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Using the multifractal detrended cross-correlation analysis (MF-DCCA) method and the Empirical Mode Decomposition (EMD)-MF-DCCA method, this study quantifies the dynamic interrelation between carbon emission allowance returns in the Chinese and EU markets. The cross-correlation statistics indicate a moderate acceptance of the cross-correlation between the two carbon markets. Applying the MF-DCCA and EMD-MF-DCCA methods to the two markets reveals that their cross-correlation exhibits a power-law nature. Moreover, the apparent persistence of the cross-correlation and notable Hurst index show that the cross-correlation between long-term trends of the returns of the Guangdong and EU carbon emission markets exhibits stronger fractality over the long term, whereas the cross-correlation between the short-term fluctuations of the Hubei and EU carbon emission markets demonstrates stronger fractality. Subsequent investigations show that both fat tails and long memory contribute to the various fractals of the cross-correlation between the returns of the Chinese and EU carbon emission markets, especially for the fractals between the Hubei and EU carbon emission markets. Ultimately, the sliding window analysis demonstrates that national policy, trading activity, and other factors can make the observed multiple fractals more sensitive. The aforementioned findings facilitate an understanding of the current state of the Chinese carbon emission market and inform strategies for its future development.

In this paper, we investigated the influence of climatic factors, particularly low temperature and humidity, on the grounding resistance of transmission towers in severely cold regions. Drawing on a full year of field monitoring data, we first identified a clear negative linear correlation between temperature and grounding resistance. Notably, the inclusion of precipitation as an additional variable led to a significant increase in the model's explanatory power and indicated that the resistance behavior was influenced by multiple environmental factors. To further explore the nonlinear and dynamic aspects of this relationship, we used multifractal detrended fluctuation analysis (MF-DFA) and multifractal detrended cross-correlation analysis (MF-DCCA). The computational results showed that the resistance time series exhibits strong multifractal characteristics and suggests high variability across temporal scales. Moreover, the combined influence of temperature and precipitation demonstrated a markedly stronger cross-correlation with resistance than temperature alone. These findings emphasize the complex and multiscale nature of grounding behavior in harsh climates and underscore the importance of moving beyond simplified linear models. Our research offers both methodological insights and practical implications for the design, maintenance, and risk assessment of power transmission infrastructure operating under extreme weather conditions, particularly in high-latitude or alpine environments.

In this study, we apply multifractal detrended fluctuation analysis (MF-DFA) to explore the differences in China’s financial markets efficiency around the Russia-Ukraine Conflict. We investigate the stock markets for fossil oil, fertilizer and grain. The results show that the three industries around the conflict both have multifractal characteristics, and the multifractal characteristics after the conflict are stronger. This phenomenon shows that the efficiency of the stock markets have decreased after the conflict. Then, we adopt multifractal detrended cross-correlation analysis (MF-DCCA) to examine the nonlinear cross-correlations between fossil oil / chemical fertilizer and fossil oil / grain. The results indicate that there are cross correlations between the two time series pairs. In addition, the cross-correlations between chemical fertilizer and fossil oil after the conflict increase significantly, while that between grain and fossil oil are increase slightly. This paper is great interest by policy makers and participants involved in these markets given the economic and financial consequences derived from such dynamics.

PurposeIn this paper, we study the effect of global energy and food inflation on household inflation expectations during the period 1988M01–2020M03 for a set of European economies.Design/methodology/approachWe use multifractal de-trended cross-correlation analysis to estimate the non-linear and time-varying cross-correlation. We provide additional robustness tests using the Autoregressive-Distributed Lag method.FindingsWe find that household inflation expectations, global energy inflation and global food inflation are all multifractal. We also find that the household inflation expectations, global energy inflation and global food inflation are positively correlated (i.e., they are persistent). However, household inflation expectations respond more when the volatility of the global energy inflation is lower than when the volatility is higher. The correlation between household inflation expectations and global food inflation does not depend on the level of volatility.Research limitations/implicationsFirst, paying attention to the global commodity inflation might help anchor inflation expectations better. It is so because Central Bank's efficacy in achieving price stability may be weakened if there is a relationship between commodity inflation and inflation expectation. This task would become even more difficult in the average inflation targeting regime than inflation targeting regime if actual inflation is persistently different from the target inflation. Second, our results also emphasize the importance of effective strategy for communicating to households about actual inflation, inflation target and keep them updated about how monetary policy functions.Originality/valueWe contribute to the literature by estimating the cross-correlation between household inflation expectations with the global commodity inflation, conditional to the volatility of the commodity inflation under consideration.

Traditional linear models struggle to capture the complex behavior of financial markets. This study revisits RMB exchange rate volatility through a nonlinear perspective based on G-expectation and multifractal theory. Using multifractal detrended fluctuation analysis (MF-DFA), we examine the scaling properties and efficiency of RMB volatility. We further apply multifractal detrended cross-correlation analysis (MF-DCCA) to explore nonlinear linkages among different RMB exchange rate volatilities. Mixing and phase randomization are employed to identify the sources of multifractality. The results reveal that adverse shocks weaken market efficiency and amplify multifractality. Significant cross-correlations are detected across RMB volatilities, with the Hurst exponent and multifractal spectrum indicating persistent long-range dependence and fat-tailed distributions. Moreover, USDCNY volatility exhibits stronger multifractality than other RMB pairs, underscoring its dominant role in volatility transmission. The time-varying Hurst exponent effectively captures nonlinear and memory effects, offering predictive value for exchange rate trends. These findings deepen our understanding of RMB exchange rate dynamics and provide implications for monetary regulation and risk management under uncertainty.

In the current context of the global energy landscape, China is facing a growing challenge in oil and gas exploration and development. It is difficult to evaluate the log data because of the lithological composition of igneous rocks, which displays an unparalleled degree of complexity and unpredictability. Against this backdrop, this study deploys advanced multifractal detrended fluctuation analysis (MF-DFA) to comprehensively analyze key parameters within igneous rock logging data, including natural gamma-ray logging, resistivity logging, compensated neutron logging, and acoustic logging. The results unequivocally demonstrate that these logging data possess distinct multifractal characteristics. This multifractality serves as a powerful tool to elucidate the inherent complexity, heterogeneity, and structural and property variations in igneous rocks caused by diverse geological processes and environmental changes during their formation and evolution, which is crucial for understanding the subsurface reservoir behavior. Subsequently, through a series of rearrangement sequences and the replacement sequence on the original logging data, we identify that the probability density function and long-range correlation are the fundamental sources of the observed multifractality. These findings contribute to a deeper theoretical understanding of the data-generating mechanisms within igneous rock formations. Finally, multifractal detrended cross-correlation analysis (MF-DCCA) is employed to explore the cross-correlations among different types of igneous rock logging data. We uncover correlations among different igneous rocks’ logging data. These parameters exhibit different properties. There are negative long-range correlations between natural gamma-ray logging and resistivity logging, natural gamma-ray logging and compensated neutron logging in basalt, and resistivity logging and compensated neutron logging in diabase. The logging data on other igneous rocks have long-range correlations. These correlation results are of great significance as they provide solid data support for the formulation of oil and gas exploration and development plans.

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.

In this paper, we introduce a method called multiscale multifractal detrended cross-correlation analysis (MM-DCCA) to describe the cross-correlation properties depend on the timescale in which the multifractality is computed. For traffic time series, we show that the fractal properties of cross-correlations have a relationship with the range of scale indicating the great necessity to study the cross-correlation properties between two time series at multiple scales. MM-DCCA gains a new insight into measuring different fractal properties of the cross-correlations between traffic series by sweeping all the range of scale, and it provides much richer information than multifractal detrended cross-correlation analysis (MF-DCCA). The Hurst surfaces present multifractal properties and strong long-range persistent cross-correlations between traffic series. By comparing Hurst surfaces before and after removing dominant periodicities, we find that periodicity is not the only reason which causes the crossover and dominates the cross-correlation. There are other interesting factors or underlying traffic mechanisms containing in the cross-correlation between traffic series. Moreover, the cross-correlation between the whole traffic series can be considered as a combination of both weekday and weekend parts. The results also suggest that the different periodic patterns hidden in the weekday and weekend patterns are the main distinction between them and play an important role in the Hurst surface of cross-correlation investigation.

Global climate change has become the greatest threat to mankind, endangering the ecological security of the earth and the long-term development of human society. Therefore, how to effectively reduce greenhouse gas emissions and curb the trend of global warming has become a common challenge facing all countries in the world. Fossil energy combustion is the fundamental cause of climate change. In this paper, the price return series of domestic energy and carbon markets are taken as the research objects. Firstly, the cross-correlation test is used to verify that there is an obvious cross-correlation between the return series of the energy and carbon markets. Based on this, the multifractal characteristics of energy market and carbon market cross-series are empirically studied. The empirical results show that there is an interactive correlation between energy and carbon markets and this relationship has multifractal characteristics; the interactive correlation between return series has multifractal characteristics. The long-range correlation between small fluctuations and large fluctuations and the fat tail distribution of return series are all reasons for the formation of multifractality. These conclusions will help to understand the non-linear dependence and potential dynamic mechanism between energy and carbon markets in China.

The Bonhoeffer–van der Pol (BVP) oscillator has widely application in the modeling of biological processes, and it also has rich nonlinear behavior including different topological properties between the continuous-time BVP oscillator and the discrete one. Multifractal Detrended Cross-Correlation Analysis (MF-DCCA) has proved useful in describing the correlations and detecting the scaling exponent of time series. We investigate the autocorrelations and cross-correlations of the time series in BVP model by using the MF-DCCA method. Our results show that there exist long range autocorrelations and cross-correlations in the BVP model time series, and that multifractal features are significant in the analyzed BVP model.