prominent, signifying a complex micro-fracture process in the composite samples.

Analysis of the relationship of various pathologies with the degree of multifractality of electrical activity of the brain

The review is devoted to the analysis of the relationship between dynamic changes in patterns of electrical activity of the brain during the occurrence of mental disorders in the form of paranoid schizophrenia and depression and in patterns of brain activity in cardiovascular pathology associated with permanent atrial fibrillation, as well as indicators of multifractality of the studied patterns. To assess these indicators of electroencephalographic patterns, we describe a method of multifractal analysis based on the search for maxima of wavelet coefficient modules, and to isolate the fractal component of the signal in the power spectrum we describe a method of autospectral analysis with irregular resampling. It has been shown that the main differences between the multifractal properties of the electrical activity of the brain in health and in pathology are the different widths of the multifractality spectrum and its location, associated with different types of sequential pattern values. In this regard, the multifractality indicators can serve as informative markers of neuronal disorders and can be included in a set of tests for studying various pathologies.

Multifractal organization of EEG signals in multiple sclerosis

Quantifying the complex/multifractal organization of the brain signals is crucial to fully understanding the brain processes and structure. In this contribution, we performed the multifractal analysis of the electroencephalographic (EEG) data obtained from a controlled multiple sclerosis (MS) study, focusing on the correlation between the degree of multifractality, disease duration, and disability level. Our results reveal a significant correspondence between the complexity of the time series and multiple sclerosis development, quantified respectively by scaling exponents and the Expanded Disability Status Scale (EDSS). Namely, for some brain regions, a well-developed multifractality and little persistence of the time series were identified in patients with a high level of disability, whereas the control group and patients with low EDSS were characterized by persistence and monofractality of the signals. The analysis of the cross-correlations between EEG signals supported these results, with the most significant differences identified for patients with EDSS >1 and the combined group of patients with EDSS ≤1 and controls. No association between the multifractality and disease duration was observed, indicating that the multifractal organization of the data is a hallmark of developing the disease. The observed complexity/multifractality of EEG signals is hypothetically a result of neuronal compensation – i.e., of optimizing neural processes in the presence of structural brain degeneration. The presented study is highly relevant due to the multifractal formalism used to quantify complexity and due to scarce resting-state EEG evidence for cortical reorganization associated with compensation.

THE (IN)EFFICIENCY OF USA EDUCATION GROUP STOCKS: BEFORE, DURING AND AFTER COVID-19

This paper represents a pioneering effort to investigate multifractal dynamics that exclusively encompass the return time series of USA Education Group Stocks concerning two non-overlapping periods (before, during, and after COVID-19). Given this, we employ the Multifractal Detrended Fluctuations Analysis (MF-DFA). In this sense, we investigate the generalized Hurst exponent [Formula: see text] and the Rényi exponent [Formula: see text] for each asset and quantify their statistical properties, which allowed us to observe separately the contributing small scale (primarily via the negative moments [Formula: see text]) and the large scale (via the positive moments [Formula: see text]). We perform a fourth-degree polynomial regression fit to estimate the complexity parameters that describe the degree of multifractality of the underlying process. Also, we shall apply the inefficiency multifractal index to assess the COVID-19 shock for both periods. Our findings show that for both periods, the majority of these assets are marked by multifractal dynamics associated with persistent behavior [Formula: see text], a higher degree of multifractality and the dominance of large fluctuations. At the same time, most of these assets show asymmetry parameter [Formula: see text] for both periods, indicating that large fluctuations contributed more to multifractality in the time series of returns.

Análise multifractal das plantas-daninhas em sistema de semeadura direta na região Pré-Amazônia

ABSTRACT Weeds have several mechanisms of dispersal and reproduction, resulting high spatial variability. The objective of this study was to assess the scale and spatial heterogeneity of weeds using multifractal analysis in a no-tillage system in the Pre-Amazon region. Sampling was conducted in a commercial soybean (Glycine max) production plot in the Mata Roma, Maranhão, Brazil, comprising 1,071 points marked on a 10 × 10 m grid. Data were analyzed using descriptive statistics and multifractal analysis through the box-counting method. Weeds showed varying degrees of multifractality, resulting in different scales and spatial heterogeneity in the study area. Euphorbia hirta and Turnera subulata exhibited asymmetry of branches to the left in the singularity spectrum, indicating dominance of high measurement values.

QUANTIFYING THE COVID-19 SHOCK IN CRYPTOCURRENCIES

This paper sheds light on the changes suffered in cryptocurrencies due to the COVID-19 shock through a nonlinear cross-correlations and similarity perspective. We have collected daily price and volume data for the seven largest cryptocurrencies considering trade volume and market capitalization. For both attributes (price and volume), we calculate their volatility and compute the Multifractal Detrended Cross-Correlations (MF-DCCA) to estimate the complexity parameters that describe the degree of multifractality of the underlying process. We detect (before and during COVID-19) a standard multifractal behavior for these volatility time series pairs and an overall persistent long-term correlation. However, multifractality for price volatility time series pairs displays more persistent behavior than the volume volatility time series pairs. From a financial perspective, it reveals that the volatility time series pairs for the price are marked by an increase in the nonlinear cross-correlations excluding the pair Bitcoin versus Dogecoin [Formula: see text]. At the same time, all volatility time series pairs considering the volume attribute are marked by a decrease in the nonlinear cross-correlations. The K-means technique indicates that these volatility time series for the price attribute were resilient to the shock of COVID-19. While for these volatility time series for the volume attribute, we find that the COVID-19 shock drove changes in cryptocurrency groups.

Multifractal detrended fluctuation analysis of rainfall time series in the Guadeloupe archipelago

Due to the vulnerability of the Caribbean islands to the climate change issue, it is important to investigate the behavior of rainfall. In addition, the soil of the French West Indies Islands has been contaminated by an organochlorine insecticide (Chlordecone) whose decontamination is mainly done by drainage water. Thus, it is crucial to investigate the fluctuations of rainfall in these complex environments. In this study, 19 daily rainfall series recorded in different stations of Guadeloupe archipelago from 2005 to 2014 were analyzed with the multifractal detrended fluctuation analysis (MF-DFA) method. The aim of this work is to characterize the long-range correlations and multifractal properties of the time series and to find geographical patterns over the three most important islands: Basse-Terre, Grande-Terre and Marie-Galante. This is the first study that addresses the analysis of multifractal properties of rainfall series in the Caribbean islands. This region is typically characterized by the almost constant influence of the trade winds and a high exposure to changes in the general atmospheric circulation. 12 stations exhibit two different power-law scaling regions in rainfall series, with distinct long-range correlations and multifractal properties for large and small scales. On the contrary, the rest of stations only show a single region of scales for relatively small scales. Hurst exponents reveal persistent long-range correlations which agree with other studies in nearby tropical locations. In the most eastern analyzed areas, larger scales exhibit higher persistence than smaller scales, which suggests a relationship between persistence and the highest exposure to the trade winds. Stronger conclusions can be drawn from multifractal spectra, which indicate that most rainfall series have a multifractal nature with higher complexity and degree of multifractality at the smallest scales. Furthermore, a clear dependence of multifractal nature on the latitude is revealed. All these results showed that MF-DFA is a robust tool to assess the nonlinear properties of environmental time series in a complex area.

Characterization of synthetic porous media images by using fractal and multifractal analysis

Fractal and multifractal analysis of porous images allow the description of porous media through a scale-invariant understanding. There have been numerous works that have used these analysis techniques for the description of a great variety of real porous media. However, these studies are usually comparative, being difficult to discern the role played by the pore size and pore distribution in the results of fractal and multifractal analysis. This works develops an in-depth study of different synthetic porous media from a fractal and multifractal approach, in which both the pore size and its distribution in the medium are parameterized. Thus, a set of synthetic binary images have been generated obtaining deterministic and random structures with different fixed pore sizes and also with different rates of pore sizes. Lacunarity is also calculated in order to complete the aforementioned analysis. Results evinces that fractal dimension increases with pore size and that it is higher when the pore distribution obeys a random distribution versus a deterministic one. However, when the pore size is very large, fractal dimension is similar regardless of the pore distribution. From a multifractal approach, pore size is negatively correlated with the degree of multifractality. In fact, in images with mixtures of different pore sizes it is also found that the greater the ratio of small pores, the greater degree of multifractality. By contrast, when the ratio of large pores is relevant, the degree of multifractality also increases due to the merging of macro-pores.

Relaxing Daily Price Limits and Stock Market Cross-Correlation: Evidence from MF-X-DMA Analysis

The daily price limits in the ChiNext stock market were relaxed from [Formula: see text]% to [Formula: see text]% on 24 August 2020. Using the multifractal detrended moving average cross-correlation analysis (MF-X-DMA) method, we find that relaxing daily price limits leads to a greater degree of multifractality of the ChiNext stock market, suggesting that the relaxation of daily price limits harms stock market efficiency. In addition, the positive cross-correlation between ChiNext and Chinese main board stock markets becomes weaker, i.e., relaxing daily price limits also decreases the connection between ChiNext and other stock markets. Moreover, there is an increase in the degree of the cross-correlation multifractality between ChiNext and Chinese main board stock markets, suggesting that the linkage of ChiNext and other stock markets is more complicated and risky after the relaxation of daily price limits. Our findings fulfill related literature from the perspective of multifractality and have important implications for investors.

Multiscale adaptive multifractal cross-correlation analysis of multivariate time series

In the real world, most time series generated from complex systems are nonlinear. To effectively study their fractal properties, in this work, we first generalize the adaptive fractal analysis (AFA) to the adaptive multifractal cross-correlation analysis (AMFCCA), which can be used to study the multifractal cross-correlation between two time series. Considering the complexity of time series from complex systems, we extend AMFCCA to the case of multivariate time series, namely multivariate adaptive multifractal cross-correlation analysis (MV-AMFCCA). In order to detect multiscale multifractality, we propose multiscale multivariate adaptive multifractal cross-correlation analysis (MMV-AMFCCA). By the numerical simulation on synthetic multivariate processes, our method shows the theoretical validity. Furthermore, we applied these methods to the multifractal analysis of three pollutants in urban and suburban areas in Beijing. After removing the seasonal trend, we find that the urban and suburban systems both have multifractality, especially the multifractality of the urban system are more evident than the suburban systems, and the degree of multifractality in spring and winter stronger than that in summer and autumn. Therefore, our methods are suitable for systems with multiple outputs and provide more comprehensive methods for characterizing multivariate autocorrelation and cross-correlation.

Analysis of fractal properties of horizontal component of Earth’s magnetic field of different geomagnetic conditions using MFDFA

Depending on the orientation of the interplanetary magnetic field, solar disturbances induce perturbations in the geomagnetic field as observed by magnetometers on the ground. This study examines the signatures of fractal property of the geomagnetic field’s horizontal component (H time series), as measured by the ground-based magnetometer at Bangui [BNG] (4.33°N, 18.57°E). The Multifractal detrended fluctuation analysis (MF-DFA) method is employed in the study, as it can explore higher-dimensional fractal and multifractal characteristics hidden in the time series. By incorporating MF-DFA, we investigated the changes in the fractal properties of H time series under various geomagnetic conditions, and quantified using Hurst exponent (H) and generalized Hurst exponent h(q). A clear difference in the behaviour of H component during quiet, moderate and intense storm periods is revealed through the analysis of the scaling exponents for different levels of geomagnetic activity. The generalized Hurst exponent h(q) values are found to be higher during the quiet periods, compared to moderate and severe storms periods. It is also observed that both the storm periods and geomagnetically quiet periods are characterized by fractional Brownian motion. The strong q-dependence of h(q) and multifractal scaling exponent τq indicates strong multifractal characteristics of the geomagnetic field data. Thus, the present study reveals that the degree of multifractality is more for the time series of quiet period compared to the one belongs to storm period. Also our results show that the scaling properties of the H time series possess a long-range correlation, showing a long-term persistence of the previous state.

Multifractal analysis of standardized precipitation index in Northeast Brazil

Northeast Brazil (NEB) is one of the world's most densely populous dryland regions most vulnerable to the impacts of climate change. It is expected that the risk of natural disasters related to excess or lack of water (flash floods and severe droughts) will continue increasing in the region until the end of the century. In this work, we study multifractal properties of the Standardized precipitation index (SPI) which is commonly used to evaluate the degree of severity of drought and humid conditions at different time scales and can be compared among regions with distinct climatic conditions. The method Multifractal detrended fluctuation analysis (MFDFA) is used to analyze SPI for 1, 3, 6, and 12-month accumulation periods at 133 locations across the state of Pernambuco, with climate varying from tropical humid in the coastal area to semiarid in the deep inland region. The results show that all SPI series (independently of time scale and climatic conditions) display multifractal dynamics, which can be described by properties of the multifractal spectrum. It was found that SPI series exhibit long-term persistence and multifractality that becomes stronger as accumulation time increases. For all temporal scales, the values of Hurst exponent increase in the west-east direction indicating stronger persistence of dry/wet conditions in the coastal region Zona da Mata, with a tropical humid climate, than in the dry semiarid inland Sertão region. For SPI-1, SPI-3, and SPI-6 which describe short and medium conditions the width of the multifractal spectrum (degree of multifractality) doesn't vary across the studied area, while for SPI-12 which describes long-term conditions the width of the multifractal spectrum decreases in a west-east direction, indicating stronger multifractality and higher complexity in long duration precipitation anomalies in the semiarid Sertão region.

THE EFFECTS OF COVID-19 ON MULTIFRACTALITY AND LONG-MEMORY IN ETHEREUM’S RETURNS

The global COVID-19 pandemic has shaken the global economy, not sparing the cryptocurrency market. In this paper, we investigate the impact of the COVID-19 pandemic on the dynamics of log returns of the Ethereum. The observed period is divided into three parts: the pre-pandemic period, the pandemic-induced shock, and the period after the pandemic-induced shock on the cryptocurrency market. The research focuses on the impact of the pandemic on the degree of non-linearity and multifractality of log returns. To assess the degree of non-linearity, we used the BDS test and the value of the largest Lyapunov exponent. For multifractality, long-range correlations and information efficiency, we used MF-DFA (Multifractal Detrended Fluctuation Analysis). The research results show that all observed periods have a pronounced non-linearity, but that there is no evidence of the existence of low-dimension chaos. Also, based on the results of the MF-DFA analysis, we conclude that the COVID-19 pandemic has significantly affected the long memory of the log returns of the Ethereum; however, their dynamics and characteristics are returning to the trends present before the pandemic.

Theoretical and Experimental Designs on Several Mechanical Properties of Cu-Al-Zn Shape Memory Alloys Used in the Processing Industry.

By assimilating shape memory alloys with mathematical multifractal-type objects, a theoretical model based on Scale Relativity Theory in the form of The Multifractal Theory of Motion, in order to explain the mechanical behavior of such material, is proposed. The model is validated by analyzing the mechanical behavior of Cu-Al-Zn shape memory alloy with various chemical compositions. More precisely, the multifractal tunnel effect can "mime" the mechanical hysteresis of such a material, a situation in which a direct correspondence for several mechanical properties of Cu-Al-Zn is highlighted (the chemical composition can be correlated with the shapes of the curves controlled through the multifractality degree, while the areas delimited by the same curves can be correlated with the multifractal specific potential, as a measure of the mechanical memory degree).

Nanoscale 3D Spatial Analysis of Zirconia Disc Surfaces Subjected to Different Laser Treatments

We propose the application of morphological, fractal and multifractal analysis to differentiate surface patterns on zirconia-based ceramics after laser treatments. Furthermore, we introduce two new approaches for ceramic surfaces: the Moran correlogram, which complements the spatial autocorrelation analyses, and the Otsu binarization algorithm, which was used to identify the lacunar points in the lacunarity analysis. First, the AFM (Atomic Force Microscope) topographies revealed that samples have significant differences in terms of spatial features. Quantitatively, spatial surface texture parameters indicated that all laser treatments reduced the superficial isotropy of the Zirconia disc. Moran’s correlograms revealed a decrease in the short-range correlation in all treated samples. The Minkowski functionals (MFs) indicated a reduction in the amount of matter in the peaks, especially for the sample with Nd-YAG laser treatment. The estimated fractal dimension (FD) pointed out that all laser treatments weakened the surface complexity of the Zirconia disc. On the other hand, clear fingerprints of multifractal behavior in all the samples were detected, where the highest degree of multifractality was computed for the samples with CO2 laser treatment. Finally, our findings suggested that the morphological changes caused by laser treatments on the surfaces of zirconia discs can be monitored and differentiated through the parameters proposed here.

Investigating Dynamical Complexity and Fractal Characteristics of Bitcoin/US Dollar and Euro/US Dollar Exchange Rates around the COVID-19 Outbreak.

This article investigates the dynamical complexity and fractal characteristics changes of the Bitcoin/US dollar (BTC/USD) and Euro/US dollar (EUR/USD) returns in the period before and after the outbreak of the COVID-19 pandemic. More specifically, we applied the asymmetric multifractal detrended fluctuation analysis (A-MF-DFA) method to investigate the temporal evolution of the asymmetric multifractal spectrum parameters. In addition, we examined the temporal evolution of Fuzzy entropy, non-extensive Tsallis entropy, Shannon entropy, and Fisher information. Our research was motivated to contribute to the comprehension of the pandemic's impact and the possible changes it caused in two currencies that play a key role in the modern financial system. Our results revealed that for the overall trend both before and after the outbreak of the pandemic, the BTC/USD returns exhibited persistent behavior while the EUR/USD returns exhibited anti-persistent behavior. Additionally, after the outbreak of COVID-19, there was an increase in the degree of multifractality, a dominance of large fluctuations, as well as a sharp decrease of the complexity (i.e., increase of the order and information content and decrease of randomness) of both BTC/USD and EUR/USD returns. The World Health Organization (WHO) announcement, in which COVID-19 was declared a global pandemic, appears to have had a significant impact on the sudden change in complexity. Our findings can help both investors and risk managers, as well as policymakers, to formulate a comprehensive response to the occurrence of such external events.