Multifractal Cross-correlation Research Articles

Asymmetric multifractal cross-correlations between the main world currencies and the main cryptocurrencies

The price behavior of cryptocurrencies relative to conventional currencies remains relatively understudied, despite some attempts that consider the Bitcoin market. This study examines long-range cross-correlations and asymmetric multifractality between leading conventional currencies (Swiss Franc, Euro, British Pound, Yen, and Australian dollar) and main cryptocurrencies (Bitcoin, Litecoin, Ripple, Monero, and Dash) from June 2, 2014 to February 28, 2018. Empirical results show evidence of a significant asymmetric characteristic from the cross-correlation, that is found to be persistent and multifractal in most of the cases. Bitcoin and Litecoin are the cryptocurrencies that exhibit the most multifractal behavior, whereas Monero and Ripple generally exhibit lower multifractal behavior. All cryptocurrencies exhibit a slightly lower asymmetry for longer terms.

Analysis of multifractal characterization of Bitcoin market based on multifractal detrended fluctuation analysis

In this paper, we comprehensively investigate the multifractality of Bitcoin market, find the sources of multifractal features and go further to study the multifractal cross-correlations between Bitcoin prices and other financial markets (gold and USDX). We find both Bitcoin prices and volumes display multifractal features. The fat-tailed distributions have an essential contribution to the multifractality. Long-range correlations of prices are persistent for all fluctuations, while the results of volumes are anti-persistent. We also find significant and multifractal cross-correlations between Bitcoin and gold markets, and both fat-tailed distributions and long-rang correlations contribute to the multifractality. But cross-correlations between Bitcoin and USDX are significant only for long-term.

Asymmetric risk transmission effect of cross-listing stocks between mainland and Hong Kong stock markets based on MF-DCCA method

With the implementation of “Shanghai–Hong Kong Stock Connect” and “Shenzhen–Hong Kong Stock Connect,” the mainland and Hong Kong stock markets are becoming more closely linked. Based on the A+H cross-listed A-share and H-share market indices, this study employs asymmetric multifractal cross-correlation methods to analyze the asymmetric cross-correlation between the A-share and H-share markets from diverse perspectives of different ups and downs and various conduction directions with 79 sample stocks from January 1 a=2004 to May 26, 2017. Empirical results show that the A+H shares have long memory in different trends, which is stronger in the downward trend of stock price. It indicates that regardless of which market with A+H shares showing a downward trend are on, driving the future on the local market and the corresponding cross-listed market show a downward trend is easier than driving the rising trend. In addition, a bidirectional risk conduction effect exists between A and H shares, and the A-share market has a strong transmission effect on the H-share market.

Are cross-correlations between Turkish Stock Exchange and three major country indices multifractal or monofractal?

The analysis of linkages between financial markets has been a promising subject of study after globalization. Main consequence of these linkages is on transmission of the crisis from one country to another. Therefore, identifying and modeling of those linkages are important issues in the analysis of financial markets. According to studies the cross-correlations present nonlinear behavior and in general the well-known methods fail to predict such correlations. In this paper, we aim to show the existence of nonlinear cross-correlations between Turkish Stock Exchange and major developed country indices. For this purpose, we use the Multifractal Detrending Moving-Average Cross-correlation Analysis (MF-X-DMA) which is designed for detecting long-range power-law correlations. In the analysis we use the daily financial return and volatility series of Turkish stock market index BIST100 and developed market indexes which are S&P500, DAX30, FTSE100 for a period of 11 years between 01/01/2007-01/01/2018. The results show the existence of multifractality and long-range power-law cross-correlations.

Multifractal characterization of Brazilian market sectors

We study auto correlations and cross correlations of daily price returns for seven Brazilian market (Bovespa) sectors using multifractal detrended fluctuation analysis (MF-DFA) and multifractal detrended cross correlation analysis (MF-DXA). We discover rather distinct multifractal behavior for different market sectors, which indicates that individual sectors follow different dynamics from the entire market. Our analysis reveals that most sectors are market efficient due to the lack of long term correlations. Shuffling the series suggests that multifractality in the auto correlations arises both from a broad probability density function and from different long term correlations. Comparisons of multifractal cross correlations between Bovespa and market sectors reveals that some sectors are more affected by multifractality of the entire market, while others are more affected by multifractality of the sectors themselves. A multifractal analysis of cross correlations between different market sectors provides a multifractal description of the Brazilian sectors.

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.

Multifractal detrended cross-correlation analysis on air pollutants of University of Hyderabad Campus, India

In this paper, we study the multifractal characteristics and cross-correlation behaviour of Air Pollution Index (API) time series data through multifractal detrended cross-correlation analysis method. We analyse the daily API records of nine air pollutants of the university of Hyderabad campus for a period of three years (2013–2016). The cross-correlation behaviour has been measured from the Hurst scaling exponents and the singularity spectrum quantitatively. From the results, it is found that the cross-correlation analysis shows anti-correlation behaviour for all possible 36 bivariate time series. We also observe the existence of multifractal nature in all the bivariate time series in which many of them show strong multifractal behaviour. In particular, the hazardous particulate matter PM2.5 and inhalable particulate matter PM10 shows anti-correlated behaviour with all air pollutants.

Does Bitcoin exhibit the same asymmetric multifractal cross-correlations with crude oil, gold and DJIA as the Euro, Great British Pound and Yen?

We applied MF-ADCCA to analyze the presence and asymmetry of the cross-correlations between the major currency rates and Bitcoin, and the Dow Jones Industrial Average (DJIA), gold price and the oil crude market. We find that multifractality exists in every cross-correlation studied, and there is asymmetry in the cross-correlation exponents under different trend of the WTI, Gold and DJIA. Bitcoin shows a greater multifractal spectra than the other currencies on its cross-correlation with the WTI, the Gold and the DJIA. Bitcoin shows a clearly different relationship with commodities and stock market indices which has to be taken into consideration when investing. This has to do with the years this currency has been traded, the characteristics of cryptocurrencies and its gradual adoption by financial organizations, governments and the general public.

Asymmetric multiscale multifractal detrended cross-correlation analysis for the 1999–2000 California electricity market

In order to access the asymmetric cross-correlation between two time series in a wide range of scales, the method of asymmetric multiscale multifractal detrended cross-correlation analysis (A-MMFCCA) is proposed in this study, which is an extension of the asymmetric detrended fluctuation analysis and the multifractal cross-correlation analysis. Multiscale multifractal detrended cross-correlation analysis enables us to find that the price and the load series of California electricity market exhibit long-range persistent multifractal cross-correlation at different scale ranges during 1999–2000, and the scale range has an important impact on the fractal properties of cross-correlation. Furthermore, the asymmetric cross-correlation between the price and the load series is detected by means of our proposed A-MMFCCA method. Through comparing the local Hurst surfaces with the uptrends and downtrends, we further find that the asymmetric cross-correlation between the price and the load series in 2000 is more significant than that in 1999; the contribution of asymmetric cross-correlation in 1999–2000 mainly depends on different directional trends at different scale ranges. The findings help to interpret the power crisis phenomenon and develop effective and prospective market policy recommendations.

MULTIFRACTAL CROSS WAVELET ANALYSIS

Complex systems are composed of mutually interacting components and the output values of these components usually exhibit long-range cross-correlations. Using wavelet analysis, we propose a method of characterizing the joint multifractal nature of these long-range cross correlations, a method we call multifractal cross wavelet analysis (MFXWT). We assess the performance of the MFXWT method by performing extensive numerical experiments on the dual binomial measures with multifractal cross correlations and the bivariate fractional Brownian motions (bFBMs) with monofractal cross correlations. For binomial multifractal measures, we find the empirical joint multifractality of MFXWT to be in approximate agreement with the theoretical formula. For bFBMs, MFXWT may provide spurious multifractality because of the wide spanning range of the multifractal spectrum. We also apply the MFXWT method to stock market indices, and in pairs of index returns and volatilities we find an intriguing joint multifractal behavior. The tests on surrogate series also reveal that the cross correlation behavior, particularly the cross correlation with zero lag, is the main origin of cross multifractality.

Asymmetric multifractal cross-correlations and time varying features between Latin-American stock market indices and crude oil market

We apply MF-ADCCA to analyze the presence and asymmetry of the cross-correlations between Latin-American and US stock market indices and crude oil market. We find that multifractality exists in this cross-correlations, and that there is asymmetry on its behavior. The asymmetry degree changes accordingly to the series considered for the trend behavior. We find that fluctuation sizes greatly influence the asymmetry in the cross-correlation exponent, increasing for large fluctuations when we consider the trend of the crude oil price. We also find no clear differences in the exponents with different scales under different trends of the WTI, contrary to other studies in asymmetric scaling behavior. When we examine the time varying features of the asymmetry degree we find that the US indices show a consistent behavior in time for both trends, where the cross-correlation exponents tend to be larger for downward trends. On the other hand, given the more heterogeneous individual properties of Latin-American indices, the asymmetry behavior varies more depending on the trend considered.

Price–volume multifractal analysis of the Moroccan stock market

In this paper, we analyzed price–volume multifractal cross-correlations of Moroccan Stock Exchange. We chose the period from January 1st 2000 to January 20th 2017 to investigate the multifractal behavior of price change and volume change series. Then, we used multifractal detrended cross-correlations analysis method (MF-DCCA) and multifractal detrended fluctuation analysis (MF-DFA) to analyze the series. We computed bivariate generalized Hurst exponent, Rényi exponent and spectrum of singularity for each pair of indices to measure quantitatively cross-correlations. Furthermore, we used detrended cross-correlations coefficient (DCCA) and cross-correlation test (Q(m)) to analyze cross-correlation quantitatively and qualitatively. By analyzing results, we found existence of price–volume multifractal cross-correlations. The spectrum width has a strong multifractal cross-correlation. We remarked that volume change series is anti-persistent when we analyzed the generalized Hurst exponent for all moments q. The cross-correlation test showed the presence of a significant cross-correlation. However, DCCA coefficient had a small positive value, which means that the level of correlation is not very significant. Finally, we analyzed sources of multifractality and their degree of contribution in the series.

Multifractal temporally weighted detrended cross-correlation analysis to quantify power-law cross-correlation and its application to stock markets.

A new method-multifractal temporally weighted detrended cross-correlation analysis (MF-TWXDFA)-is proposed to investigate multifractal cross-correlations in this paper. This new method is based on multifractal temporally weighted detrended fluctuation analysis and multifractal cross-correlation analysis (MFCCA). An innovation of the method is applying geographically weighted regression to estimate local trends in the nonstationary time series. We also take into consideration the sign of the fluctuations in computing the corresponding detrended cross-covariance function. To test the performance of the MF-TWXDFA algorithm, we apply it and the MFCCA method on simulated and actual series. Numerical tests on artificially simulated series demonstrate that our method can accurately detect long-range cross-correlations for two simultaneously recorded series. To further show the utility of MF-TWXDFA, we apply it on time series from stock markets and find that power-law cross-correlation between stock returns is significantly multifractal. A new coefficient, MF-TWXDFA cross-correlation coefficient, is also defined to quantify the levels of cross-correlation between two time series.

The cross-correlation analysis of multi property of stock markets based on MM-DFA

In this paper, we propose a new method called DH-MXA based on distribution histograms of Hurst surface and multiscale multifractal detrended fluctuation analysis. The method allows us to investigate the cross-correlation characteristics among multiple properties of different stock time series. It may provide a new way of measuring the nonlinearity of several signals. It also can provide a more stable and faithful description of cross-correlation of multiple properties of stocks. The DH-MXA helps us to present much richer information than multifractal detrented cross-correlation analysis and allows us to assess many universal and subtle cross-correlation characteristics of stock markets. We show DH-MXA by selecting four artificial data sets and five properties of four stock time series from different countries. The results show that our proposed method can be adapted to investigate the cross-correlation of stock markets. In general, the American stock markets are more mature and less volatile than the Chinese stock markets.

Joint multifractal analysis based on wavelet leaders

Mutually interacting components form complex systems and the outputs of these components are usually long-range cross-correlated. Using wavelet leaders, we propose a method of characterizing the joint multifractal nature of these long-range cross correlations, a method we call joint multifractal analysis based on wavelet leaders (MF-X-WL). We test the validity of the MF-X-WL method by performing extensive numerical experiments on the dual binomial measures with multifractal cross correlations and the bivariate fractional Brownian motions (bFBMs) with monofractal cross correlations. Both experiments indicate that MF-X-WL is capable to detect the cross correlations in synthetic data with acceptable estimating errors. We also apply the MF-X-WL method to the pairs of series from financial markets (returns and volatilities) and online worlds (online numbers of different genders and different societies) and find an intriguing joint multifractal behavior.

Multifractal cross-correlations between crude oil and tanker freight rate

Analysis of crude oil price and tanker freight rate volatility attract more attention as the mechanism is not only the basis of industrialization but also a vital role in economics, especially after the year 2008 when financial crisis notably blew the maritime transportation. In this paper, we studied the cross-correlations between the West Texas International crude oil (WTI) and Baltic Exchange Dirty Tanker Index (BDTI) employing the Multifractal Detrended Cross-Correlation Analysis (MF-DCCA). Empirical results show that the degree of short-term cross-correlation is higher than that in the long term and that the strength of multifractality after financial crisis is larger than that before. Moreover, the components of multifractal spectrum are quantified with the finite-size effect taken into consideration and an improved method in terms of constructing the surrogated time series provided. Numerical results show that the multifractality is generated mostly from the nonlinear and the fat-tailed probability distribution (PDF) part. Also, it is apparent that the PDF part changes a lot after the financial crisis. The research is contributory to risk management by providing various instructions for participants in shipping markets. Our main contribution is that we investigated both the multifractal features and the origin of multifractality and provided confirming evidence of multifractality through numerical results while applying quantitative analysis based on MF-DCCA; furthermore, the research is contributory to risk management since it provides instructions in both economic market and stock market simultaneously. However, constructing the surrogated series in order to obtain consistence seems less convincing which requires further discussion and attempts.

Two-dimensional multifractal cross-correlation analysis

There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross-correlations. This paper presents two-dimensional multifractal cross-correlation analysis based on the partition function (2D-MFXPF), two-dimensional multifractal cross-correlation analysis based on the detrended fluctuation analysis (2D-MFXDFA) and two-dimensional multifractal cross-correlation analysis based on the detrended moving average analysis (2D-MFXDMA). We apply these methods to pairs of two-dimensional multiplicative cascades (2D-MC) to do a comparative study. Then, we apply the two-dimensional multifractal cross-correlation analysis based on the detrended fluctuation analysis (2D-MFXDFA) to real images and unveil intriguing multifractality in the cross correlations of the material structures. At last, we give the main conclusions and provide a valuable reference on how to choose the multifractal algorithms in the potential applications in the field of SAR image classification and detection.

Power law cross-correlations between price change and volume change of Indian stocks

We study multifractal long-range correlations and cross-correlations of daily price change and volume change of 50 stocks that comprise Nifty index of National Stock Exchange, Mumbai, using MF-DFA and MF-DCCA methods. We find that the time series of price change are uncorrelated, whereas anti-persistent long-range multifractal correlations are found in volume change series. We also find antipersistent long-range multifractal cross-correlations between the time series of price change and volume change. As multifractality is a signature of complexity, we estimate complexity parameters of the time series of price change, volume change, and cross-correlated price–volume change by fitting the fourth-degree polynomials to their multifractal spectra. Our results indicate that the time series of price change display high complexity, whereas the time series of volume change and cross-correlated price–volume change display low complexity.

基于AMF-HXA的长株潭空气质量指数互相关性分析

随着我国经济的飞速发展，近年来我国的空气污染问题越来越严重。工业污染物和生活供暖产生的细微颗粒物成为了空气污染的两大源泉。如何揭露不同城市间空气质量指数(Air Quality Index, AQI)与传统空气污染因子如工业污染物NO2和细微颗粒物如PM2.5的关系，成为了我们必须考虑的关键问题。本文利用流行的仿多重分形高度互相关分析研究了长株潭每个城市的上述三个指标的无标度性、AQI与两种污染指标的波动差异性及两两城市间的PM2.5浓度与NO2浓度的互相关及其显著性、每个城市AQI与这两种污染指标在春夏秋冬四个季节里的互相关及其显著性。结果表明每个城市的AQI与PM2.5的波动情况基本吻合，而AQI与NO2的波动具有较大差异；四个季节里长株潭两两城市间PM2.5都具有极显著的互相关性，而NO2在不同季节里互相关性不同。这些结论为探寻长株潭影响空气质量的相互影响提供了一个新视角。 As the economy soars, air pollution sweeps across the China in recent years. Industrial waste gas and life stove and heating are two main sources of the air pollution. How to uncover the relationship between the air quality index (AQI) and traditional air pollution factors, such as industrial pollutants, NO2 and fine particles, such as PM2.5 for different cities has become a key point we care about. In this paper, we apply the popular analogous multifractal height cross-correlation analysis (AMF-HXA) into investigating the air quality in neighboring Changsha city, Zhuzhou city and Xiangtan city in Central China, which includes that the scale free of AQI, PM2.5 concentration and NO2 concentration, the fluctuation difference between the AQI and PM2.5 as well as NO2, respectively, the cross-correlation of the two pollution factors in each two cities, and the cross-correlations together with the significance between the AQI and above two pollution factors in each cities. The main conclusions are: 1) the fluctuation of AQI is consistent with that of PM2.5 concentration but disagreed with that of NO2 in different seasons; 2) there is high cross-correlation significance of PM2.5 between each two cities in all of seasons but the significance of the cross-correlation of NO2 is different in different seasons. These conclusions can provide a new insight to unveil the variation tendency of air pollution between different cities.

The application of the multifractal cross-correlation analysis methods in radar target detection within sea clutter

Abstract Many complex systems generate multifractal time series which are long-range cross-correlated. This paper introduces three multifractal cross-correlation analysis methods, such as multifractal cross-correlation analysis based on the partition function approach (MFXPF), multifractal detrended cross-correlation analysis (MFDCCA) methods based on detrended fluctuation analysis (MFXDFA) and detrended moving average analysis (MFXDMA), which only consider one moment order. We do comparative analysis of the artificial time series (binomial multiplicative cascades and Cantor sets with different probabilities) by these methods. Then we do a feasibility test of the fixed threshold target detection within sea clutter by applying the multifractal cross-correlation analysis methods to the IPIX radar sea clutter data. The results show that it is feasible to use the method of the fixed threshold based on the multifractal feature parameter Δ f ( α ) by the MFXPF and MFXDFA-1 methods. At last, we give the main conclusions and provide a valuable reference on how to choose the multifractal algorithms, the detection parameters and the target detection methods within sea clutter in practice.