Detrended fluctuation analysis on spot and futures markets of West Texas Intermediate crude oil

In this paper, we study the auto-correlations and cross-correlations of West Texas Intermediate (WTI) crude oil spot and futures return series employing detrended fluctuation analysis (DFA) and detrended cross-correlation analysis (DCCA). Scaling analysis shows that, for time scales smaller than a month, the auto-correlations and cross-correlations are persistent. For time scales larger than a month but smaller than a year, the correlations are anti-persistent, while, for time scales larger than a year, the series are neither auto-correlated nor cross-correlated, indicating the efficient operation of the crude oil markets. Moreover, for small time scales, the degree of short-term cross-correlations is higher than that of auto-correlations. Using the multifractal extension of DFA and DCCA, we find that, for small time scales, the correlations are strongly multifractal, while, for large time scales, the correlations are nearly monofractal. Analyzing the multifractality of shuffled and surrogated series, we find that both long-range correlations and fat-tail distributions make important contributions to the multifractality. Our results have important implications for market efficiency and asset pricing models.     

Cross-correlations between Chinese A-share and B-share markets

In this paper, we investigate the cross-correlations between Chinese A-share and B-share markets. Qualitatively, we find that the return series of Chinese A-share and B-share markets were overall significantly cross-correlated based on the analysis of a statistic. Quantitatively, employing the detrended cross-correlation analysis, we find that the cross-correlations were strongly multifractal in the short-term and weakly multifractal in the long-term. Moreover, the cross-correlations of small fluctuations were persistent and those of large fluctuations were anti-persistent in the short-term while cross-correlations of all kinds of fluctuations were persistent in the long-term. Using the method of rolling windows, we find that the cross-correlations were weaker and weaker over time, especially after the price-limited reform. We attribute the fact to the improvement of market efficiency. On the volatility series, our results show that the cross-correlations were much stronger than those between return series. Results from rolling windows show that the short-term cross-correlations between volatility series are still high now. We also provide some relevant discussions later.     

Is Bitcoin Still a King? Relationships between Prices,Volatility and Liquidity of Cryptocurrencies during the Pandemic

We try to establish the commonalities and leadership in the cryptocurrency markets by examining the mutual information and lead-lag relationships between Bitcoin and other cryptocurrencies from January 2019 to June 2021. We examine the transfer entropy between volatility and liquidity of seven highly capitalized cryptocurrencies in order to determine the potential direction of information flow. We find that cryptocurrencies are strongly interrelated in returns and volatility but less in liquidity. We show that smaller and younger cryptocurrencies (such as Ripple’s XRP or Litecoin) have started to affect the returns of Bitcoin since the beginning of the pandemic. Regarding liquidity, the results of the dynamic time warping algorithm also suggest that the position of Monero has increased. Those outcomes suggest the gradual increase in the role of privacy-oriented cryptocurrencies.     

Cross-correlations in volume space: Differences between buy and sell volumes

We study the cross-correlations of buy and sell volumes on the Korean stock market in high frequency. We observe that the pulling effects of volumes are as small as that of returns. The properties of the correlations of buy and sell volumes differ. They are explained by the degree of synchronization of stock volumes. Further, the pulling effects on the minimal spanning tree are studied. In minimal spanning trees with directed links, the large pulling effects are clustered at the center, not uniformly distributed. The Epps effect of buy and sell volumes are observed. The reversal of the cross-correlations of buy and sell volumes is also detected.     

Memory effect and multifractality of cross-correlations in financial markets

We introduce an instantaneous and an average instantaneous cross-correlation function to detect the temporal cross-correlations between individual stocks based on the daily data of the United States and the Chinese stock markets. The memory effect of the instantaneous cross-correlations is investigated by applying the detrended fluctuation analysis (DFA), where the DFA exponents can be partly explained by the correlation function from the common sense. Long-range memory is observed for the average instantaneous cross-correlations, and persists up to a month magnitude of timescale for the United States stock market and half a month magnitude of timescale for the Chinese stock market. In addition, multifractal nature is investigated by a multifractal detrended fluctuation analysis.     

Cross-correlations between agricultural commodity futures markets in the US and China

This paper examines the cross-correlation properties of agricultural futures markets between the US and China using a cross-correlation statistic test and multifractal detrended cross-correlation analysis (MF-DCCA). The results show that the cross-correlations between the two geographically distant markets for four pairs of important agricultural commodities futures are significantly multifractal. By introducing the concept of a “crossover”, we find that the multifractality of cross-correlations between the two markets is not long lasting. The cross-correlations in the short term are more strongly multifractal, but they are weakly so in the long term. Moreover, cross-correlations of small fluctuations are persistent and those of large fluctuations are anti-persistent in the short term while cross-correlations of all kinds of fluctuations for soy bean and soy meal futures are persistent and for corn and wheat futures are anti-persistent in the long term. We also find that cross-correlation exponents are less than the averaged generalized Hurst exponent when q<0$q<0$ and more than the averaged generalized Hurst exponent when q>0$q>0$ in the short term, while in the long term they are almost the same.     

Network structure of cross-correlations among the world market indices

We report the results of an investigation of the properties of the networks formed by the cross-correlations of the daily and weekly index changes of 143 stock market indices from 59 different countries. Analysis of the asset graphs, minimum spanning trees (MST) and planar maximally filtered graphs (PMFG) of the afermentioned networks confirms that globalization has been increasing in recent years. North American and European markets are observed to be much more strongly connected among themselves compared to the integration with the other geographical regions. Surprisingly, the integration of East Asian markets among themselves as well as to the Western markets is found to be rather weak. MST and PMFG of both daily and weekly return correlations indicates that the clustering of the indices is mostly geographical. The French fsbf250 index is found to be most important node of the MST and PMFG based on several graph centrality measures.     

Multifractal detrended cross-correlation analysis in the MENA area

In this paper, we investigated multifractal cross-correlations qualitatively and quantitatively using a cross-correlation test and the Multifractal detrended cross-correlation analysis method (MF-DCCA) for markets in the MENA area. We used cross-correlation coefficients to measure the level of this correlation. The analysis concerns four stock market indices of Morocco, Tunisia, Egypt and Jordan. The countries chosen are signatory of the Agadir agreement concerning the establishment of a free trade area comprising Arab Mediterranean countries. We computed the bivariate generalized Hurst exponent, Rényi exponent and spectrum of singularity for each pair of indices to measure quantitatively the cross-correlations. By analyzing the results, we found the existence of multifractal cross-correlations between all of these markets. We compared the spectrum width of these indices; we also found which pair of indices has a strong multifractal cross-correlation.     

Financial Return Distributions: Past,Present, and COVID-19

We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017–2020, we model tails of the return distributions at different time scales by using power-law, stretched exponential, and q-Gaussian functions. We focus on the fitted function parameters and how they change over the years by comparing our results with those from earlier studies and find that, on the time horizons of up to a few minutes, the so-called “inverse-cubic power-law” still constitutes an appropriate global reference. However, we no longer observe the hypothesized universal constant acceleration of the market time flow that was manifested before in an ever faster convergence of empirical return distributions towards the normal distribution. Our results do not exclude such a scenario but, rather, suggest that some other short-term processes related to a current market situation alter market dynamics and may mask this scenario. Real market dynamics is associated with a continuous alternation of different regimes with different statistical properties. An example is the COVID-19 pandemic outburst, which had an enormous yet short-time impact on financial markets. We also point out that two factors—speed of the market time flow and the asset cross-correlation magnitude—while related (the larger the speed, the larger the cross-correlations on a given time scale), act in opposite directions with regard to the return distribution tails, which can affect the expected distribution convergence to the normal distribution.     

A multifractal detrended fluctuation analysis (MDFA) of the Chinese growth enterprise market (GEM)

A multifractal, detrended fluctuation approach is used to analyze the growth enterprise market (GEM) in China involving a range of correlations in fluctuations of share prices (fat tail), persistent and anti-persistent states. Our analysis exhibits company-specific multifractal characteristics, which vary among the companies listed in the same industry, e.g., the power-law cross-correlations between computer and electronics sectors. These results may help reduce the risk in complex financial markets.     

Progress in physical properties of Chinese stock markets

In the past two decades, statistical physics was brought into the field of finance, applying new methods and concepts to financial time series and developing a new interdiscipline “econophysics”. In this review, we introduce several commonly used methods for stock time series in econophysics including distribution functions, correlation functions, detrended fluctuation analysis method, detrended moving average method, and multifractal analysis. Then based on these methods, we review some statistical properties of Chinese stock markets including scaling behavior, long-term correlations, cross-correlations, leverage effects, antileverage effects, and multifractality. Last, based on an agent-based model, we develop a new option pricing model — financial market model that shows a good agreement with the prices using real Shanghai Index data. This review is helpful for people to understand and research statistical physics of financial markets.     

Multifractal detrended cross-correlation analysis between the Chinese stock market and surrounding stock markets

In this paper, we investigate the cross-correlations between the stock market in China and markets in Japan, South Korea and Hong Kong. We use not only the qualitative analysis of the cross-correlation test, but also the quantitative analysis of the MF-X-DFA. Our findings confirm the existence of cross-correlations between the stock market in China and markets in Japan, South Korea and Hong Kong, which have strongly multifractal features. We find that the cross-correlations display the characteristic of multifractality in the short term. Moreover, the cross-correlations of small fluctuations are persistent and those of large fluctuations are anti-persistent in the short term, while the cross-correlations of all kinds of fluctuations are persistent in the long term. Furthermore, based on the multifractal spectrum, we also find that the multifractality of cross-correlation between stock markets in China and Japan are stronger than those between China and South Korea, as well as between China and Hong Kong.     

Price–volume cross-correlation analysis of CSI300 index futures

We investigate the cross-correlation between price returns and trading volumes for the China Securities Index 300 (CSI300) index futures, which are the only stock index futures traded on the China Financial Futures Exchange (CFFEX). The basic statistics suggest that distributions of these two time series are not normal but exhibit fat tails. Based on the detrended cross-correlation analysis (DCCA), we obtain that returns and trading volumes are long-range cross-correlated. The existence of multifractality in the cross-correlation between returns and trading volumes has been proven with the multifractal detrended cross-correlation analysis (MFDCCA) algorithm. The multifractal analysis also confirms that returns and trading volumes have different degrees of multifractality. We further perform a cross-correlation statistic to verify whether the cross-correlation significantly exists between returns and trading volumes for CSI300 index futures. In addition, results of the test for lead-lag effect demonstrate that contemporaneous cross-correlation of return and trading volume series is stronger than cross-correlations of leaded or lagged series.     

Analysis of cross-correlations between financial markets after the 2008 crisis

We analyze the cross-correlation matrix C of the index returns of the main financial markets after the 2008 crisis using methods of random matrix theory. We test the eigenvalues of C for universal properties of random matrices and find that the majority of the cross-correlation coefficients arise from randomness. We show that the eigenvector of the largest deviating eigenvalue of C represents a global market itself. We reveal that high volatility of financial markets is observed at the same times with high correlations between them which lowers the risk diversification potential even if one constructs a widely internationally diversified portfolio of stocks. We identify and compare the connection and cluster structure of markets before and after the crisis using minimal spanning and ultrametric hierarchical trees. We find that after the crisis, the co-movement degree of the markets increases. We also highlight the key financial markets of pre and post crisis using main centrality measures and analyze the changes. We repeat the study using rank correlation and compare the differences. Further implications are discussed.     

Random matrix theory analysis of cross-correlations in the US stock market: Evidence from Pearson’s correlation coefficient and detrended cross-correlation coefficient

In this study, we first build two empirical cross-correlation matrices in the US stock market by two different methods, namely the Pearson’s correlation coefficient and the detrended cross-correlation coefficient (DCCA coefficient). Then, combining the two matrices with the method of random matrix theory (RMT), we mainly investigate the statistical properties of cross-correlations in the US stock market. We choose the daily closing prices of 462 constituent stocks of S&P 500 index as the research objects and select the sample data from January 3, 2005 to August 31, 2012. In the empirical analysis, we examine the statistical properties of cross-correlation coefficients, the distribution of eigenvalues, the distribution of eigenvector components, and the inverse participation ratio. From the two methods, we find some new results of the cross-correlations in the US stock market in our study, which are different from the conclusions reached by previous studies. The empirical cross-correlation matrices constructed by the DCCA coefficient show several interesting properties at different time scales in the US stock market, which are useful to the risk management and optimal portfolio selection, especially to the diversity of the asset portfolio. It will be an interesting and meaningful work to find the theoretical eigenvalue distribution of a completely random matrix R for the DCCA coefficient because it does not obey the Mar?enko–Pastur distribution.     

Blockchain Technology,Cryptocurrency: Entropy-Based Perspective

The large-scale application of blockchain technology is an expected to be an inevitable trend. This study revolves around published papers and articles related to blockchain technology, relevance analysis and sorting through the retrieved documents with six core layers of blockchain: Application Layer, Contract Layer, Actuator Layer, Consensus Layer, Network Layer and Data Layer. Based on the analysis results, this study found that China’s research is more towards the preference and application of landing and industry and smart cities with blockchain as the underlying technology. International research is more focused on the research of finance as the underlying technology of blockchain and tries to combine crypto assets with real industries, such as crypted assets and payment systems for traditional industries. This paper studies the impact of monetary entropy on cryptocurrencies in smart cities and uses the monetary entropy formula to measure the crypto-economic entropy. We use Kolmogorov entropy to describe the degree of chaos in the cryptocurrency market in a smart city. The study illustrates the current status of blockchain technology and applications from the perspective of cryptocurrency in a smart city. We find that smart cities and cryptocurrencies have a mutually reinforcing effect.     

Correlations in commodity markets

In this paper we analyzed dependencies in commodity markets, investigating correlations of future contracts for commodities over the period 1998.09.01-2007.12.14. We constructed a minimal spanning tree based on the correlation matrix. The tree provides evidence for sector clusterization of investigated contracts. We also studied dynamical properties of commodity dependencies. It turned out that the market was constantly getting more correlated within the investigated period, although the increase of correlation was distributed non-uniformly among all contracts, and depended on contracts branches.     

Multifractal detrended cross-correlations between the Chinese exchange market and stock market

Based on the daily price data of the Chinese Yuan (RMB)/US dollar exchange rate and the Shanghai Stock Composite Index, we conducted an empirical analysis of the cross-correlations between the Chinese exchange market and stock market using the multifractal cross-correlation analysis method. The results demonstrate the overall significance of the cross-correlation based on the analysis of a statistic. Multifractality exists in cross-correlations, and the cross-correlated behavior of small fluctuations is more persistent than that of large fluctuations. Moreover, using the rolling windows method, we find that the cross-correlations between the Chinese exchange market and stock market vary with time and are especially sensitive to the reform of the RMB exchange rate regime. The previous reduction in the flexibility of the RMB exchange rate in July 2008 strengthened the persistence of cross-correlations and decreased the degree of multifractality, whereas the enhancement of the flexibility of the RMB exchange rate in June 2010 weakened the persistence of cross-correlations and increased the multifractality. Finally, several relevant discussions are provided to verify the robustness of our empirical analysis.     

Study of cross-correlation in a self-affine time series of taxi accidents

We study in this paper the cross-correlation between self-affine time series of real variables recorded simultaneously in cases of taxi accidents. For this purpose, we apply the DCCA method and show that the cross-correlation can be divided into three distinct groups, if we look for the detrended covariance function, i.e., long-range cross-correlations, short-range cross-correlations and no cross-correlations. Finally, it will be seen that the detrended covariance function is robust, if compared with other methods, in identifying these types of cross-correlations.     

An ever-closer union? Examining the evolution of linkages of European equity markets via minimum spanning trees

The concept of a minimum spanning tree (MST) is used to study the process of comovements for 21 European Union stock market indices. We show how the minimum spanning tree and its related hierarchical tree evolve over time and describe the dynamics. Over the period studied, 1999-2006, the French equity market provides the main linkages in the system. The 2004 Accession states are more loosely connected to the other markets; they form two groupings, with the Czech Republic, Hungary, and Poland having tighter links to the main markets than the remaining Accession markets. Shorter distances between markets indicate a potential reduction of the benefits of international portfolio diversification in European markets, with the possible exception of those markets at the outer limits of the MST.