Multifractal Detrended Cross-correlation Analysis Research Articles

Multifractal detrended cross-correlation analysis of wind speed and solar radiation.

In this work, the multifractal properties of wind speed and solar radiation are studied in a small region in which a wide variety of micro-climates are concentrated. To achieve this, two years of hourly data are analyzed in Guadeloupe archipelago. The four selected stations for wind speed were chosen according to trade winds direction, while solar radiation is recorded at a representative location at the center of the island. First, the results of the multifractal detrended fluctuation analysis (MF-DFA) showed the multifractal and persistent behaviors of wind speed at all locations. Due to the continental effect that increases along the transect, the Hurst exponent (H) values decrease from east to west. In addition, the MF-DFA clearly highlighted the presence of a nocturnal radiative layer that weakens wind speed in the surface layer. The multifractality degree [Δh(q)] values confirm the peculiarity of wind speed regimes at the center of the island. Thereafter, the MF-DFA results of solar radiation exhibited its multifractal and persistent behavior. Due to the solar radiation planetary scale, its Δh(q) is lower than those obtained for wind speed, which strongly depends on synoptic and local scales. The source of multifractality of wind speed and solar radiation is due to correlations of small and large fluctuations. Finally, the results of the multifractal detrended cross-correlation analysis between wind speed and solar radiation pointed out that the multifractal cross-correlation degree [Δhxy(q)] is identical for each site, which is not the case for Hurst exponent values.

Multifractal Analysis of Market Efficiency across Structural Breaks: Implications for the Adaptive Market Hypothesis

The primary objective of this paper is to assess the behavior of long memory in price, volume, and price-volume cross-correlation series across structural breaks. The secondary objective is to find the appropriate structural breaks in the price series. The structural breaks in the series are identified using the Bai and Perron procedure, and in each segment, Multifractal Detrended Fluctuation Analysis (MFDFA) and Multifractal Detrended Cross-Correlation Analysis (MFDCCA) are conducted to capture the long memory in each series. The price series is persistent in small fluctuations and anti-persistent in large fluctuations across all the structural segments. This confirms that long memory in the series is not affected by the structural breaks. Both volume and price-volume cross-correlation are anti-persistent in all the structural segments. In other words, volume acts as a carrier of the information only in the non-volatile (normal) market. The varying Hurst exponent across the structural segments indicates the varying levels of persistence and signifies the volatile market. The findings of the study are useful for understanding the practical implications of the Adaptive Market Hypothesis (AMH).

Segment Stock Market, Foreign Investors, and Cross-Correlation: Evidence from MF-DCCA and Spillover Index

Employing the tools of multifractal detrended cross-correlation analysis (MF-DCCA) and Diebold–Yilmaz spillover index (D.Y. spillover index), we examine the effect that the foreign investors have on the cross-correlations between the two-segment stock markets, that are the accessible and the inaccessible stock markets, and the other ten respective stock markets. The shares cross-listed by the same corporates on both the A-share and H-share stock markets of China serve as the best sample to compile the two stock indices, which stands for the inaccessible stock market (AHA) and the accessible stock market (AHH), respectively. Empirical results show that the cross-correlations between the two-segment stock markets and the other ten pairs are multifractal, the multifractal strength of cross-correlations is stronger in AHH than AHA, and the intensified growth of the multifractal cross-correlations in AHA can be seen as the increasing of the openness in the inaccessible market. The empirical result of D.Y. spillover index is consistent with the multifractal analysis above, and another interesting finding is that among the selected markets, the three markets with the strongest spillover effects with AHA and AHH are Taiwan, South Korea, and Singapore, respectively, and the weakest one is Australia during the sample scenarios.

Multifractal detrended cross-correlation analysis on benchmark cryptocurrencies and crude oil prices

In this paper, we investigate the cross-correlations between three benchmark cryptocurrencies (including Bitcoin, Ethereum and Ripple) and some of the well-known crude oils (West Texas Intermediate and Brent). The data of the study spans from 7 August 2015 to 10 June 2019. We utilized the multifractal detrending moving average cross-correlation analysis (MF-X-DMA) method to examine the multifractal features among data. We find that the cross-correlations between each pair of time series are significant by using the cross-correlation test statistic Qcc(m)”-analysis and detrended moving average cross-correlation analysis (DMCA) coefficient. Also, the cross-correlation coefficients ρDMCA show that the data are positively correlated, but the degree of correlation has been elevated by increasing the window intervals v. The observed results obtained through the MF-X-DMA method infer the existence of multifractal cross-correlations on ten bivariate time series in the study and that the strength of multifractality between Ethereum and Ripple is the highest, followed by the strength of multifractality between WTI crude oil and Ethereum.

MARGIN-TRADING ACTIVITIES AND FUTURE STOCK RETURNS: NEW EVIDENCE FROM NONLINEAR ANALYSIS

Using multifractal detrended cross-correlation analysis (MF-DCCA) and nonlinear Granger causality test, this paper examines the return predictability of margin-trading activities. Results show that the predictive power of margin-trading activities on subsequent stock returns varies with respect to the different aspects of margin trading. In line with previous studies, we find no significant correlation between margin-buying amount and subsequent stock returns. However, the margin-covering amount is negatively associated with subsequent stock returns; and margin debt is positively associated with the future stock returns. In general, our findings suggest that margin traders may have no positive information when they conduct a margin-buying position, but may possess negative information when covering their positions.

A Review on Fractal Analysis and its Applications in Structural Engineering

Fractals refer to rough or fragmented geometric shape in which each sub-section is a reduced-size copy of the whole. Its potential to describe the complex and irregular phenomena leads to wider applicability, and its enormous unexplored potential in the field of structural engineering is to be attended by the research community. This paper first presents a brief theoretical background of the most popular algorithms, such as the box-counting method, Multifractal Detrended Fluctuation Analysis (MFDFA), and Multifractal Detrended Cross-Correlation Analysis (MFDCCA). This paper further presents a comprehensive review of the potential of fractals and multifractals in four specific domains, such as crack identification, pore structure analysis and chloride resistance, and structural damage detection. The review of literature further reveals that 2 dimensional and multi-dimensional extension of fractal theory can be effectively coupled with image analysis for micro-level examination of pore structures, which opens the scope for abundant applications in research in the field of structural materials. The applications of MFDFA and cross-correlation analysis structural health monitoring are very recent research contributions in the field, and they are in the infant stage of applications. The review of research works performed in this study shows that the complete potential of fractals in the structural engineering field is not yet explored by the researchers.

Multifractal analysis of Indian public sector enterprises

In this paper, we apply the methods, Multifractal Detrended Fluctuation Analysis (MF-DFA) and Multifractal Detrended Cross-Correlation Analysis (MF-DXA) to study the auto correlation/cross-correlation behaviour and multifractal characteristics on twenty three stock market indices of Department of Public Enterprises (DPE), India. The auto correlation and cross-correlation have been measured from the Hurst scaling exponents and the singularity spectrum quantitatively. From the calculated power law scaling exponents we observe the volume and price-volume change time series possess strong anti-persistent behaviour. The price change of different time series shows persistent, stochastic and anti-persistent behaviour. We also observe the existence of multifractal characteristics in all price, volume and price-volume change time series. The price changes in the time series shows high complexity compared to volume and cross correlated price-volume.

China's copper futures market efficiency analysis: Based on nonlinear Granger causality and multifractal methods

Abstract: Price discovery and market efficiency are the centerpiece of the market microstructure design. This study investigates the nonlinear correlation between the spot and futures prices in China's copper market using nonlinear Granger causality and multifractal methods, and it further analyzes the dynamic efficiency of China's copper futures market. According to the results of the nonlinear Granger causality test, there is a significant bidirectional nonlinear causality between the spot and futures prices in China's copper market. Excluding the effects of the first and second orders, there is still a high-order correlation between the spot and futures prices of the copper market. Additionally, the multifractal detrended cross-correlation analysis (MF-DCCA) method is used to obtain the long-term correlations of high order in the spot and futures markets. The time-varying rolling Hurst exponent indicates that the efficiency of China's copper futures market has gradually become more effective over time.

Asymmetric Multifractal Analysis of Rebar Futures and Spot Market in China

In this study, a wavelet denoising method is first used to eliminate the influence of noise. Then, an overlapping smooth window technique is introduced into the asymmetric multifractal detrended cross-correlation analysis method, which was combined with the multiscale multifractal analysis method, resulting in the proposed asymmetric multiscale multifractal detrended cross-correlation analysis method. This method not only remedies the pseudo-fluctuation defect of the traditional method, but also explores the asymmetric multifractal cross-correlation between China’s rebar futures and spot markets at different scales. The results show the existence of an asymmetric multifractal cross-correlation between rebar futures and spot markets with upward and downward trends at different scales. This cross-correlation is highly complex at the small-scale, and more pronounced when the futures market is in an uptrend.

Analysis of the impact of COVID-19 on the correlations between crude oil and agricultural futures.

In this study, we explored the impact of COVID-19 on the cross-correlations between crude oil and agricultural futures markets. A multifractal detrended cross-correlation analysis (MF-DCCA) approach was utilized to analyze the cross-correlations between the Brent crude oil and agricultural futures such as London Sugar, London Wheat, USA Cotton #2, and USA Orange Juice futures. We initially confirmed their correlations by calculating the DCCA coefficient. Then, from the multifractal aspect, the cross-correlations were further explored, and the sources for forming the correlations were discussed. The results show that the Brent Crude Oil has the strongest cross-correlation with London Sugar Future market among other three agricultural future markets. Then we investigated the influence of COVID-19 on the cross-correlations of multifractality between crude oil and agricultural futures. The experimental results indicated that the persistence under the influence of COVID-19 became stronger, and the cross-correlations of multifractality between crude oil and sugar future market is the strongest. In addition, the cross-correlations of all the agricultural futures increased after the emergence of COVID-19 except the orange juice future market. In general, COVID-19 has a great impact on the cross-correlation of multifractal property between crude oil and most selected agricultural future markets.

MF-DCCA between molecular properties and aqueous solubility

In this paper, we propose a framework, based on Multi-Fractal De-trended Fluctuation Cross-Correlation Analysis (MF-DCCA), to investigate the cross-correlation features between the molecular properties and aqueous solubility using the data set of Delaney-processed widely used for Deep Learning (DL). The molecular properties of Minimum Degree, Number of H-Bond Donors, Number of Rings, Number of Rotatable bonds and Polar Surface Area have a weak power-law cross-correlation with aqueous solubility; the Molecular Weight has a weak long-range cross-correlation. Obvious oscillation of long-range cross-correlation captures through a sliding window approach between molecular properties and aqueous solubility based on the pseudo-time series. Experimental comparison of time-varying cross-correlation widths shows that window widths are more robust to time-varying Hurst exponent. This work can provide a reference for reducing the data dimension for neural network molecular property prediction tasks and help in high-accuracy predicting molecular aqueous solubility on DL.

CROSS-CORRELATIONS BETWEEN BACTERIAL FOODBORNE DISEASES AND METEOROLOGICAL FACTORS BASED ON MF-DCCA: A CASE IN SOUTH KOREA

In this study, we apply multifractal detrended cross-correlation analysis (MF-DCCA) to examine the nonlinear cross-correlations between bacterial foodborne diseases (FBDs) and meteorological factors in South Korea. The results demonstrate that power-law cross-correlations between bacterial FBD and meteorological factors exist; and that multifractal characteristics are significant. In addition, the cross-correlation between bacterial FBD and temperature is more persistent than that between bacterial FBD and humidity. Comparison of the strengths of multifractal spectra showed that the degree of multifractality of the Humidity/FBD time series pair is greater than that of Temperature/FBD pair; this indicates that the monthly number of outpatient FBD cases is more sensitive to humidity. Furthermore, to document the major source of multifractality, we shuffle the original series. We conclude that both the long-range correlations and fat-tail distribution contribute to the multifractality of the Temperature/FBD time series pair. The long-range correlations are also an important source that contributes to the multifractality between bacterial FBD and humidity time series.

Multifractal detrended cross-correlation analysis between respiratory diseases and haze in South Korea

Abstract Recently, air pollution such as the respirable particulate PM10 results in negative impact on human health. We study the non-linear cross-correlations between respiratory diseases and haze in South Korea, using multifractal detrended cross-correlation analysis (MF-DCCA). The empirical tests indicate that there exists cross-correlations between the monthly average PM10/Bronchitis time series pair, and monthly average PM10/Rhinitis time series pair. Metrics such as Hurst exponents, scaling exponents, and multifractal spectrums show that the multifractal characteristics of both the time series pairs are significant. In addition, we compare the degrees of multifractal spectrums and find that the cross-correlation of the time series pair PM10/Bronchitis is stronger than that of PM10/Rhinitis, which indicates that the monthly outpatient quantity of bronchitis is more sensitive to PM10 concentration. Furthermore, to identify the main source of multifractality for two time series pairs, we phase-randomize and shuffle the original series. The computational results demonstrate that fat-tailed distribution contributes to the multifractality between respiratory diseases and haze.

Multifractal description of daily rainfall fields over India

This study investigated the scaling characteristics of daily rainfall time series over India and their spatio-temporal variability using Multifractal Detrended Fluctuation Analysis (MF-DFA) method. In the study, fine resolution gridded (1ox1o) dataset of daily rainfall for the period 1951–2016 was used for the analysis. The scaling characterization using MF-DFA shows that rainfall data of most of the grid points (over 87%) display short term persistence. The analysis of spatial variability of multifractal characteristics shows that the multifractal strength is strongest in the western and central India while the strength is the lowest in the north east region. Further, the evaluation of multifractal properties of rainfall time series of pre and post 1976/77 period of Pacific climate shift shows that there is a clear reduction in the multifractal strength and complexity for the post 1976/77 with contrasting behavior for the persistence. Finally, the association of daily rainfall with mean, maximum, minimum temperature values and the diurnal temperature range (DTR) time series of the 1951–2016 period were investigated using Multifractal Detrended Cross Correlation analysis (MF-DCCA). The nature and strength of association between the two variables of rainfall and temperature differs with time scales and it was found that the joint persistence of these variables lies between individual persistence property. There is a distinct difference in the persistence cross-correlation properties at the Peninsular region and coastal belts when compared with other regions in India and the difference is most perceptible in the Tmin-rainfall link.

MULTIFRACTAL DETRENDED CROSS-CORRELATION ANALYSIS OF HIGH-FREQUENCY STOCK SERIES BASED ON ENSEMBLE EMPIRICAL MODE DECOMPOSITION

We used the multifractal detrended cross-correlation analysis (MFDCCA) method based on ensemble empirical mode decomposition (EEMD) to study the 5-min high-frequency data of two Chinese stocks and two US stocks. Using EEMD method to decompose the original high-frequency stock data can effectively reduce the interference of noise on the series, which helps to reveal the internal characteristics of the stock system and extract more accurate and rich information. We first conducted a cross-correlation test and cross-correlation coefficient analysis on the reconstructed stock data of two groups, and found that there is a cross-correlations between them. Then we used the EEMD-based MFDCCA method to analyze the cross-correlation between the data and found that there are significant cross-correlations between DJI and NASDAQ and between SSEC and SZSE. The cross-correlation of the two Chinese stocks is stronger than that of the two US stocks. The MFDCCA results of the comparison of the original series with the reconstructed series after decomposition by the EEMD method show that the reconstructed series can display more internal details of the multifractal cross-correlation metrics compared with the original series.

Multifractal Detrended Cross-Correlation Analysis of Global Methane and Temperature

Multifractal Detrended Cross-Correlation Analysis (MF-DCCA) was applied to time series of global methane concentrations and remotely-sensed temperature anomalies of the global lower and mid-troposphere, with the purpose of investigating the multifractal characteristics of their cross-correlated time series and examining their interaction in terms of nonlinear analysis. The findings revealed the multifractal nature of the cross-correlated time series and the existence of positive persistence. It was also found that the cross-correlation in the lower troposphere displayed more abundant multifractal characteristics when compared to the mid-troposphere. The source of multifractality in both cases was found to be mainly the dependence of long-range correlations on different fluctuation magnitudes. Multifractal Detrended Fluctuation Analysis (MF-DFA) was also applied to the time series of global methane and global lower and mid-tropospheric temperature anomalies to separately study their multifractal properties. From the results, it was found that the cross-correlated time series exhibit similar multifractal characteristics to the component time series. This could be another sign of the dynamic interaction between the two climate variables.

An Online Contaminant Classification Method Based on MF-DCCA Using Conventional Water Quality Indicators

Emergent contamination warning systems are critical to ensure drinking water supply security. After detecting the existence of contaminants, identifying the types of contaminants is conducive to taking remediation measures. An online classification method for contaminants, which explored abnormal fluctuation information and the correlation between 12 water quality indicators adequately, is proposed to realize comprehensive and accurate discrimination of contaminants. Firstly, the paper utilized multi-fractal detrended fluctuation analysis (MF-DFA) to select indicators with abnormal fluctuation, used multi-fractal detrended cross-correlation analysis (MF-DCCA) to measure the cross-correlation between indicators. Subsequently, the algorithm fused the abnormal probability of each indicator and constructed the abnormal probability matrix to further judge the abnormal fluctuation of indicators using D–S evidence theory. Finally, the singularity index of the cross-correlation function and the selected indicators were used to classification by cosine distance. Experiments of five chemical contaminants at three concentration levels were implemented, and analysis results show the method can weaken disturbance of water quality background noise and other interfering factors. It effectively improved the classification accuracy at low concentrations compared with another three methods, including methods using triple standard deviation threshold and single indicator fluctuation analysis-only methods without fluctuation analysis. This can be applied to water quality emergency monitoring systems to reduce contaminant misclassification.

Multifractal analysis of the WTI crude oil market, US stock market and EPU

This paper adopts multifractal methods to analyze the nonlinear correlations among economic policy uncertainty (EPU), the crude oil market and the stock market. First, using multifractal detrended fluctuation analysis (MF-DFA), we find that each of the three series shows multifractality, and the sources of multifractality are all from long-range correlations and fat-tailed distributions. However, for the stock and oil price series, the long-range correlation has a greater impact, while the fat-tailed distribution contributes more to EPU multifractality. Furthermore, we apply multifractal detrended cross-correlation analysis (MF-DCCA) to analyze the cross-correlation multifractal features among the three series. The generalized Hurst exponents of any two series are significantly greater than 0.5, and the stock and oil price series have the strongest cross-correlation values. Coupling detrended fluctuation (CDFA) analysis of the three series shows that the coupling correlation among the three sequences is also multifractal. The chi-squared statistic reveals that the contribution of the stock market to the multifractality of the coupling correlation is greater than that of other series, and EPU has the smallest influence on the coupling correlation. Finally, we employ multiscale multifractal analysis (MMA) to visualize the dynamic behaviors of the correlations among the series. The results show that the cross-correlation of stock with the oil price has some symmetry at small- and large-scale fluctuations. Additionally, the influence of EPU on the overall coupling features is mainly reflected under small-scale fluctuations, and at large scales, the coupling correlation of the three series remains similar to the Hurst surface of stock with the oil price. These results are useful for building predictive models.

Stock market trading volumes and economic uncertainty dependence: before and during Sino-U.S. trade friction

This article mainly studies the interaction between the economic uncertainty and stock market trading volumes changes before and during Sino-U.S. trade friction using multifractal detrended fluctuation analysis (M.F.-D.F.A.) and multifractal detrended cross-correlation analysis (M.F.-D.C.C.A.). Our research aims to reveal whether the economic uncertainty increased by Sino-U.S. trade friction affects stock market trading volume more susceptible, as well as how policymaker strengthen risk management and maintain financial stability. The results show that the dynamic volatility linkages between economic uncertainty and stock market trading volumes changes are multifractal, and the cross-correlation of volatility linkages are anti-persistent. Through the rolling-windows analysis, we also find that the economic uncertainty and trading volumes are anti-persistent dynamic cross-correlated. This means that while economic uncertainty increases, trading volume decreases. Besides, Sino-U.S. trade friction has impact on the cross-correlated behaviour significantly, suggesting that stock markets’ risks are relatively large and trading volumes changes are more susceptible by economic uncertainty during Sino-U.S. trade friction in the U.S. Our study complements existing literature about the stock markets trading volumes and economic uncertainty dependence relationship by multifractal theory’s methods. The overall findings imply that the increased economic uncertainty caused by Sino-U.S. trade friction exacerbates financial risks, which are useful for policymakers and investors.

China’s soybean crush spread: Nonlinear analysis based on MF-DCCA

In this paper, we investigate cross-correlations among the soybean, soymeal, and soyoil futures return series at China’s Dalian Commodity Exchange using both multifractal detrended fluctuation analysis (MF-DFA) and multifractal detrended cross-correlation analysis (MF-DCCA) methods. We find that there exists multifractality in the soybean, soymeal and soyoil futures return series using MF-DFA method. Moreover, results of MF-DCCA demonstrate that there exists a power-law cross-correlation and significant multifractal features among soybean, soymeal and soyoil futures returns. Furthermore, by comparing the multifractality of the original series to the shuffled and surrogated series, we find that both the long-range correlations and fat-tailed distribution contribute to the multifractality in cross-correlation among soybean, soymeal and soyoil futures return series in Dalian Commodity Exchanges. Furthermore, we use nonlinear Granger causality test and show that anyone of the three products returns is the Granger cause of the other two products returns.