Multifractal Cross-correlation Research Articles

Deep multifractal detrended cross-correlation analysis algorithm for multifractals

In the natural and social sciences, multifractal properties between two non-stationary time series are influenced not only by each other, but also by exogenous variables and historical data. However, traditional multifractal detrended cross-correlation analysis did not realize this problem, but directly explored the multifractal nature of time series. To eliminate the influence of exogenous variables and historical data as much as possible, the deep multifractal detrended cross-correlation analysis (DMF-DCCA) is developed to research the multifractal cross- correlation nature between two non-stationary time series. Furthermore, the effectiveness of DMF-DCCA has been validated using a simulated dataset and two real-world datasets.

Green cryptocurrencies versus sustainable investments dynamics: Exploration of multifractal multiscale analysis, multifractal detrended cross-correlations and nonlinear Granger causality

Within this study, we analyse green cryptocurrencies versus sustainable investments dynamics by calculating a multifractal multiscale analysis (MMA) with Hurst surfaces paired with powerlaw distributional coherence tests for each series. Next, we determine multifractal cross-correlations by applying a maximal overlap discrete wavelet transform (MODWT) based trend-filtered variation of a multifractal detrended cross-correlation analysis (MF-DCCA). Finally, to determine the strength and directionality of potential causations, we determine the results of a nonlinear Granger causality test. The results for the MMA state q-dependent unstable multifractality for each series. The coherence tests indicate that the series follow powerlaws or exponentially nested powerlaws and yield fat-tails in some cases. Moreover, we find strong scaling and multifractal cross-correlations between the cryptocurrencies and the sustainability series. Finally, the nonlinear Granger causality tests across four lags indicate a complex interplay between some of the selected cryptocurrencies and various indices. These results suggest the existence of potential predictive powers of these cryptocurrencies on the market indices.

Complex non-linear relationship between conventional and green bonds: Insights amidst COVID-19 and the RU–UA conflict

In times of crisis, such as global pandemics or conflicts, investors’ preference between green and conventional bonds may lean towards the latter due to increased risk aversion and a focus on short-term stability. However, some investors motivated by increased awareness of sustainability issues may maintain or increase their allocation to green bonds, seeing them as an opportunity for long-term resilience and sustainable investing. We use multifractal detrended cross-correlation analysis, wavelet coherence, and copula-based dependence analysis to examine the complex relationship between the S&P Green Bond Index and the S&P 500 Bond Index. The results indicate the presence of multifractal cross-correlations, the strength of which is most pronounced in times of crisis, especially in the post-COVID-19 period. The wavelet-based analysis also detects the COVID-19 break and shows significant interdependence at all frequency levels after the RU–UA conflict. The copula-based correlation values exhibit a distinct oscillating pattern over time, characterized by an initial break coinciding with the impact of COVID-19. In light of these findings on the impact of COVID-19 and the RU–UA conflict, we have included the Geopolitical Risk Index in our analysis to better understand how geopolitical tensions and conflicts influence the observed interdependence and to gain insight into how changes in the global risk environment affect both bond market dynamics. Overall, the results of this study provide insights into the interconnectedness between conventional and green bond markets and highlight potential spillover effects and systemic risks in an increasingly complex financial landscape.

Skewed multifractal cross-correlation between price and volume during the COVID-19 pandemic: Evidence from China and European carbon markets

This article presents skewed multifractal cross-correlations between price and volumes on the carbon emissions trading markets in China and Europe. The BEAST algorithm is first used to detect change points in financial time series and to divide series into two adjacent intervals. The study performs a skewed multifractal detrended cross-correlations analysis and further investigates the impact of the COVID-19 pandemic on multifractality and risk between price and volumes on both markets, from 30 April 2014 to 25 July 2023. The results demonstrate that the multifractality of cross-correlations in both markets underwent significant changes before and after the change points, indicating skewed multifractality. In both markets, the price-volume nexus exhibited increased anti-persistence, higher multifractal risks, and reduced market efficiency after the outbreak of the pandemic. This may be attributed to the pandemic-induced shifts in carbon emissions trading market trends and heightened volatility. In conclusion, the outbreak of the pandemic had increased the instability of the carbon markets and the Hubei market exhibited higher levels of multifractality and multifractal risk.

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.

Interplay Multifractal Dynamics Among Carbon Trading Market, Geopolitical Risk and Economic Policy Uncertainty

This paper explores the variations in cross-correlations among the carbon trading market, geopolitical risk (GPR) and economic policy uncertainty (EPU), focusing on their multifractality and asymmetric properties. Therefore, the study employs the multifractal detrended cross-correlation analysis (MF-DCCA) and multifractal asymmetric detrended cross-correlation analysis (MF-ADCCA) approaches to examine these relationships from a three-dimensional perspective. Also, the study looks into cross-correlations at different phases of carbon trading. Our findings reveal that the multifractal cross-correlations between the carbon trading market and GPR or EPU exhibit anti-persistence and asymmetry. The anti-persistent cross-correlations are notably stronger when GPR experiences a downtrend or when EPU undergoes an uptrend. Furthermore, distinct fluctuation patterns emerge across various trends and scales on Hurst surfaces. In the short term, the carbon trading market exhibits heightened sensitivity to changes in GPR or EPU when they rise or fall. The cross-correlations remain multifractal, anti-persistent and asymmetric across different stages of carbon trading. Notably, the multifractality of cross-correlations is most pronounced for the series pair EUA/GPR in Phase II and for the series pair EUA/UK EPU in Phase III and Phase IV. Except for the series pair EUA/UK EPU in Phase II, the anti-persistent cross-correlations are more pronounced during uptrend than downtrend for the other series pairs. Moreover, the series pair EUA/UK EPU exhibits the highest degree of asymmetry at all stages.

Multifractal Detrended Cross-Correlations between Green Bonds and Commodity Markets: An Exploration of the Complex Connections between Green Finance and Commodities from the Econophysics Perspective

Green bonds represent a compelling financial innovation that presents a financial perspective solution to address climate change and promote sustainable development. On the other hand, the recent process of financialisation of commodities disrupts the dynamics of the commodity market, increasing its correlation with financial markets and raising the risks associated with commodities. In this context, understanding the dynamics of the interconnectivity between green bonds and commodity markets is crucial for risk management and portfolio diversification. This study aims to reveal the multifractal cross-correlations between green bonds and commodities by employing methods from statistical physics. We apply multifractal detrended cross-correlation analysis (MFDCCA) to both return and volatility series, demonstrating that green bonds and commodities exhibit multifractal characteristics. The analysis reveals long-range power-law cross-correlations between these two markets. Specifically, volatility cross-correlations persist across various fluctuations, while return series display persistence in small fluctuations and antipersistence in large fluctuations. These findings carry significant practical implications for hedging and risk diversification purposes.

Blockchain ETFs and the cryptocurrency and Nasdaq markets: Multifractal and asymmetric cross-correlations

Blockchain exchange-traded funds (ETFs) are nascent products in the financial industry. A limited literature focuses on the multifractal analysis of some conventional ETFs, but the multifractal behaviour of the blockchain ETF market has not been studied. In this paper, we investigate the multifractal and asymmetric cross-correlation features between blockchain ETFs and the cryptocurrency and Nasdaq markets. Multifractality exists in the cross-correlations between blockchain ETFs and the cryptocurrency and Nasdaq markets. There is a higher persistence in the cross-correlation behaviours between blockchain ETFs and cryptocurrencies in the uptrend, whereas the persistence between blockchain ETFs and Nasdaq is more pronounced in the downtrend. On one hand, this suggests that large fluctuations in the cryptocurrency markets lead to large fluctuations in blockchain ETF markets. On the other hand, large fluctuations in the Nasdaq index lead to small fluctuations in blockchain ETF markets. These results reflect stronger ties between blockchain ETFs and cryptocurrencies compared to blockchain ETFs and the Nasdaq index. Such heterogeneous behaviour in the cross-correlation structure provides insights for short-term investment, hedging strategies, and market efficiency. Further analysis shows that long-range cross-correlation and fat-tail distributions are sources of multifractality.

Navigating Choppy Waters: Interplay between Financial Stress and Commodity Market Indices

Financial stress can have significant implications for individuals, businesses, asset prices and the economy as a whole. This study examines the nonlinear structure and dynamic changes in the multifractal behavior of cross-correlation between the financial stress index (FSI) and four well-known commodity indices, namely Commodity Research Bureau Index (CRBI), Baltic Dry Index (BDI), London Metal Index (LME) and Brent Oil prices (BROIL), using multifractal detrended cross correlation analysis (MFDCCA). For analysis, we utilized daily values of FSI and commodity index prices from 16 June 2016 to 9 July 2023. The following are the most important empirical findings: (I) All of the chosen commodity market indices show cross correlations with the FSI and have notable multifractal characteristics. (II) The presence of power law cross-correlation implies that a noteworthy shift in FSI is likely to coincide with a considerable shift in the commodity indices. (III) The multifractal cross-correlation is highest between FSI and Brent Oil (BROIL) and lowest with LME. (IV) The rolling windows analysis reveals a varying degree of persistency between FSI and commodity markets. The findings of this study have a number of important implications for commodity market investors and policymakers.

Interplay of multifractal dynamics between shadow policy rates and energy markets

This study examines the interconnections between short shadow rates (SSR) and energy markets. We conduct multifractal detrended cross-correlation analysis (MF-DXA) on the daily SSR from four major economies (USA, Eurozone, Japan, and UK) and the daily prices of four energy markets (WTI, Brent, Natural Gas, and Heating Oil) spanning January 1995 to March 2022. Our analysis shows that all energy market-short shadow rate pairs display significant multifractal characteristics. The presence of power law cross-correlation suggests that substantial changes in short shadow rates are associated with significant price changes in energy markets. The highest multifractal cross-correlation is observed between energy prices and shadow short rates of Japan and the US. Energy markets demonstrate persistent cross-correlations for small fluctuations compared to large fluctuations. However, the rolling windows analysis reveal a shift from persistent to anti-persistence cross-correlations during global financial crises (GFC), the 2014–2016 energy crises and the COVID-19 pandemic. Lastly, the cross-correlation exhibit positive skewness. We suggest that integrating these long-term dependency features into financial analysis has the potential to support decision-making for market participants.

Gold and Sustainable Stocks in the US and EU: Nonlinear Analysis Based on Multifractal Detrended Cross-Correlation Analysis and Granger Causality

Geopolitical risks and conflicts wield substantial influence on the global economy and financial markets, fostering uncertainty and volatility. This study investigates the intricate relationship between gold and representatives of green and sustainable stocks in the US and EU during the Russia-Ukraine conflict, employing multifractal detrended cross-correlation analysis (MF-DCCA) and nonlinear Granger causality. MF-DCCA reveals significant multifractal properties and nonlinear cross-correlations across all time series pairs. Notably, conflict weakened the multifractal cross-correlations between US stocks and gold, except for the TESLA/gold pair. A similar significant change in the EU market’s multifractal properties was observed during the conflict. In conjunction with MF-DCCA, Granger causality tests indicate bidirectional nonlinear relationships between gold and green/sustainable stock markets in the USA and EU. Gold’s past movements significantly influence changes in all the considered green and sustainable stocks, enabling predictions of their behavior. These findings shed light on multifractal dynamics during geopolitical crises and emphasize the bidirectional relationships between gold and green and sustainable stock markets. This comprehensive analysis informs investors and policy makers, enhancing their understanding of financial market behavior amid geopolitical instability.

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.

Exploring the Multifractality in the Precious Metal Market

This study proposes a novel approach to investigating the multifractality of time series using the multifractal cross-correlation detrended moving average analysis (MF-X-DMA). The study demonstrates the behavioral differences of MF-X-DMA in coherent and non-coherent time periods. Due to the lack of a mechanism to capture the dynamical cross-correlation in time series, correlated time series with multifractal structure present a barrier for analysis. The study shows that when the wavelet coherence method is applied to time series, co-movement between time series can be easily captured in certain time intervals, providing an efficient way to find time intervals to apply MF-X-DMA. The study applies the wavelet coherence method to the daily spot prices of gold and platinum from January 1987. It shows that the wavelet coherence method is an excellent engine to extract designated time series in certain frequency and time intervals, eliminating the need for windowing or shuffling methods. Additionally, the study observes a long-term power law cross-correlation using detrended cross-correlation analysis coefficients of inversed series for both low-correlated and high-correlated series. Finally, the findings indicate that MF-X-DMA leads to superior results compared to MF-DFA when provided with highly correlated data.

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.

NFTs, DeFi, and other assets efficiency and volatility dynamics: An asymmetric multifractality analysis

This paper examines the efficiency and asymmetric multifractal features of NFTs, DeFi, cryptocurrencies, and traditional assets using Asymmetric Multifractal Cross-Correlations Analysis covering the period from November 2017 to February 2022. Considering the full sample with a significant variation among asset classes, the study reveals DeFi-DigiByte is the most efficient while the cryptocurrency-Tether is the least efficient. However, S&P 500 showed high efficiency before COVID-19, and DeFi-Enjin Coin advanced as the most efficient asset during COVID-19. The volatility dynamics of NFTs, DeFi, and cryptocurrencies follow strong nonlinear cross-correlations, but evidence of weaker nonlinearity exists in traditional assets. Additionally, the sensitivity to smaller events in bull markets is high for NFTs and DeFi. The findings have significant implications for portfolio diversification when an investor's portfolio set includes traditional assets and cryptocurrency and relatively new blockchain-based assets like NFTs and DeFi.

On Asymmetric Correlations and Their Applications in Financial Markets

Progress on asymmetric correlations of asset returns has recently advanced considerably. Asymmetric correlations can cause problems in hedging effectiveness and overstate the value of diversification. Furthermore, considering the asymmetric correlations in portfolio construction significantly enhances performance. The purpose of this paper is to trace developments and identify areas that require further research. We examine three aspects of asymmetric correlations: first, the existence of asymmetric correlations between asset returns and their significance tests; second, the test on the existence of asymmetric correlations between different markets and financial assets; and third, the root cause analysis of asymmetric correlations. In the first part, the contents of extreme value theory, the H statistic and a model-free test are covered. In the second part, commonly used models such as copula and GARCH are included. In addition to the GARCH and copula formulations, many other methods are included, such as regime switching, the Markov switching model, and the multifractal asymmetric detrend cross-correlation analysis method. In addition, we compare the advantages and differences between the models. In the third part, the causes of asymmetry are discussed, for example, higher common fundamental risk, correlation of individual fundamental risk, and so on.

An investigation of the relationship between the CME and the Geomagnetic Storm

The primary objective of this work is to look for any conceivable link between the geomagnetic storm and coronal mass ejection (CME) events. The relevant data for both CME and geomagnetic storm occurrences have been obtained from the Solar and Heliospheric Observatory mission’s LASCO and the NOAA Space Weather Prediction Center, respectively, for the same time span (February 1999 to December 2007). We performed Multivariate Singular Spectral Analysis (MSSA), Semblance Analysis, and Multifractal cross-correlation detrended fluctuation (MFXDFA) analysis to achieve our target. We also applied MSSA to investigate the causal link between the two data sets mentioned above. The analysis identifies the supportiveness factor between the data series and the possibility of a one-way statistical relationship between the data series is also verified. Then, Semblance and MFXDFA were used to detect the presence of any conceivable local phase relationship (time and frequency-dependent) and cross-correlation in the data sets. To make our analysis more persuasive, we must use all three methods. The Semblance analysis reveals positive and negative phase correlation between the signals under investigation at different time sub-intervals, whilst the MFXDFA validates the long-term power-law cross-correlations.

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.