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.     

Crossover Phenomena in Detrended Fluctuation Analysis Used in Financial Markets

A systematic analysis of Shanghai and Japan stock indices for the period of Jan. 1984 to Dec. 2005 is performed. After stationarity is verified by ADF （Augmented Dickey-Fuller） test, the power spectrum of the data exhibits a power law decay as a whole characterized by 1/f^β processes with possible long range correlations. Subsequently, by using the method of detrended fluctuation analysis （DFA） of the general volatility in the stock markets, we find that the long-range correlations are occurred among the return series and the crossover phenomena exhibit in the results obviously.Further, Shanghai stock market shows long-range correlations in short time scale and shows short-range correlations in long time scale. Whereas, for Japan stock market, the data behaves oppositely absolutely. Last, we compare the varying of scale exponent in large volatility between two stock markets. All results obtained may indicate the possibility of characteristic of multifractal scaling behavior of the 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.     

Detrended cross-correlation analysis of electroencephalogram

In the paper we use detrended cross-correlation analysis (DCCA) to study the electroencephalograms of healthy young subjects and healthy old subjects. It is found that the cross-correlation between different leads of a healthy young subject is larger than that of a healthy old subject. It was shown that the cross-correlation relationship decreases with the aging process and the phenomenon can help to diagnose whether the subject's brain function is healthy or not.     

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.     

Cross-correlations between West Texas Intermediate crude oil and the stock markets of the BRIC

In this paper, we investigate the cross-correlation properties between West Texas Intermediate crude oil and the stock markets of the BRIC. We use not only the qualitative analysis of the cross-correlation test, but also take the quantitative analysis of the MF-DXA, confirming the cross-correlation relationship between West Texas Intermediate crude oil and the stock markets of the BRIC (Brazil, Russia, India and China) respectively, which have strongly multifractal features, and the cross-correlations are more strongly multifractal in the short term than in the long term. Furthermore, based on the multifractal spectrum, we also find the multifractality strength between the crude oil WTI and Chinese stock market is stronger than the multifractality strength of other pairs. Based on the Iraq war (Mar 20, 2003) and the Financial crisis in 2008, we divide sample period into four segments to research the degree of the multifractal (ΔH$\Delta H$) and the market efficiency (and the risk). Finally, we employ the technique of the rolling window to calculate the time-varying EI  (efficiency index) and dependent on the EI  , we can easily observe the change of stock markets. Furthermore, we explore the relationship between bivariate cross-correlation exponents (_Hxy(q)$H_{xy}\left(q\right)$) and the generalized Hurst exponents.     

Auto-correlated behavior of WTI crude oil volatilities: A multiscale perspective

In this paper, we investigate the long-range auto-correlated behavior of WTI crude oil volatility series employing multifractal detrended fluctuation analysis. Our findings show that the for small time scales, the auto-correlations of volatilities were multifractal while for large time scales, the auto-correlations were nearly monofractal. Based on multiscale analysis, we also investigate the dynamics of auto-correlations for different intervals of time scales and find that several shocks could make significant effects on the auto-correlated behaviors for small time scales. Analyzing the dynamics of multifractality degrees of auto-correlations for small time scales, we find that the stronger auto-correlations were always related to the lower degrees of multifractality. At last, we have discussions on the determination factors of price behavior, the predictive implications of scaling behavior in volatilities for oil markets and the reasons why long-range auto-correlations of volatility were always strong for both small time scales and large time scales. Our results are very important theoretically and practically.     

基于双树复小波变换的非平稳时间序列去趋势波动分析方法

多重分形去趋势波动分析是研究非平稳时间序列非均匀性和奇异性的有效工具, 针对该方法中趋势项难以确定的问题, 提出一种基于双树复小波变换的方法, 实现了非平稳信号的多重分形自适应去趋势波动分析. 利用双树复小波变换提取信号的多尺度趋势和波动信息, 通过小波系数的希尔伯特变换确定每个时间尺度不重叠子区间的长度, 使多重分形分析具有信号自适应性及较高的计算效率. 以具有解析形式分形特征的倍增级联信号和分数布朗运动时间序列为例验证本文方法的有效性, 所得结果与解析解相吻合. 与传统的多项式去趋势多重分形方法相比, 本文方法根据信号自身特点自适应地确定信号的趋势和不重叠等长度子区间长度, 所得结果更加精确. 对倍增级联信号时间序列取不同的长度, 验证了算法的稳定性. 分别与基于极大重叠离散小波变换和离散小波变换多重分形方法进行比较, 表明本文方法具有更精确的结果和更快的运算速度.     

Multifractal Detrended Fluctuation Analysis of Interevent Time Series in a Modified OFC Model

We use multifractal detrended fluctuation analysis(MF-DFA) method to investigate the multifractal behavior of the interevent time series in a modified Olami-Feder-Christensen(OFC) earthquake model on assortative scale-free networks.We determine generalized Hurst exponent and singularity spectrum and find that these fluctuations have multifractal nature.Comparing the MF-DFA results for the original interevent time series with those for shuffled and surrogate series,we conclude that the origin of multifractality is due to both the broadness of probability density function and long-range correlation.     

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.     

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.     

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.     

Interest rates factor model

Interdependence of the interest rates of the US, the UK, and Japan is analyzed in this work by means of spectral analysis and network methods. A predominant effective factor in the interest rate market is which country floats a bond issue, and a minor effective factor is time to maturity of bonds. Power-law cross-correlation among different countries is analyzed by the detrended cross-correlation analysis method. Long-range cross-correlation is found between the first factors of interest rate, while there is no cross-correlation between some of the second factors. The tail dependency is indicated by tail indices from Archimedean copulas, including an empirical copula. In contrast to other pairs, the US-UK first factor pair has tail dependencies in both the upper-tail and lower-tail. Dynamic properties of interest rate are modeled by a stochastic volatility model. The properties of mean reverting and volatility clustering are observed and reflected in this model. The proposed simulation method combines the dependence structures and the factor dynamics model; it simultaneously describes the interest rates of different countries.     

Cryptocurrency Market Consolidation in 2020–2021

Time series of price returns for 80 of the most liquid cryptocurrencies listed on Binance are investigated for the presence of detrended cross-correlations. A spectral analysis of the detrended correlation matrix and a topological analysis of the minimal spanning trees calculated based on this matrix are applied for different positions of a moving window. The cryptocurrencies become more strongly cross-correlated among themselves than they used to be before. The average cross-correlations increase with time on a specific time scale in a way that resembles the Epps effect amplification when going from past to present. The minimal spanning trees also change their topology and, for the short time scales, they become more centralized with increasing maximum node degrees, while for the long time scales they become more distributed, but also more correlated at the same time. Apart from the inter-market dependencies, the detrended cross-correlations between the cryptocurrency market and some traditional markets, like the stock markets, commodity markets, and Forex, are also analyzed. The cryptocurrency market shows higher levels of cross-correlations with the other markets during the same turbulent periods, in which it is strongly cross-correlated itself.     

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.     

Regime switching dynamics in credit default swaps: Evidence from smooth transition autoregressive model

This paper investigates the dynamics of credit default swap (CDS) spread. We first find auto-correlations and cross-correlations of the CDS series and the CDS average by employing detrended cross-correlation analysis (DCCA). We then employ smooth transition autoregressive (STAR) models to characterize the regime switching behavior of 28 US corporate CDS series from January 2007 through October 2009. In each case, we find clear evidence for transitions between low-price and high-price regimes. The threshold estimations of the STAR model effectively differentiate the price regimes, where the first transition consistently coincides with the explosion of the crisis in late 2008.     

Is the efficiency of stock market correlated with multifractality? An evidence from the Shanghai stock market

In this paper, we propose an efficiency index and multifractality degree for financial markets, and investigate the dynamics of the relationship between the two indices for the Shanghai stock market employing the technique of rolling window. By using the DCCA cross-correlation coefficient, we find that, for the Shanghai stock market, the increase in the degree of market multifractality can lead to a lower degree of market efficiency before the equity division reforms, whereas it can result in a lower degree of market efficiency in the short-term and a higher degree of market efficiency in the long-term after the equity division reforms. This finding reflects the process of development of the Shanghai stock market and also provides strong evidence which supports Liu’s argument that the increase in the degree of market complexity can improve the market efficiency Liu (2009) [1].     

Detecting characteristics of information masked by a laser-triggered microwave system via Hilbert-Huang transform

A two-wave-mixing microwave system under a delayed feedback control is proposed for chaotic communications in this study. Under the consideration of simple chaotic masking, Hilbert-Huang transform is proved to be an efficient way to detect characteristics of information signals via the spectrum of intrinsic mode functions. Based upon detrended fluctuation as well as multiscale entropy analyses on masking efficiency in the present system, we may suggest that Hilbert-Huang transform would be an alternative method to analyze complex dressed signals from nonlinear optoelectronic systems.     

A New Look at Calendar Anomalies: Multifractality and Day-of-the-Week Effect

Stock markets can become inefficient due to calendar anomalies known as the day-of-the-week effect. Calendar anomalies are well known in the financial literature, but the phenomena remain to be explored in econophysics. This paper uses multifractal analysis to evaluate if the temporal dynamics of market returns also exhibit calendar anomalies such as day-of-the-week effects. We apply multifractal detrended fluctuation analysis (MF-DFA) to the daily returns of market indices worldwide for each day of the week. Our results indicate that distinct multifractal properties characterize individual days of the week. Monday returns tend to exhibit more persistent behavior and richer multifractal structures than other day-resolved returns. Shuffling the series reveals that multifractality arises from a broad probability density function and long-term correlations. The time-dependent multifractal analysis shows that the Monday returns’ multifractal spectra are much wider than those of other days. This behavior is especially persistent during financial crises. The presence of day-of-the-week effects in multifractal dynamics of market returns motivates further research on calendar anomalies for distinct market regimes.     

Temporal variations of serial correlations of trading volume in the US stock market

Serial correlations in the trading volume of the US stock market are investigated in this paper. The use of the detrended fluctuation analysis implemented within a rolling window indicated that, for the period 1929–2011, the strength of correlations exhibits important temporal variations with a trend shift by the 1990s, and 4-year and 21-year cycles. These empirical findings are compared to those obtained for mature international stock markets (FTSE-100 and Nikkei) and discussed in terms of potential economic and financial implications.