Components Of Multifractality Research Articles

The Dynamic Effects of COVID-19 and the March 2020 Crash on the Multifractality of NASDAQ Insurance Stock Markets

Triggered by COVID-19, one of the most dramatic crashes in the stock market in history occurred in March 2020. The sharp reductions in NASDAQ insurance stock indexes were observed after the occurrence of COVID-19 and in March 2020. In this study, the NASDAQ insurance stock markets (including NASDAQ Insurance Index, Developed Markets Insurance Index, and Emerging Markets Insurance Index) and NASDAQ Composite Index are utilized. The “scissors difference” between the NASDAQ Insurance Index and NASDAQ Composite Index is observed. The dynamic effects of the COVID-19 epidemic and the March 2020 crash on the multifractality of four series are explored. Firstly, the apparent and intrinsic multifractality, the components of multifractality, and the dynamic effects of the COVID-19 epidemic on these indexes are analyzed. Secondly, the multifractal cross-correlation between the NASDAQ Insurance Index and NASDAQ Composite Index is investigated. The dynamic influence of the COVID-19 epidemic on the cross-correlation is examined. The multifractal analysis results reveal that four series both before and after the occurrence of COVID-19 have multifractal characteristics. The stronger multifractal characteristics and the greater multifractal degree are obtained after the occurrence of COVID-19. The intrinsic multifractality of the three indexes ascends largely after the occurrence of COVID-19. The multifractal cross-correlation analysis illustrates that the cross-correlation between two indexes before and after the occurrence of COVID-19 is multifractal. The stronger multifractal cross-correlations and greater multifractal degrees are shown. The contribution of the intrinsic multifractal cross-correlation increased after the occurrence of COVID-19.

Multiscale assessment of the degree of multifractality for physiological time series.

Recent advancements in detrended fluctuation analysis (DFA) allow evaluating multifractal coefficients scale-by-scale, a promising approach for assessing the complexity of biomedical signals. The multifractality degree is typically quantified by the singularity spectrum width (WSS), a method that is critically unstable in multiscale applications. Thus, we aim to propose a robust multiscale index of multifractality, compare it with WSS and illustrate its performance on real biosignals. The proposed index is the cumulative function of squared increments between consecutive DFA coefficients at each scale n: αCF(n). We compared it with WSS calculated scale-by-scale considering monofractal/monoscale, monofractal/multiscale, multifractal/monoscale and multifractal/multiscale random processes. The two indices provided qualitatively similar descriptions of multifractality, but αCF(n) differentiated better the multifractal components from artefacts due to crossovers or detrending overfitting. Applied on 24 h heart rate recordings of 14 participants, the singularity spectrum failed to always satisfy the concavity requirement for providing meaningful WSS, while αCF(n) demonstrated a statistically significant heart rate multifractality at night in the scale ranges 16-100 and 256-680 s. Furthermore, αCF(n) did not reject the hypothesis of monofractality at daytime, coherently with previous reports of lower nonlinearity and monoscale multifractality during the day. Thus, αCF(n) appears a robust index of multiscale multifractality that is useful for quantifying complexity alterations of physiological series. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.

Study of the structural degradation of steel 15Kh5M upon continuous duty

Structural degradation of the material upon long-term thermal and force impacts is a complex process which includes migration of the grain boundaries, diffusion of the active elements of the external and technological environment, hydrogen embrittlement, aging, grain boundary corrosion and other mechanisms. Application of the fractal and multifractal formalism to the description of microstructures opens up wide opportunities for quantitative assessment of the structural arrangement of the material, clarifies and reveals new aspects of the known mechanisms of structural transformations. Multifractal parameterization allows us to study the processes of structural degradation from the images of microstructures and identify structural changes that are hardly distinguishable visually. Any quantitative structural indicator can be used to calculate the multifractal spectra of the microstructure, but the most preferable is that provides the maximum range of variation in the numerical values of the multifractal components. The results of studying structural degradation of steel 15Kh5M upon continuous duty are presented. It is shown that structural degradation of steel during operation under high temperatures and stresses is accompanied by enlargement of the microstructural objects, broadening of the grain boundaries and allocation of the dispersed particles which are represented as point objects in the images. The processes of structural degradation lead to an increase in the range of changes in the components of the multifractal spectra. High values of complex indicators of structural arrangement indicate to an increase in heterogeneity and randomness at the micro-scale level, but at the same time, to manifestation of the ordered combinations of individual submicrostructures. Those structural transformations adapt the material to external impacts and provide the highest reliability and fracture resistance of the material.

The effectiveness of the monetary policy in China: New evidence from long-range cross-correlation analysis and the components of multifractality

This study examines the long-range cross-correlations between the Chinese Renminbi (RMB) exchange rate and the Shanghai Interbank Offered Rate (Shibor) markets both on qualitative and quantitative basis, using a comprehensive dataset covering the period from October 8, 2006 to September 30, 2016. Our empirical results suggest that a nonlinear time-varying correlation exists between the markets. We also verify that the third stage of China’s monetary policy reform from 2011 to 2016 had a greater influence on both small and large foreign exchange (FX) market fluctuations. Using the multifractality analysis, we conclude that China’s monetary policy can significantly reduce the multifractality of cross-correlations between the RMB exchange rate and Shibor rate markets, and that market efficiency in the third stage of policy reform is improved. Furthermore, the source of multifractality of cross-correlations is found mostly in the nonlinear correlation and fat-tailed probability distribution (PDF) components.

Insights from multifractality analysis of tanker freight market volatility with common external factor of crude oil price

This paper is intended for exploring the multifractal features of tanker freight rate market volatility with the common external factor of crude oil price by both the multifractal cross-correlation analysis method (MF-CCA) and the multifractal detrended partial cross-correlation analysis method (MF-DPXA) with consideration of finite size effect. The multifractal spectrums of original, random and surrogate time series are employed to separate the three components of multifractality, and to uncover the influence of financial crisis and oil price on volatility and cross-correlated fluctuations of the tanker freight rates. After the financial crisis in terms of the generalized Hurst exponent, stronger non-linear characteristic and noticeable anti-persistent characteristic in cross correlations between freight rates are supported by the MF-DPXA analysis. Meanwhile, stronger multifractality is indicated by the MF-CCA analysis. These results deepen the understanding of multifractality in tanker freight rate market, and provide investors, shipping related operators or even market players with insight to adjust their marketing strategies.

Finite-size effect and the components of multifractality in transport economics volatility based on multifractal detrending moving average method

Abstract Analysis of freight rate volatility characteristics attracts more attention after year 2008 due to the effect of credit crunch and slowdown in marine transportation. The multifractal detrended fluctuation analysis technique is employed to analyze the time series of Baltic Dry Bulk Freight Rate Index and the market trend of two bulk ship sizes, namely Capesize and Panamax for the period: March 1st 1999–February 26th 2015. In this paper, the degree of the multifractality with different fluctuation sizes is calculated. Besides, multifractal detrending moving average (MF-DMA) counting technique has been developed to quantify the components of multifractal spectrum with the finite-size effect taken into consideration. Numerical results show that both Capesize and Panamax freight rate index time series are of multifractal nature. The origin of multifractality for the bulk freight rate market series is found mostly due to nonlinear correlation.

The gauge of multifractal components for some self-similar sets

The gauge of multifractal components for some self-similar sets

Components of multifractality in the central England temperature anomaly series

We study the multifractal nature of the Central England Temperature (CET) anomaly, a time series that spans more than 200 years. The data are analyzed in two ways: as a single set and by using a sliding window of 11 years. In both cases, we quantify the width of the multifractal spectrum as well as its components, which are defined by the deviations from the Gaussian distribution and the dependence between measurements. The results of the first approach show that the key contribution to the multifractal structure comes from the dynamical dependencies, mainly weak ones, followed by a residual contribution of the deviations from the Gaussian. The sliding window approach indicates that the peaks in the evolution of the non-Gaussian contribution occur almost at the same dates associated with climate changes that were determined in previous works using component analysis methods. Moreover, the strong non-Gaussian contribution from the 1960 s onwards is in agreement with global results recently presented.

Finite-size effect and the components of multifractality in financial volatility

Many financial variables are found to exhibit multifractal nature, which is usually attributed to the influence of temporal correlations and fat-tailedness in the probability distribution (PDF). Based on the partition function approach of multifractal analysis, we show that there is a marked finite-size effect in the detection of multifractality, and the effective multifractality is the apparent multifractality after removing the finite-size effect. We find that the effective multifractality can be further decomposed into two components, the PDF component and the nonlinearity component. Referring to the normal distribution, we can determine the PDF component by comparing the effective multifractality of the original time series and the surrogate data that have a normal distribution and keep the same linear and nonlinear correlations as the original data. We demonstrate our method by taking the daily volatility data of Dow Jones Industrial Average from 26 May 1896 to 27 April 2007 as an example. Extensive numerical experiments show that a time series exhibits effective multifractality only if it possesses nonlinearity and the PDF has an impact on the effective multifractality only when the time series possesses nonlinearity. Our method can also be applied to judge the presence of multifractality and determine its components of multifractal time series in other complex systems.

The singularity spectrum of some non-regularity moran fractals

In this paper, we shall study the multifractal decomposition behavior for a family of sets E known as Moran fractals. For each value of the parameter α ∈ ( α min, α max), we define “multifractal components” E α of E, and show that they are non-regularity fractals (in the sense of Taylor). By obtaining the new sufficient conditions for the valid multifractal formalisms of non-regularity Moran measures, we give explicit formula for the Hausdorff dimension and Packing dimension of E α respectively. In particular, we describe a large class of non-regularity Moran measure satisfying the explicit formula.

Microcanonical multifractal formalism: Application to the estimation of ocean surface velocities

In this paper we investigate the validity of the multifractal formalism to study sea surface temperature (SST). It is shown that SST patterns observed in moderate resolution SST images have anomalous scaling properties characteristic of a multifractal structure. The most probable origin of the observed structures is the turbulent character of the oceanic flow as they evolve slowly and are very persistent in times compatible with ocean mesoscale dynamics (several days). The spectrum of singularity exponents indicates that the dynamics of the processes leading to the geometrical arrangement of the SST patterns is quite general over the available range of scales. As a consequence, multifractal techniques can be used to extract properties of the underlying flow. In particular, the geometry of the SST multifractal components is closely linked with the ocean flow, which allows to build a reasonable guess of the streamfunction (defined as the maximum singular streamfunction (MSS)) from a single SST image. Thus the ocean surface velocity field can be easily inferred, with some limitations. As multifractal analysis is in essence a geometrical approach, the method is able to retrieve a high resolution velocity field, well localized in space, but with some indetermination on the modulus and sense of velocity vectors. To solve this, a general framework for the integration of extra information is proposed, what is illustrated with an example merging MSS with altimetric data.

Components of multifractality in high-frequency stock returns

We analyzed multifractal properties of 5-min stock returns from a period of over two years for 100 highly capitalized American companies. The two sources: fat-tailed probability distributions and non-linear temporal correlations, vitally contribute to the observed multifractal dynamics of the returns. For majority of the companies the temporal correlations constitute a much more significant related factor, however.

The Singularity Spectrum f(?) of Some Moran Fractals

We show that the multifractal decomposition behaves as expected for a family of sets E known as homogeneous Moran fractals associated with the Fibonacci sequence ω, using probability measures μ(ω) associated with the Fibonacci sequence ω. For each value of a parameter α∈ (αmin, αmax), we define ‘multifractal components’ Eα of E, and show that they are fractals in the sense of Taylor. We give the explicit formula for the dimension of Eα. Also our method can be used for the Moran fractals associated with some more general sequences.

Multifractal Components of Multiplicative Set Functions

Multifractal Components of Multiplicative Set Functions

Multifractal Decompositions of Digraph Recursive Fractals

We prove that the multifractal decomposition behaves as expected for a family of sets K known as digraph recursive fractals, using measures μ of Markov type. For each value of a parameter α between a minimum α min and maximum α max , we define «multifractal components» K (α) of K, and show that they are fractals in the sense of Taylor. The dimension f(α) of K (α) is computed from the data of the problem. The typical concave «multifractal f(α)» dimension spectrum curve results