Multifractal Cross-correlation Analysis Research Articles

Auto- and Cross-Correlation Multifractal Analysis of Sea Surface Temperature Variability

In this study, we investigate multiscale auto- and cross-correlation structural characteristics of sea surface temperature (SST) variability using our new methodology, called the multifractal asymmetric cross-correlation analysis (MF-ACCA), incorporating signs of a segment’s detrended covariance and linear trend. SST is greatly affected by air–sea interactions and the advection of water masses with a wide range of spatiotemporal scales. Since these force factors are imprinted on SST variability, their features can be revealed in terms of long-range auto- and cross-correlation structures of SST variability via a multifractal analysis. By applying the MF-ACCA methodology to SST variability in the East/Japan Sea, we have found the following features: (1) the auto- and cross-correlation multifractal features are dependent on several parameters, such as the location, linear trends (rising or falling), level of fluctuations, and temporal scales; (2) there are crossover behaviors that are discrete for small scales (less than 1000 days) but continuous for large scales (more than 1000 days); (3) long-range persistence of auto- and cross-correlations is random for large scales during the falling phase; (4) long-range persistence is stronger during the rising phase than during the falling phase; (5) the degree of asymmetry is greater for large scales than for small scales.

Dynamics of asymmetric multifractal cross-correlations between cryptocurrencies and global stock markets: Role of gold and portfolio implications

Understanding the risk transmission mechanism between cryptocurrencies and global stock markets is crucial for investors' risk management strategies. This study delves into this relationship, drawing on the Fractal Market Hypothesis and acknowledging the nonlinearity and asymmetry present in financial market correlations. We introduce a combined approach, integrating Multifractal Detrended Partial Cross-Correlation Analysis (MF-DPCCA) and Asymmetric Multifractal Cross-Correlation Analysis (MF-ACCA), resulting in the Asymmetric Multifractal Partial Cross-Correlation Analysis (MF-APCCA) method. By applying this method, we aim to uncover the dynamics between cryptocurrencies and global stock markets. We focus on stock indices from E7 and G7 countries and consider the Bitcoin market for our analysis. Our initial findings, using the MF-ACCA method, reveal pronounced asymmetric cross-correlations between cryptocurrencies and these stock markets. Notably, the correlation strength between Bitcoin and the G7 stock markets surpasses that of Bitcoin and the E7 markets. Further, when we account for and remove the influence of the common factor, gold, our analysis with the MF-APCCA method indicates an enhanced long-memory cross-correlation between Bitcoin and these stock markets. This cross-correlation tends to amplify during periods of positive returns but shows anti-persistence during negative returns. Remarkably, these asymmetries become more pronounced during significant market shifts. When comparing Bitcoin's relationship with the G7 and E7 indices, the latter displays heightened asymmetric risk correlations in both upward and downward market phases. In conclusion, gold, recognized as a safe-haven asset, can serve as a buffer, diminishing the portfolio risk between Bitcoin and the stock market. These empirical findings bear significant weight, urging investors to reassess the intricate relationship between stock and cryptocurrency markets. It also underscores the importance of well-informed cross-market portfolio investments and the need for regulatory vigilance to prevent systemic financial pitfalls.

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.

Assessment of Multifractal Fingerprints of Reference Evapotranspiration Based on Multivariate Empirical Mode Decomposition

This study analyzed the multifractal characteristics of daily reference evapotranspiration (ETo) time series of the Tabriz and Urmia stations of northwestern Iran and its cross-correlation with five other meteorological variables. The results of multifractal detrended fluctuation analysis (MFDFA) of ETo, temperature, pressure, relative humidity solar radiation, and wind velocity showed that all the time series of both stations exhibited multifractality and long memory persistence with higher persistence and complexity in the datasets of Urmia station. Then, a multivariate empirical mode decomposition (MEMD)-(MFDFA) coupled framework was proposed to identify the dominant modes suitable for the forecasting of the different variables. The examination of reconstructed time series consistently displayed an increase in persistence and multifractality. The cross-correlation between different candidate variables and ETo was examined using a recently proposed multifractal cross-correlation analysis (MFCCA) method. The results showed that in each pair-wise cross-correlation analysis, the joint persistence is approximately half of the persistence of an individual time series, reinforcing the universality in the fractal cross-correlation analysis. The cross-correlation properties displayed diverse patterns in different pair-wise combinations of cross-correlation analysis despite the similarity of patterns among the data of the two stations.

Multifractal cross-correlation analysis between crude oil and agricultural futures markets: evidence from Russia–Ukraine conflict

PurposeThis study investigates the impacts of the Russia–Ukraine conflict on the cross-correlation between agricultural commodity prices and crude oil prices.Design/methodology/approachThe authors used MultiFractal Detrended Fluctuation Cross-Correlation Analysis (MF-X-DFA) to explore the correlation behavior before and during conflict. The authors analyzed the price connections between future prices for crude oil and agricultural commodities. Data consists of daily futures price returns for agricultural commodities (Corn, Soybean and Wheat) and Crude Oil (Brent) traded on the Chicago Mercantile Exchange from Aug 3, 2020, to July 29, 2022.FindingsThe results suggest that cross-correlation behavior changed after the conflict. The multifractal behavior was observed in the cross correlations. The Russia–Ukraine conflict caused an increase in the series' fractal strength. The study findings showed that the correlations involving the wheat market were higher and anti-persistent behavior was observed.Research limitations/implicationsThe study was limited by the number of observations after the Russia–Ukraine conflict.Originality/valueThis study contributes to the literature that investigates the impact of the Russia–Ukraine conflict on the financial market. As this is a recent event, as far as we know, we did not find another study that investigated cross-correlation in agricultural commodities using multifractal analysis.

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.

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

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

ASYMMETRIC MULTIFRACTAL CROSS-CORRELATION DYNAMICS BETWEEN FIAT CURRENCIES AND CRYPTOCURRENCIES

This paper performs the asymmetric multifractal cross-correlation analysis to examine the COVID-19 effects on three relevant high-frequency fiat currencies, namely euro (EUR), yen (YEN) and the Great Britain pound (GBP), and two cryptocurrencies with the highest market capitalization and traded volume (Bitcoin and Ethereum) considering two periods (Pre-COVID-19 and during COVID-19). For both periods, we find that all pairs of these financial assets are characterized by overall persistent cross-correlation behavior [Formula: see text]. Moreover, COVID-19 promoted an increase in the multifractal spectrum’s width, which implies an increase in the complexity for all pairs considered here. We also studied the Generalized Cross-correlation Exponent, which allows us to verify that there is no asymmetric behavior between Bitcoin and fiat currencies and between Ethereum and fiat currencies. We conclude that investing simultaneously in major fiat currencies and leading cryptocurrencies can reduce the portfolio risk, leading to improvement in the investment results.

The Dynamic Impacts of COVID-19 Pandemic Lockdown on the Multifractal Cross-Correlations between PM2.5 and O3 Concentrations in and around Shanghai, China

Although the outbreak of the COVID-19 pandemic caused serious restrictions on human activities in and around Shanghai, China, the period can be viewed as a helpful experiment to investigate the correlation between PM2.5 and O3 concentrations. In this study, the hourly PM2.5 and O3 series in four cities (i.e., Shanghai, Jiaxing, Nantong and Suzhou) from 27 November 2019 to 23 March 2020 are used. The “seesaw effect” is observed in the study data. The dynamic impacts of the COVID-19 pandemic on the multifractal cross-correlations and the coordinated control degree of PM2.5-O3 are examined in these cities. First of all, the multifractal cross-correlations, multifractality components and dynamic influences of the COVID-19 pandemic on cross-correlations between PM2.5 and O3 in four cities are illustrated. Furthermore, a new quantification index, ζ, evaluating the coordinated control degree of PM2.5-O3 is developed, validated and compared. The multifractal cross-correlation analysis results reveal that the cross-correlations between PM2.5 and O3 in and around Shanghai both before and during the COVID-19 partial lockdown have multifractal characteristics. Moreover, there are weaker multifractal cross-correlation degrees of PM2.5-O3 in four cities during the COVID-19 partial lockdown. The multifractal cause analysis based on stochastic simulation illustrates that the impacts of multifractality due to the nonlinear correlation part are greater than the linear correlation part and the fat-tailed probability distribution part in and around Shanghai. The intrinsic multifractal cross-correlations decreased in all cities during the COVID-19 lockdown. However, the effects of the COVID-19 lockdown on the multifractal cross-correlations are limited from the perspective of intrinsic multifractality. The mean values of ζ in and around Shanghai all increase during the COVID-19 partial lockdown, which indicates that the PM2.5-O3 coordinated control degrees in all four cities become weaker.

On the inner dynamics between Fossil fuels and the carbon market: a combination of seasonal-trend decomposition and multifractal cross-correlation analysis.

This study examines the inner dynamics of multifractality between the carbon market (EU ETS) and four major fossil fuel energy markets: Brent Crude Oil (BRN), Richards Bay Coal (RBC), UK Natural Gas (NGH2), and FTSE350 electricity index (FTSE350) from January 04, 2016, to March 04, 2022. First, we decompose the daily price changes by applying seasonal and trend decomposition using loess (STL). Then, we examine the inner dynamics of multifractality and cross-correlation by employing multifractal detrended fluctuation analysis (MFDFA) and multifractal detrended cross-correlation analysis (MFDCCA) using the remaining components of the return series. Our findings reveal that all series and the cross-correlations of carbon and fossil fuels markets have multifractal characteristics. We find crude oil to be the most efficient market (lowest multifractal), while coal is the least efficient (highest multifractal). Only coal shows persistent, whereas the other markets exhibit antipersistent behavior. Interestingly, the coal and EU ETS pair demonstrates a higher degree of multifractal patterns. In contrast, the pair of natural gas and EU ETS exhibits the lowest multifractal characteristics among the energy markets. Only the crude oil market shows persistent cross-correlations in the multifractality. These findings have important academic and managerial implications for investors and policymakers.

CONNECTEDNESS BETWEEN CRUDE OIL AND US EQUITIES: THE IMPACT OF THE COVID-19 PANDEMIC

This paper contributes to the literature by employing a multifractal cross-correlation analysis (MFCCA) to study the effect of the global COVID-19 pandemic on cross-correlations between oil and US equity markets. First, we examine the detrended moving average cross-correlation coefficient between oil and S&P 500 returns before and during COVID-19 and find that US stock markets became more correlated with oil during the pandemic in the long term. Second, we find that the pandemic has caused an increase in the long-range cross-correlations over the small fluctuations. Third, the MF-DCCA method shows that the pandemic caused an increase in cross-correlations between the two markets. In sum, the pandemic caused a closer correlation between oil and US equities in the long range and a deeper dynamic connection between oil and US equity markets, as indicated by the multifractality tests. We also investigate the connectedness between oil and the S&P 500 using a dynamic procedure based on time-varying parameter vector autoregression. We find that oil is a net transmitter of shocks to the forecast error variance of the S&P 500 during March, April and May 2020, whereas the S&P 500 is a net transmitter of shocks to oil variance early in the pandemic (January and February 2020).

Market Efficiency and Cross-Correlations of Chinese New Energy Market with Other Assets: Evidence from Multifractality Analysis.

Despite the upgrading of the attention and investment of new energy in Chinese public, its market efficiency and associations with other assets are relatively rarely explored. This paper, firstly, explores the multifractal feature and market efficiency of Chinese new energy market (NEI) by the multifractal detrended fluctuation analysis. Secondly, the multifractal cross-correlation analysis is performed to discuss the multifractality of cross-correlations between NEI and crude oil, external new energy indices (Global (SPGCE), United States (ECO) and Europe (ERIX)) and safe-haven asset (GOLD) respectively. The results show that Chinese new energy market has obvious multifractality with low market efficiency, which is mainly sourced from long-range correlation. It has the strongest linkages with external new energy markets and most insignificant association with gold. The heterogeneous sources contribute to their multifractal cross-correlations. It provides useful enlightenment for decision-makers to implement energy policy and reform, and for investors to make investment decisions.

The impact of COVID-19 pandemic on the dynamic correlations between gold and U.S. equities: evidence from multifractal cross-correlation analysis.

This study exploits multifractal cross-correlation analysis (MFCCA) to investigate the impact of the COVID-19 pandemic on the cross-correlations between gold and U.S. equity markets using 1-min high-frequency data from January 1, 2019, to December 29, 2020. The MFCCA method shows that the pandemic caused an increase of multifractality in cross-correlations between the two markets. Specifically, the cross-correlations of small fluctuations became more persistent while those of large fluctuations became less persistent, explaining the source of multifractality. The findings of this study carry significant implications for investors, academicians, and policymakers. For example, the increase of multifractality of cross-correlation means that the non-linear relationship between gold and U.S. equity returns prevails more during economic downturns. Therefore, academicians may resort to non-linear techniques to evaluate the relationship between gold and U.S. equity markets during the health pandemic. Moreover, investors can know the value of hedging benefits over different investment time horizons during the pandemic. Finally, policymakers can better assess the economic downturns (i.e., those caused by health pandemics) over the dynamics of cross-correlation between gold and equity markets to make sound financial policies.

Spillover effects and nonlinear correlations between carbon emissions and stock markets: An empirical analysis of China's carbon-intensive industries

This study analyzes the correlations between carbon emissions and related industry stock markets in China. We propose a carbon-intensive industry index firstly. According to the Spillover Index, the two markets interact and the carbon-intensive stock market acts as an information receiver in most cases. We apply the Multifractal Cross-Correlation Analysis, Detrended Cross-Correlation Coefficient, and the modified Time-lagged Detrended Cross-Correlation to characterize the nonlinear correlations between carbon allowance price returns and the stock returns of carbon-intensive industries. The carbon emission trading market is found to be more volatile and inefficient than the stock market; the properties of the carbon trading pilot explain the direction and magnitude of the nonlinear correlations. The level of intervention by the government authority affects the magnitude of correlations; the strongest dynamic return spillovers and the most persistent time-lag cross-correlations were observed in the Shenzhen pilot—the most market-oriented carbon emission trading pilot in China. The allowance allocation method plays an important role in deciding the direction of the nonlinear correlations. Our empirical results show the stock returns of carbon-intensive industries and the carbon allowance price returns were positively cross-correlated in Shenzhen and Shanghai pilots, while the cross-correlations were negative in Beijing, Guangdong, and Hubei pilots.

EXAMINING THE FRACTAL MARKET HYPOTHESIS CONSIDERING DAILY AND HIGH FREQUENCY FOR CRYPTOCURRENCY ASSETS

Cryptocurrencies play a pivotal role in the financial market. Given this, we perform the asymmetric multifractal cross-correlation analysis to examine the weak form of the Efficient Market Hypotheses (EMH) considering two temporal scales. In the daily scale, we find that the pair Bitcoin–Litecoin displays the largest multifractal spectrum. While, in the hourly scale, the pair Bitcoin–Ethereum presents the largest multifractal spectrum. Our empirical evidence has rejected the weak form of the EMH and clearly suggests that the dynamics of the analyzed cryptocurrency pairs are in line with the Fractal Market Hypothesis (FMH). Cross-correlation asymmetries are more persistent for small fluctuations than for large fluctuations. The results are essential for investors, portfolio and risk managers, and policymakers.

Asymmetric multifractality in China’s energy market based on improved asymmetric multifractal cross-correlation analysis

Based on the asymmetric multifractal detrending cross-correlation analysis (MF-ADCCA) method and the multifractal cross-correlation analysis (MFCCA) method, we propose a new method—the asymmetric multifractal cross-correlation analysis (MF-ACCA) method. The simulation results show that the algorithm can describe the asymmetric multifractal characteristics of two time series from qualitative and quantitative perspectives and we compare the MF-ACCA method and the MF-ADCCA method by using Binary ARFIMA model. In addition, the MF-ACCA method is used to analyze the asymmetric cross-correlation relationships among energy markets with different trends. We confirm that when a market experiences large fluctuations, the overall energy market in China exhibits multifractal characteristics, and the multifractal cross-correlations among energy markets are asymmetric.

Asymmetry and conduction direction of the interdependent structure between cryptocurrency and US dollar, renminbi, and gold markets

The risk conduction mechanism between a cryptocurrency and the US dollar (USD), the renminbi (RMB), and gold markets is helpful for investors' risk management. Based on the non-linearity and asymmetry of the correlation between the fractal market hypothesis and the financial market, this study uses asymmetric multifractal cross-correlation analysis to study the correlation between a cryptocurrency and USD, RMB, and gold markets. First, using the MF-ADCCA method, an obvious asymmetric cross-correlation is found between a cryptocurrency and USD, RMB, and gold markets. USD, RMB, and gold markets are more effective than cryptocurrency markets. In particular, the impact of the RMB market on the cryptocurrency market is the largest among USD, RMB, and gold. When USD and RMB are rising, the risk conduction to cryptocurrencies is more significant. When gold is falling, the risk conduction to cryptocurrencies is more significant. When cryptocurrencies are falling, the risk conduction to USD is more significant. Among cryptocurrencies, Bitcoin, Ethereum, Litecoin, and New Economic Coin have more significant risk conduction to RMB when it falls. Through the DMF-ADCCA method, a two-way asymmetric conduction effect is found between the lagging cryptocurrency and the USD, RMB, and gold markets. Compared with USD and gold, the risk correlation and conduction between RMB and cryptocurrency are the highest. Preventing and controlling the risk impact of cryptocurrency on the RMB and further strengthening the research between cryptocurrency and the RMB are crucial to the internationalization of the RMB and the improvement of international competitiveness.

Cross-correlations between economic policy uncertainty and precious and industrial metals: A multifractal cross-correlation analysis

This study combines Seasonal-Trend decomposition using LOESS (STL) and multifractal cross-correlation analysis (MFCCA) to estimate the cross-correlations between the evolution of the economic policy uncertainty (EPU) of the USA and return of precious and industrial metals. Based on daily closing values of EPU and eight metals ranging from 01-Jan-2010 to 02-May-2021, the empirical findings confirm the presence of nonlinear dependencies, based on all EPU-Metal relationships, suggesting that EPU and metal markets are interlinked. Furthermore, there is evidence of multifractality, although with a varying degree, between EPU and metal markets. The strongest multifractality is found in EPU-Tin and EPU-Silver, while EPU-Platinum and EPU-Gold exhibit the weakest multifractality. Precious metals show persistent cross-correlations while industrial metals have anti-persistent cross-correlations with EPU, with that cross-correlation behavior being more persistent in the case of small fluctuations, which have different implications for the different market agents.

MULTIFRACTAL CROSS-CORRELATION ANALYSIS BETWEEN CARBON SPOT AND FUTURES MARKETS CONSIDERING ASYMMETRIC CONDUCTION EFFECT

The cross-correlation between carbon spot and futures markets reflects the risk conduction mechanism between the two markets. Deeply depicting and analyzing this risk conduction mechanism is of great significance for investors to carry out risk management strategies. Considering the nonlinear and asymmetric characteristics of cross-correlation between carbon spot and futures markets, this paper applies multifractal cross-correlation analysis method to investigate the cross-correlation between carbon spot and futures markets. Firstly, through Empirical Mode Decomposition (EMD)-Multifractal Detrended Cross-Correlation Analysis (MF-DCCA) detection, it is found that there is an obvious cross-correlation between carbon spot and futures markets, and the cross-correlation has multifractal characteristic. Secondly, by using EMD-time delay-DCCA method, we find the conduction direction between carbon spot and futures markets is bidirectional, and the futures market has a greater impact on the spot market in the short term. Thirdly, through using EMD-MF-ADCCA method, we find the cross-correlation between the two markets is asymmetric, and the cross-correlation between the two markets is more significant when carbon market is in a downward trend than in an upward trend. Fourthly, through constructing EMD-time delay-ADCCA model, we find that there is a two-way asymmetric conduction effect between carbon spot and futures markets when the lag period is short, and when the carbon market is in a downward trend, the conduction effect between the two markets is stronger. However, with the extension of time lag, the conduction effect of the two markets no longer presents obvious asymmetric characteristics.

The excessive gaming and gambling during COVID-19

PurposeBy combining econometrics and multifractal methods, utilizing a financial framework, this paper will examine with objectivity the economic, financial and social impact of coronavirus disease 2019 (COVID-19) on society.Design/methodology/approachThrough Granger causality, the authors test the effect of the COVID-19 pandemic on excessive gaming and gambling activities, and through econometrics and multifractal methods, they combine the results to analyze a possible long-run relationship.FindingsThe COVID-19 confirmed cases Granger cause all examined stocks. Based on the co-integration technique, and the multifractal cross-correlation analysis, a long-run relationship exists between all examined stocks and COVID-19.Originality/valueThis is an empirical examination of a very important subject in the field of economics, namely, the consequences of the COVID-19-related events on the behavior of global citizens. It proposes a different and more objective approach (than the interviews and questionnaires) in the examination of this specific subject, through a financial framework, depicting the stock performance of the gaming and online gambling-related companies, and reflecting on the activity of these companies. It combines two different approaches from two different disciplines, namely econometrics and multifractal analysis, to test and describe the causal and the long-run relationship between the phenomena examined, combining the results to an overall and multidimensional view of this occurrence.