Detrended Cross-correlation Analysis Research Articles

Characteristics of groundwater drought and its correlation with meteorological and agricultural drought over the North China Plain based on GRACE

Groundwater drought is distinctive comparing with other droughts, featuring high concealment, long duration, and obvious hysteresis. It may have significant negative effects on agriculture, eco-environment, and social economy sectors. Therefore, investigating the temporal and spatial characteristics of groundwater drought and its driving factors is meaningful for monitoring and assessing the risks of groundwater shortage. In this study, a groundwater drought index based on groundwater storage anomalies (GWSAs) derived from GRACE satellites was developed to detect and analyze drought events. The spatiotemporal variations and trends of historical groundwater droughts from 2002 to 2021 in the North China Plain were evaluated. In addition, the correlations between groundwater drought and meteorological and agricultural drought were analyzed by the detrended cross-correlation analysis. The results indicated that (1) the standardized groundwater storage anomaly index (SGSAI) could better identify and characterize groundwater drought by eliminating the spatial heterogeneity of GWSAs; (2) from 2002 to 2021, the intensity, frequency, duration, and area of groundwater drought showed an increasing trend; (3) groundwater drought had an obvious hysteresis (>9 months) to meteorological drought and the correlation between groundwater drought and meteorological drought increased, while the relationship with agricultural drought decreased; (4) long-term overexploitation of groundwater resources might be the main driving factor for the exacerbating groundwater drought in this area.

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.

Combining detrended cross-correlation analysis with Riemannian geometry-based classification for improved brain-computer interface performance.

Riemannian geometry-based classification (RGBC) gained popularity in the field of brain-computer interfaces (BCIs) lately, due to its ability to deal with non-stationarities arising in electroencephalography (EEG) data. Domain adaptation, however, is most often performed on sample covariance matrices (SCMs) obtained from EEG data, and thus might not fully account for components affecting covariance estimation itself, such as regional trends. Detrended cross-correlation analysis (DCCA) can be utilized to estimate the covariance structure of such signals, yet it is computationally expensive in its original form. A recently proposed online implementation of DCCA, however, allows for its fast computation and thus makes it possible to employ DCCA in real-time applications. In this study we propose to replace the SCM with the DCCA matrix as input to RGBC and assess its effect on offline and online BCI performance. First we evaluated the proposed decoding pipeline offline on previously recorded EEG data from 18 individuals performing left and right hand motor imagery (MI), and benchmarked it against vanilla RGBC and popular MI-detection approaches. Subsequently, we recruited eight participants (with previous BCI experience) who operated an MI-based BCI (MI-BCI) online using the DCCA-enhanced Riemannian decoder. Finally, we tested the proposed method on a public, multi-class MI-BCI dataset. During offline evaluations the DCCA-based decoder consistently and significantly outperformed the other approaches. Online evaluation confirmed that the DCCA matrix could be computed in real-time even for 22-channel EEG, as well as subjects could control the MI-BCI with high command delivery (normalized Cohen's κ: 0.7409 ± 0.1515) and sample-wise MI detection (normalized Cohen's κ: 0.5200 ± 0.1610). Post-hoc analysis indicated characteristic connectivity patterns under both MI conditions, with stronger connectivity in the hemisphere contralateral to the MI task. Additionally, fractal scaling exponent of neural activity was found increased in the contralateral compared to the ipsilateral motor cortices (C4 and C3 for left and right MI, respectively) in both classes. Combining DCCA with Riemannian geometry-based decoding yields a robust and effective decoder, that not only improves upon the SCM-based approach but can also provide relevant information on the neurophysiological processes behind MI.

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.

Weighted Signed Networks Reveal Interactions between US Foreign Exchange Rates.

Correlations between exchange rates are valuable for illuminating the dynamics of international trade and the financial dynamics of countries. This paper explores the changing interactions of the US foreign exchange market based on detrended cross-correlation analysis. First, we propose an objective way to choose a time scale parameter appropriate for comparing different samples by maximizing the summed magnitude of all DCCA coefficients. We then build weighted signed networks under this optimized time scale, which can clearly display the complex relationships between different exchange rates. Our study shows negative cross-correlations have become pyramidally rare in the past three decades. Both the number and strength of positive cross-correlations have grown, paralleling the increase in global interconnectivity. The balanced strong triads are identified subsequently after the network centrality analysis. Generally, while the strong development links revealed by foreign exchange have begun to spread to Asia since 2010, Europe is still the center of world finance, with the euro and Danish krone consistently maintaining the closest balanced development relationship. Finally, we propose a fluctuation propagation algorithm to investigate the propagation pattern of fluctuations in the inferred exchange rate networks. The results show that, over time, fluctuation propagation patterns have become simpler and more predictable.

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.

Fingerprints of decreased cognitive performance on fractal connectivity dynamics in healthy aging

Analysis of brain functional connectivity (FC) could provide insight in how and why cognitive functions decline even in healthy aging (HA). Despite FC being established as fluctuating over time even in the resting state (RS), dynamic functional connectivity (DFC) studies involving healthy elderly individuals and assessing how these patterns relate to cognitive performance are yet scarce. In our recent study we showed that fractal temporal scaling of functional connections in RS is not only reduced in HA, but also predicts increased response latency and reduced task solving accuracy. However, in that work we did not address changes in the dynamics of fractal connectivity (FrC) strength itself and its plausible relationship with mental capabilities. Therefore, here we analyzed RS electroencephalography recordings of the same subject cohort as previously, consisting of 24 young and 19 healthy elderly individuals, who also completed 7 different cognitive tasks after data collection. Dynamic fractal connectivity (dFrC) analysis was carried out via sliding-window detrended cross-correlation analysis (DCCA). A machine learning method based on recursive feature elimination was employed to select the subset of connections most discriminative between the two age groups, identifying 56 connections that allowed for classifying participants with an accuracy surpassing 92%. Mean of DCCA was found generally increased, while temporal variability of FrC decreased in the elderly when compared to the young group. Finally, dFrC indices expressed an elaborate pattern of associations—assessed via Spearman correlation—with cognitive performance scores in both groups, linking fractal connectivity strength and variance to increased response latency and reduced accuracy in the elderly population. Our results provide further support for the relevance of FrC dynamics in understanding age-related cognitive decline and might help to identify potential targets for future intervention strategies.

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.

Quantifying the direct and indirect interactions for EEG signals by using detrended permutation mutual information

In this paper, we extend detrended cross-correlations analysis (DCCA) and introduce a novel method called detrended permutation mutual information (DPMI) by utilizing information-theoretic tools. The main mechanism of this paper is to use the invariance of the nonlinear monotonic transformation and robustness in permutation mutual information (PMI), which solves the limitations of DCCA only applicable to linear measurements and enhances the robustness of DPMI to noise. We compare the performance of DPMI with DCCA on multifractal binomial measures and Hénon maps for testing the effectiveness of the new method. By analyzing EEG signals obtained from children with attention deficit hyperactivity disorder (ADHD) as well as healthy children, we demonstrate that DPMI surpasses DCCA in processing physiological signals. Furthermore, we conclude that DPMI is more effective in distinguishing between different states within distinct groups. Given that EEG signals in physiological systems are associated with other channel signals, we propose a method called partial DPMI (PDPMI) that combines partial-correlation technique with DPMI. PDPMI can further reveal the direct interactions between two considered signals by eliminating potential influences from other unconsidered signals. In summary, PDPMI serves as a complementary perspective to DPMI, enhancing our understanding in the interactive structure of physiological network.

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.

Variation of Total Electron Content over Nepal during Geomagnetic Storms: GPS Observations

Geomagnetic storms have very profound effects on the Total Electron Content (TEC) of the ionosphere. In order to investigate the equatorial and low-latitude ionospheric response to the geomagnetic storms of varying intensities, a detailed study of vertical TEC (VTEC) variations resulting from Global Positioning System (GPS) data acquired at four GPS stations in Nepal along 80°–90° E longitude and 26°–30° N latitude sector has been carried out in the present work. The results were analyzed with other favorable inducing factors (solar wind parameters and geomagnetic indices) affecting TEC to constrain the causative factor. Positive phases are observed for all the storms studied. During the severe geomagnetic activity, the deviation was ~18 TECU, while it was recorded ~12 TECU and ~8 TECU during moderate and minor geomagnetic activity, respectively. The Detrended Cross-Correlation Analysis (DXA) illustrates that the value of the hourly average VTEC of the BESI station was found to have a strong positive correlation with other stations in all types of storm events, indicating a similar response of all stations towards the space weather events. In addition, the correlation of VTEC with solar wind parameters and geomagnetic indices illustrated that the VTEC shows a strong positive association with solar wind velocity (Vsw) in all three geomagnetic events. In contrast, the correlation of plasma density (Nsw), interplanetary magnetic field (IMF-Bz), the symmetric horizontal component of geomagnetic field (SYM-H), and Geomagnetic Auroral Electrojet (AE) index with VTEC vary with the intensity of the storm. Overall results of the study have revealed the characteristic features of TEC variation over Nepal regions during magnetic storms, which validates earlier research on ionospheric responses to geomagnetic storms and theoretical assumptions.

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.

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.

Impact of the COVID-19 Pandemic on Cryptocurrency Markets: A DCCA Analysis

Extraordinary events, regardless of their financial or non-financial nature, are a great challenge for financial stability. This study examines the impact of one such occurrence—the COVID-19 pandemic—on cryptocurrency markets. A detrended cross-correlation analysis was performed to evaluate how the links between 16 cryptocurrencies were changed by this event. Cross-correlation coefficients that were calculated before and after the onset of the pandemic were compared, and the statistical significance of their variation was assessed. The analysis results show that the markets of the assessed cryptocurrencies became more integrated. There is also evidence to suggest that the pandemic crisis promoted contagion, mainly across short timescales (with a few exceptions of non-contagion across long timescales). We conclude that, in spite of the distinct characteristics of cryptocurrencies, those in our sample offered no protection against the financial turbulence provoked by the COVID-19 pandemic, and thus, our study provided yet another example of ‘correlations breakdown’ in times of crisis.

Response of cross-correlations between high PM2.5 and O3 with increasing time scales to the COVID-19: different trends in BTH and PRD

The air pollution in China currently is characterized by high fine particulate matter (PM2.5) and ozone (O3) concentrations. Compared with single high pollution events, such double high pollution (DHP) events (both PM2.5 and O3 are above the National Ambient Air Quality Standards (NAAQS)) pose a greater threat to public health and environment. In 2020, the outbreak of COVID-19 provided a special time window to further understand the cross-correlation between PM2.5 and O3. Based on this background, a novel detrended cross-correlation analysis (DCCA) based on maximum time series of variable time scales (VM-DCCA) method is established in this paper to compare the cross-correlation between high PM2.5 and O3 in Beijing-Tianjin-Heibei (BTH) and Pearl River Delta (PRD). At first, the results show that PM2.5 decreased while O3 increased in most cities due to the effect of COVID-19, and the increase in O3 is more significant in PRD than in BTH. Secondly, through DCCA, the results show that the PM2.5-O3 DCCA exponents α decrease by an average of 4.40% and 2.35% in BTH and PRD respectively during COVID-19 period compared with non-COVID-19 period. Further, through VM-DCCA, the results show that the PM2.5-O3 VM-DCCA exponents [Formula: see text] in PRD weaken rapidly with the increase of time scales, with decline range of about 23.53% and 22.90% during the non-COVID-19 period and COVID-19 period respectively at 28-h time scale. BTH is completely different. Without significant tendency, its [Formula: see text] is always higher than that in PRD at different time scales. Finally, we explain the above results with the self-organized criticality (SOC) theory. The impact of meteorological conditions and atmospheric oxidation capacity (AOC) variation during the COVID-19 period on SOC state are further discussed. The results show that the characteristics of cross-correlation between high PM2.5 and O3 are the manifestation of the SOC theory of atmospheric system. Relevant conclusions are important for the establishment of regionally targeted PM2.5-O3 DHP coordinated control strategies.