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We introduce a new method, multifractal cross-correlation analysis based on statistical moments (MFSMXA), to investigate the long-term cross-correlations and cross-multifractality between time series generated from complex system. Efficiency of this method is shown on multifractal series, comparing with the well-known multifractal detrended cross-correlation analysis (MFXDFA) and multifractal detrending moving average cross-correlation analysis (MFXDMA). We further apply this method on volatility time series of DJIA and NASDAQ indices, and find some interesting results. The MFSMXA has comparative performance with MFXDMA and sometimes perform slightly better than MFXDFA. Multifractal nature exists in volatility series. In addition, we find that the cross-multifractality of volatility series is mainly due to their cross-correlations, via comparing the MFSMXA results for original series with those for shuffled series.

We address the question of how to precisely identify correlated behavior between different firms in the economy by applying methods of random matrix theory (RMT). Specifically, we use methods of random matrix theory to analyze the cross-correlation matrix of price changes of the largest 1000 US stocks for the 2-year period 1994–1995. We find that the statistics of most of the eigenvalues in the spectrum of agree with the predictions of random matrix theory, but there are deviations for a few of the largest eigenvalues. To prove that the rest of the eigenvalues are genuinely random, we test for universal properties such as eigenvalue spacings and eigenvalue correlations. We demonstrate that shares universal properties with the Gaussian orthogonal ensemble of random matrices. In addition, we quantify the number of significant participants, that is companies, of the eigenvectors using the inverse participation ratio, and find eigenvectors with large inverse participation ratios at both edges of the eigenvalue spectrum — a situation reminiscent of results in localization theory.

In this paper, we investigate the relationship between unexpected information from postings and news, and the unexpected information is measured by the residual of regressions of trading volume on numbers of news or postings. We mainly find that (i) There are significant positive contemporaneous correlations between the unexpected information coming from postings and different kinds of news; the correlation between the unexpected information coming from postings and new media news is stronger than that between the unexpected information coming from postings and mass media news; (ii) The unexpected information coming from postings could cause the unexpected information coming from news, but only the unexpected information coming from the mass media news could cause that coming from postings; (iii) There are persistent power-law cross-correlations between the unexpected information coming from postings and that coming from mass media news and new media news. The cross-correlation between the unexpected information coming from postings and new media news is more persistent than the one between the unexpected information coming from postings and mass media news. The cross-correlations are all more stable in long term than in short term. We attribute our findings above to the dissemination speed of the information on the Internet.

This paper explores the COVID-19 influences on the cross-correlation between the movie market and the financial market. The nonlinear cross-correlations between movie box office data and Google search volumes of financial terms such as Dow Jones Industrial Average (DJIA), NASDAQ and PMI are investigated based on multifractal detrended cross-correlation analysis (MF-DCCA). The empirical results show there are nonlinear cross-correlations between movie market and financial market. Metrics such as Hurst exponents, singular exponents and multifractal spectrum demonstrate that the cross-correlation between movie market and financial market is persistent, and the cross-correlation in long term is more stable than that in short term. In the COVID-19 period, the multifractal features of cross-correlation become stronger implying that COVID-19 enhanced the complexity between the movie industry and the financial market. Furthermore, through the rolling window analysis, the Hurst exponent dynamic trends indicate that COVID-19 has a clear influence on the cross-correlation between movie market and financial market.

With the rapid development of economic globalization, the stock markets in China and the US are increasingly linked. The fluctuation features and cross-correlations of the two countries’ markets have attracted extensive attention from market investors and researchers. In this paper, the fractal analysis methods including multifractal asymmetric detrended cross-correlation analysis (MF-ADCCA) and coupled detrended cross-correlation analysis (CDCCA) are applied to explore the volatilities of CSI300 and SP500 sector stock indexes as well as the cross-correlations and coupling cross-correlations between the two corresponding sector stock indexes. The results show that the auto-correlations, cross-correlations and coupling cross-correlations have multifractal fluctuation characteristics, and that the cross-correlations are asymmetric. Additionally, the coupling cross-correlation strengths are distinct due to the different influence of long-range correlations and fat-tailed distribution. Further, the co-movement between China and the US sector stock markets is susceptible to external market factors such as major economic events and national policies.

The ongoing COVID-19 shocked financial markets globally, including China’s crude oil future market, which is the third-most traded crude oil futures after WTI and Brent. As China’s first crude oil futures are accessible to foreign investors, the Shanghai crude oil futures (SC) have attracted significant interest since launch at the Shanghai International Energy Exchange. The impact of COVID-19 on the new crude oil futures is an important issue for investors and policy makers. Therefore, this paper studies the short-term influence of COVID-19 pandemic on SC via multifractal analysis. We compare the market efficiency of SC before and during the pandemic with the multifractal detrended fluctuation analysis and other commonly used random walk tests. Then, we generate shuffled and surrogate data to investigate the components of multifractal nature in SC. And we examine cross-correlations between SC returns and other financial assets returns as well as SC trading volume changes by the multifractal detrended cross-correlation analysis. The results show that market efficiency of SC and its cross-correlations with other assets increase significantly after the outbreak of COVID-19. Besides that, the sources of its multifractal nature have changed since the pandemic. The findings provide evidence for the short-term impacts of COVID-19 on SC. The results may have important implications for assets allocation, investment strategies and risk monitoring.

Taking six representative futures in the international energy and agricultural markets as the research objects, we use multifractal analysis methods to study the fluctuation characteristics, market risks and cross-correlations within and between these markets before and after the outbreak of the Russia–Ukraine conflict in this paper. The empirical results show that both the auto-correlations and cross-correlations have obvious multifractal features. It is confirmed that the multifractal strength and market risks of the international energy markets have weakened, while those of the international agricultural markets have enhanced after the Russia–Ukraine conflict broke out. In addition, the Russia–Ukraine conflict has intensified the strength of the multifractality and the degree of fluctuation complexity between these two classes of international markets. Further, the intrinsic multifractal natures of cross-correlations are tested, and the apparent and intrinsic multifractality before and after the conflict are revealed. Finally, some policy suggestions are put forward based on the empirical results.

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