Multifractal Detrended Cross-correlation Analysis Research Articles

Multi-asset portfolio model optimization based on mean multifractal detrended cross correlation analysis

ABSTRACT In order to make the constructed investment portfolio model better adapt to the actual securities market, this paper incorporates the multifractal correlations into the portfolio model of multi-risk assets optimization. On the basis of using variable detrended covariance to measure multifractal correlations, the variable detrended covariance is embedded into the reward-risk criterion, the mean multifractal detrended cross correlation analysis portfolio (M-D) model of multi-risk assets is constructed, and the analytical solution of the M-D model of multi-risk assets is given. The empirical analysis shows that the M-D model not only can improve investment performance but also meet the return-risk criterion much more, reaching the goal of optimizing the multi-risk asset portfolio model.

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.

The link between transportation industry and transportation cryptocurrencies – A comparison among airline, rail, and shipping industries

This work examines the link between some of the most important transportation companies’ stock performance with the corresponding transportation cryptocurrencies. To do so, airlines, rail, and shipping companies’ stocks are investigated, examining for a probable link with the transportation cryptocurrencies, and also investigating the attributes of this link. The variable-Lag time-series causality is employed to test the channel of causality (if such exists), and the multifractal detrended cross-correlation analysis is utilized to investigate the relationship’s attributes. According to the results, the three transportation industries differ in the way they relate to transportation-related cryptocurrencies. More precisely, the transportation industries differ in the way they relate to transportation cryptocurrencies since airlines, and railway companies affect the price of the cryptocurrencies related to transportation, and cryptocurrencies also affect in a similar magnitude these fields. On the other hand, the shipping companies have a greater effect on the cryptocurrencies, while the cryptocurrencies in very few cases affect these stocks. Finally, a long-run relationship is identified, implying that transportation companies and the corresponding cryptocurrencies are positively and long-term related. The results important because they unveil a link between the transportation companies and the corresponding cryptocurrencies, with this link differing among these industries. This finding should be taken into account in the adoption of relevant technologies from the transportation field.

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.

Effect of NO2 on SO2–SO42- conversion in atmosphere: Evidence from long-term precipitation

Sulfate aerosol (SO42−) is an important factor leading to acid rain and aggravating atmospheric particulate pollution. SO42− is mainly converted from gaseous SO2, in which the oxidant gas NO2 may play a key role. In real atmosphere with complexity and nonlinearity, the impact of NO2 on SO2–SO42- conversion exhibits scale dependence due to the combined effect of meteorology, atmospheric chemistry, and pollution emission. Here, based on the long-term atmospheric precipitation data from 2014 to 2021 of Nanchong City in the Sichuan Basin, the Extended Ensemble Empirical Mode Decomposition (EEMD) and Multifractal Detrended Cross-Correlation Analysis (MF-DCCA) methods have been employed to analyze the nonlinear correlations between gaseous SO2 and SO42− in rainwater at different time scales. A multifractal parameter Δh has been described as the scaling features of SO2–SO42- conversion efficiency in the real atmosphere. Then, the impact of NO2 on SO2–SO42- conversion in cold and warm seasons has been quantified, using sliding window analysis and Pearson correlation analysis. The results show that NO2 significantly promoted SO2–SO42- conversion in the cold season, but had little effect on it in the warm season. As direct evidence from atmospheric precipitation analysis, this finding has provided a new theoretical basis for evaluating the impact of NO2 on secondary aerosol generation.

Exploring the Cross-Correlations between Tesla Stock Price, New Energy Vehicles and Oil Prices: A Multifractal and Causality Analysis

The interaction between new energy vehicle (NEV) stock prices and the crude oil market is crucial for resource allocation and risk management. This study employs Multifractal detrended cross-correlation analysis (MF-DCCA) to investigate the multifractal characteristics of the cross-correlation between Tesla stock price (TSLA) and crude oil price (Brent), as well as between TSLA and other NEV stocks (excluding TSLA). The experimental results reveal long-term persistence and multiple fractal characteristics in the cross-correlations. Additionally, multifractal asymmetric detrended cross-correlation analysis (MF-ADCCA) demonstrates the asymmetry of the cross-correlation during upward or downward trends between TSLA and Brent, as well as between TSLA and other NEV stocks (excluding TSLA). Furthermore, utilizing the transfer entropy (TE) method, we assess the strength and direction of information flows between TSLA and Brent, and between TSLA and other NEV stocks (excluding TSLA). Interestingly, we observe bidirectional information transmission between TSLA and other NEV stocks, while only unidirectional information transmission from NIO to TSLA is evident. These findings provide valuable insights for resource allocation, supply chain management and sustainable development strategies for decision-makers in the NEV market.

Impact of atmospheric O3 and NO2 on the secondary sulfates in real atmosphere

As an important component of secondary aerosols, sulfate plays a crucial role in regulating atmospheric radiative balance and influencing the secondary formation of ozone (O3). In real atmosphere, atmospheric oxidants NO2 and O3 can promote the oxidation of SO2 to form sulfate (SO42−) through multiphase chemistry that occur at different time scales. Due to the combined impact of meteorology, pollution sources, atmospheric chemistry, etc., time-scale dependence of SO2-SO42− conversion makes the impact of NO2/O3 on it more complex. In this study, based on long-term time series (2013-2020) of air pollution variables from seven stations in Hong Kong, the Multifractal Detrended Cross-Correlation Analysis (MFDCCA) method has been employed to quantify the cross-correlations between SO2 and SO42− in real atmosphere at different time scales, for examining the time-scale dependence of SO2-SO42− conversion efficiency. Furthermore, the Pearson correlation analysis has been used to study the influence of NO2/O3 on SO2-SO42− conversion, and the regional and seasonal differences have been analyzed by considering factors such as meteorology, pollution sources, and regional transport. Changes in the main components of secondary aerosols are closely linked with the co-control of regional PM2.5 and O3. Therefore, the exploration of the impact of co-existing NO2/O3 gases on the secondary formation of sulfates in real atmosphere is significant.

An Econophysics Perspective on Green Bonds and Stock Market Nexus: Can Green Finance be an Investment Option for Emerging Stock Markets?

Green bonds are one of the most fascinating financial innovations that offer a solution to climate change and sustainable development from the financial point of view. In this study, we employ methods from statistical physics to examine the multifractal features of cross-correlations between green bonds and emerging stock markets. Utilizing multifractal detrended cross-correlation analysis (MFDCCA) on return and volatility series, our findings reveal significant cross-correlations between green bonds and emerging stock markets. The MFDCCA results uncover multifractal features and long-range cross-correlations between the two assets. Notably, volatility cross-correlations exhibit persistent behavior, while return cross-correlations vary across small and large fluctuation periods. These findings hold practical implications for policymakers and investors involved in green bonds and emerging stock markets.

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.

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.

Time-Varying Fractal Analysis of Exchange Rates

The foreign exchange (forex) market is a dynamic and complex financial arena where the exchange rates of various currency pairs fluctuate continuously. Among these currency pairs, EUR/TRY and USD/TRY hold significant economic relevance due to their roles in international trade and finance. In this study, we analyze the multifractality of hourly EUR/TRY and USD/TRY exchange rate data for the whole period, as well as its time-varying individual and cross correlations, spanning from May 31, 2018, to March 21, 2022. We employ multifractal detrended cross-correlation analysis (MF-DCCA) and multifractal detrended fluctuation analysis (MF-DFA) methodologies. The aim of studying multifractality in exchange rates is to comprehend and model the complex and intricate nature of price movements and dynamics of the EUR/TRY and USD/TRY exchange rates. In the analysis of the whole period, multifractality is detected in individual exchange rates and cross correlations. In the rolling window analysis, we demonstrated how multifractality and cross correlation multifractality change over time. Additionally, contributions of the sources of the multifractality are investigated in a time-varying framework. Multifractal nature of these exchange rates indicate that they exhibit complex and scale-dependent behaviors, which go beyond the traditional linear models. The existence of multifractality in EUR/TRY and USD/TRY exchange rates has significant implications for financial modeling, risk management, and trading strategies. It implies that standard linear models may not capture the full complexity of these markets, necessitating the development of more sophisticated models that account for multifractal properties.

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.

Is gold a safe haven for the CIVETS countries under extremely adverse market conditions? Some new evidence from the MF-DCCA analysis

This paper investigates the safe haven attributes of gold under extreme market conditions. Our main goal is to understand if this property still holds under exceptional times characterized by unusual high levels of uncertainty. To this end, we gathered data from 2018 to 2023 for a group of emerging markets – the CIVETS (Colombia, Indonesia, Vietnam, Egypt, Turkey and South Africa) – thus encompassing a stable and a particularly turbulent period, which was marked by two consecutive crises: the COVID-19 and the Russian-Ukrainian war. We chose these countries as they are fast growing economies, which represent important investing opportunities, and because among the emerging markets these are the least studied. To achieve our goal we employed the Multifractal Detrended Cross-Correlation Analysis (MF-DCCA). Our results showed that before the pandemic the cross-correlations between gold and the financial markets were mainly negative. However, with the onset of the crisis they became positive. This demonstrates that gold lost its popular safe haven attributes and highlights the need for investors to seek alternative investments to protect downward risk, especially under extremely turbulent scenarios.

Interplay of multifractal dynamics between shadow policy rates and stock markets

Stock markets are generally perceived as a barometer of the economy and respond to international monetary policies even before economic activities. Many central banks have turned to unconventional policy measures in response to various financial crises such as the global financial crisis of 2007–2009 or the recent crisis caused by COVID-19. To examine the cross-correlation of overall international monetary policies with stock markets, we employ the daily shadow short rate (SSR), which has the advantage of allowing comparison across unconventional and conventional regimes. The analysis is made through a multifractal context using multifractal detrended cross correlation analysis (MF-DXA), considering daily data from 1st January 2000 to 31st March 2022 and country specific SSR and the stock markets of eight developed economies. The main empirical findings are the following: (i) all the country specific pairs of SSR with stock markets have significant multifractal characteristics (ii) the pairs of NZ-SSR/NZX50, US-SSR/DJIA, and CN-SSR/S&P TSX have the highest multifractal patterns while EU-SSR/Euro-area Index has the lowest multifractal patterns (iii) Australian and New Zealand stock markets exhibit anti-persistent cross-correlation with SSR while the remainder have persistent cross-correlation in their multifractality. Lastly, the findings of this study have several important implications for central banks and stock market participants.

Exploring the Asymmetric Multifractal Characteristics of Price–Volume Cross-Correlation in the Chinese Rebar Futures Market Based on MF-ADCCA

In this paper, we employ multifractal detrended cross-correlation analysis (MF-DCCA) to study the cross-correlation between closing price and trading volume and the multifractal characteristics of the relationship. The results show that the price, volume and price–volume cross-correlation in the rebar futures market have significant multifractal features. We find that the multifractal characteristics of price–volume cross-correlation are derived from long-term correlation and fat-tailed distribution. However, MF-DCCA cannot be used to explore the price–volume cross-correlation under different market trends (upwards or downwards). Therefore, we further adopt multifractal asymmetric detrended cross-correlation analysis (MF-ADCCA) to explore the asymmetric multifractal characteristics of price–volume cross-correlation. The empirical results show that the price–volume cross-correlation in the rebar futures market has significant asymmetric multifractality. Specifically, the asymmetry of the price–volume cross-correlation is more robust for both the price changes and the volume changes in a downtrend than that in an uptrend, indicating that the downward market tends to be more complex and riskier than the upward market in Shanghai Futures Exchange (SHFE) rebar futures market. Therefore, investors should pay extra attention to the downward market of the rebar futures and make reasonable investment strategies according to their risk appetite.

Analysis of Risk Spillover and Asymmetry Between Three Crude Oil Markets and Chinese Financial Markets

Providing a scientific basis and method to ensure the smooth functioning of the Chinese crude oil market would be hugely significant to China’s future economic development and security. To this end, attempts have been made to both internationalize the Shanghai crude oil market and minimize financial risks. This paper selects three crude oil markets (INE, WTI and Brent) and five Chinese financial markets (the futures, bond, fund, stock and foreign exchange markets) as the research objects. The Diebold and Yilmaz spillover index model and the multifractal asymmetric detrended cross-correlation analysis (MF-ADCCA) method are used to study the volatility spillover effect and the asymmetric cross-correlation between crude oil markets and financial markets. When the volatility spillover effect and the asymmetric relationship that exists between the financial markets are examined, the volatility spillover of the oil market to the financial market is found to be significantly higher than that of the financial market to the oil market. In particular, the spillover effect was even more significant from late-2019 to early-2020. Analysis demonstrates an asymmetric cross-correlation between crude oil markets and the abovementioned five Chinese financial markets. In particular, the impact of the Chinese crude oil market on the stock market is greatest, especially with respect to the Brent and WTI crude oil markets. Except for the bond market, when the INE and Brent markets are increasing, the risk exposure to financial markets is more significant. Among financial markets, INE-Bond market asymmetry is stronger than WTI-bond market asymmetry, but weaker than that of the Brent-Bond market when there are large fluctuations.

Stock Index Return Volatility Forecast via Excitatory and Inhibitory Neuronal Synapse Unit with Modified MF-ADCCA

Financial prediction persists a strenuous task in Fintech research. This paper introduces a multifractal asymmetric detrended cross-correlation analysis (MF-ADCCA)-based deep learning forecasting model to predict a succeeding day log return via excitatory and inhibitory neuronal synapse unit (EINS) using asymmetric Hurst exponent as input features, with return and volatility increment of Shanghai Stock Exchanges Composite Index (SSECI) from 2014 to 2020 as proxies for analysis. Experimental results revealed that multifractal elements by MF-ADCCA method as input features are applicable to time series forecasting in deep learning than multifractal detrended fluctuation analysis (MF-DFA) method. Further, the proposed biologically inspired EINS model achieved satisfactory performances in effectiveness and reliability in time series prediction compared with prevalent recurrent neural networks (RNNs) such as LSTM and GRU. The contributions of this paper are to (1) introduce a moving-window MF-ADCCA method to obtain asymmetric Hurst exponent sequences used directly as an input feature for deep learning prediction and (2) evaluate performances of various asymmetric multifractal approaches for deep learning time series forecasting.