Cross-correlation Exponents Research Articles

ASYMMETRIC MULTIFRACTAL CROSS-CORRELATION DYNAMICS BETWEEN FIAT CURRENCIES AND CRYPTOCURRENCIES

This paper performs the asymmetric multifractal cross-correlation analysis to examine the COVID-19 effects on three relevant high-frequency fiat currencies, namely euro (EUR), yen (YEN) and the Great Britain pound (GBP), and two cryptocurrencies with the highest market capitalization and traded volume (Bitcoin and Ethereum) considering two periods (Pre-COVID-19 and during COVID-19). For both periods, we find that all pairs of these financial assets are characterized by overall persistent cross-correlation behavior [Formula: see text]. Moreover, COVID-19 promoted an increase in the multifractal spectrum’s width, which implies an increase in the complexity for all pairs considered here. We also studied the Generalized Cross-correlation Exponent, which allows us to verify that there is no asymmetric behavior between Bitcoin and fiat currencies and between Ethereum and fiat currencies. We conclude that investing simultaneously in major fiat currencies and leading cryptocurrencies can reduce the portfolio risk, leading to improvement in the investment results.

TIME-DELAY MULTISCALE MULTIFRACTAL DETRENDED PARTIAL CROSS-CORRELATION ANALYSIS OF HIGH-FREQUENCY STOCK SERIES

To study the time-delay multiscale partial cross-correlation between the high-frequency stock series SSEC and SZSE in the Chinese stock market, this paper proposes a new partial cross-correlation exponent, namely the [Formula: see text]-order time-delay multiscale partial cross-correlation exponent (denoted by [Formula: see text]). We integrate the time-delay factor and the multiscale range fluctuation function into partial cross-correlation analysis. Numerical experiments show that the newly proposed exponent [Formula: see text] can be used to detect the partial cross-correlation of two time series with time delay. After excluding the influence of other stock indexes, we found that the persistence and multifractal characteristics between SSEC and SZSE have become stronger. Among them, the American high-frequency stock series has a greater impact on the two Chinese stocks than the Asian high-frequency stock series. Comparing the methods of time-delay multiscale multifractal detrended partial cross-correlation analysis method (time-delay MM-DPXA) and time-delay multiscale multifractal detrended cross-correlation analysis method (time-delay MM-DCCA), we find that cross-correlation and partial cross-correlation have different properties on different time scales and different time delays.

Extended Methodology for DFA and DCCA: Application of Automatic Search Procedure and Correlation Map to the Weierstrass-Mandelbrot Functions.

Detrended fluctuation analysis and detrended cross-correlation analysis are used in this study to identify and characterize correlated data. The objective of these two techniques is to separate different fluctuations from the contributions due to external trends by evaluating the autocorrelation and cross-correlation exponents, in order to determine if scale properties persist with the size of the series. Two new methodologies were extended from cross-correlation coefficients for local analysis, which we call the \textit{automatic search procedure.

Chaos based novel non-invasive approach to assess intracranial pressure in the brain using ECG and arterial BP data

The study explores the applicability of a multifractal cross-correlated method to assess the degree of correlation of intracranial pressure (ICP) signals with ECG and ABP in traumatic brain injury (TBI) patients. Multifractal width (w) and cross-correlation exponent (γx ) estimated using multifractal detrended cross-correlation (MFDXA) method describe interesting features about the complexity of ICP signals of traumatic brain injury (TBI) patients. The degree of multifractality (w) of ECG signals reveal that even without going into complicated ICP signal measurement which is not only invasive but costly procedure, the trauma suffered due to brain injury can easily be assessed. With the help of two quantitative parameters w and γx appropriate software can easily be developed and coupled with ECG system.

Exploring the dynamic relationship between crude oil price and implied volatility indices: A MF-DCCA approach

This paper investigates the cross-correlation between crude oil prices and implied volatility indices — theinvestor’s fear gauges, using a cross-correlation statistical test and multifractal detrended cross-correlation analysis (MF-DCCA). The results show that the cross-correlations between crude oil prices and three different implied volatility indices are multifractal. By finding the “crossover”, we separate the three pairs of series into the short- and long-term, respectively, and find that the cross-correlations are strongly anti-persistent in both short- and long-term. Moreover, cross-correlations of small and large fluctuations are anti-persistent in the short- and long-term, suggesting that crude oil prices and implied volatility indices are susceptible to each other. We also find that the cross-correlation exponents are less than the average generalized Hurst exponent when q<0 and more than the average generalized Hurst exponent when q>0 in the short-term and that the opposite results are true in the long-term.

Gene Expression Is Not Random: Scaling, Long-Range Cross-Dependence, and Fractal Characteristics of Gene Regulatory Networks.

Gene expression is a vital process through which cells react to the environment and express functional behavior. Understanding the dynamics of gene expression could prove crucial in unraveling the physical complexities involved in this process. Specifically, understanding the coherent complex structure of transcriptional dynamics is the goal of numerous computational studies aiming to study and finally control cellular processes. Here, we report the scaling properties of gene expression time series in Escherichia coli and Saccharomyces cerevisiae. Unlike previous studies, which report the fractal and long-range dependency of DNA structure, we investigate the individual gene expression dynamics as well as the cross-dependency between them in the context of gene regulatory network. Our results demonstrate that the gene expression time series display fractal and long-range dependence characteristics. In addition, the dynamics between genes and linked transcription factors in gene regulatory networks are also fractal and long-range cross-correlated. The cross-correlation exponents in gene regulatory networks are not unique. The distribution of the cross-correlation exponents of gene regulatory networks for several types of cells can be interpreted as a measure of the complexity of their functional behavior.

Does Bitcoin exhibit the same asymmetric multifractal cross-correlations with crude oil, gold and DJIA as the Euro, Great British Pound and Yen?

We applied MF-ADCCA to analyze the presence and asymmetry of the cross-correlations between the major currency rates and Bitcoin, and the Dow Jones Industrial Average (DJIA), gold price and the oil crude market. We find that multifractality exists in every cross-correlation studied, and there is asymmetry in the cross-correlation exponents under different trend of the WTI, Gold and DJIA. Bitcoin shows a greater multifractal spectra than the other currencies on its cross-correlation with the WTI, the Gold and the DJIA. Bitcoin shows a clearly different relationship with commodities and stock market indices which has to be taken into consideration when investing. This has to do with the years this currency has been traded, the characteristics of cryptocurrencies and its gradual adoption by financial organizations, governments and the general public.

Asymmetric multifractal cross-correlations and time varying features between Latin-American stock market indices and crude oil market

We apply MF-ADCCA to analyze the presence and asymmetry of the cross-correlations between Latin-American and US stock market indices and crude oil market. We find that multifractality exists in this cross-correlations, and that there is asymmetry on its behavior. The asymmetry degree changes accordingly to the series considered for the trend behavior. We find that fluctuation sizes greatly influence the asymmetry in the cross-correlation exponent, increasing for large fluctuations when we consider the trend of the crude oil price. We also find no clear differences in the exponents with different scales under different trends of the WTI, contrary to other studies in asymmetric scaling behavior. When we examine the time varying features of the asymmetry degree we find that the US indices show a consistent behavior in time for both trends, where the cross-correlation exponents tend to be larger for downward trends. On the other hand, given the more heterogeneous individual properties of Latin-American indices, the asymmetry behavior varies more depending on the trend considered.

Assessment of 48 Stock markets using adaptive multifractal approach

In this paper, Stock market comovements are examined using cointegration, Granger causality tests and nonlinear approaches in context of mutual information and correlations. Since underlying data sets are affected by non-stationarities and trends, we also apply Adaptive Multifractal Detrended Fluctuation Analysis (AMF-DFA) and Adaptive Multifractal Detrended Cross-Correlation Analysis (AMF-DXA). We find only 170 pair of Stock markets cointegrated, and according to the Granger causality and mutual information, we realize that the strongest relations lies between emerging markets, and between emerging and frontier markets. According to scaling exponent given by AMF-DFA, h(q=2)>1, we find that all underlying data sets belong to non-stationary process. According to Efficient Market Hypothesis (EMH), only 8 markets are classified in uncorrelated processes at 2σ confidence interval. 6 Stock markets belong to anti-correlated class and dominant part of markets has memory in corresponding daily index prices during January 1995 to February 2014. New-Zealand with H=0.457±0.004 and Jordan with H=0.602±0.006 are far from EMH. The nature of cross-correlation exponents based on AMF-DXA is almost multifractal for all pair of Stock markets. The empirical relation, Hxy≤[Hxx+Hyy]∕2, is confirmed. Mentioned relation for q>0 is also satisfied while for q<0 there is a deviation from this relation confirming behavior of markets for small fluctuations is affected by contribution of major pair. For larger fluctuations, the cross-correlation contains information from both local (internal) and global (external) conditions. Width of singularity spectrum for auto-correlation and cross-correlation are Δαxx∈[0.304,0.905] and Δαxy∈[0.246,1.178], respectively. The wide range of singularity spectrum for cross-correlation confirms that the bilateral relation between Stock markets is more complex. The value of σDCCA indicates that all pairs of stock market studied in this time interval belong to cross-correlated processes.

Dynamic relationship between Japanese Yen exchange rates and market anxiety: A new perspective based on MF-DCCA

This paper investigates the dynamic relationship between Japanese Yen exchange rates and market anxiety during the period from January 5, 1998 to April 18, 2016. A quantitative technique of multifractal detrended cross-correlation analysis (MF-DCCA) is used to explore the multifractal features of the cross-correlations between USD/JPY, AUD/JPY exchange rates and the market anxiety gauge VIX. The investigation shows that the causal relationship between Japanese Yen exchange rates and VIX are bidirectional in general, and the cross-correlations between the two sets of time series are multifractal. Strong evidence suggests that the cross-correlation exponents tend to exhibit different volatility patterns in response to diverse external shocks such as financial distress and widening in interest rate spread, suggesting that the cross-correlated behavior between Japanese Yen exchange rates and VIX are susceptible to economic uncertainties and risks. In addition, the performances of two market anxiety gauges, the VIX and the TED spread, are compared and the sources of multifractality are also traced. Thus, this paper contributes to the literature by shedding light on the unique driving forces of the Yen exchange rate fluctuations in the international foreign exchange market.

Examining the efficiency and interdependence of US credit and stock markets through MF-DFA and MF-DXA approaches

This study examines the power law properties of 11 US credit and stock markets at the industry level. We use multifractal detrended fluctuation analysis (MF-DFA) and multifractal detrended cross-correlation analysis (MF-DXA) to first investigate the relative efficiency of credit and stock markets and then evaluate the mutual interdependence between CDS-equity market pairs. The scaling exponents of the MF-DFA approach suggest that CDS markets are relatively more inefficient than their equity counterparts. However, Banks and Financial credit markets are relatively more efficient. Basic Materials (both CDS and equity indices) is the most inefficient sector of the US economy. The cross-correlation exponents obtained through MF-DXA also suggest that the relationship of the CDS and equity sectors within and across markets is multifractal for all pairs. Within the CDS market, Basic Materials is the most dependent sector, whereas equity market sectors can be divided into two distinct groups based on interdependence. The pair-wise dependence between Basic Materials sector CDSs and the equity index is also the highest. The degree of cross-correlation shows that the sectoral pairs of CDS and equity markets belong to a persistent cross-correlated series within selected time intervals.

Multifractal Detrended Cross-Correlation Analysis of Geochemical Element Concentration

We use multifractal detrended cross -fluctuation analysis (MF-DXA) to investigate nonlinear behavior of geochemical element concentration, Au-Cu-Pb-Zn-Ag, in Shangzhuang Deposit, Shandong Province, China. We find that the generalized Hurst exponent h(q) and cross-correlation exponent hxy(q) decrease with the increase of q, which indicate that all element concentration series and their cross pairs exhibit multifractal phenomena. By comparing the variability of h(q) and hxy(q), we have found that the multifractal behavior is more obvious when q &gt; 0 than q &lt; 0 for the element Au- Cu-Pb-Zn and their cross pairs. These analyses, given quantitative information about the complexity of the element concentration, lead to a better understanding of the geochemical phenomena underlying mineralization process.

Multifractal detrended cross-correlation analysis on gold, crude oil and foreign exchange rate time series

We apply the recently developed multifractal detrended cross-correlation analysis method to investigate the cross-correlation behavior and fractal nature between two non-stationary time series. We analyze the daily return price of gold, West Texas Intermediate and Brent crude oil, foreign exchange rate data, over a period of 18 years. The cross correlation has been measured from the Hurst scaling exponents and the singularity spectrum quantitatively. From the results, the existence of multifractal cross-correlation between all of these time series is found. We also found that the cross correlation between gold and oil prices possess uncorrelated behavior and the remaining bivariate time series possess persistent behavior. It was observed for five bivariate series that the cross-correlation exponents are less than the calculated average generalized Hurst exponents (GHE) for q<0 and greater than GHE when q>0 and for one bivariate series the cross-correlation exponent is greater than GHE for all q values.

Multifractal detrended cross-correlation analysis of the oil-dependent economies: Evidence from the West Texas intermediate crude oil and the GCC stock markets

In this paper, we firstly investigate the cross-correlations between the crude oil market and the six GCC stock markets. Based on the analysis of the significant statistic Qcc(m) and the cross-correlation coefficient, we find that the cross-correlations between the crude oil market and the six GCC stock markets are all significant. Employing the method of the MF-DFA and MF-DXA, we further find that the auto-correlations of the crude oil market and the six GCC stock markets and cross-correlations between them are all the multifractality. Moreover, using the multifractal spectrum, we can also verify the multifractal characteristics between the crude oil market and the six GCC stock markets. Furthermore, we use the penalized contrast function to detect the structural break points of the WTI-Oil return series and its conditional volatility, and then discuss the cross-correlations between the crude oil and the six GCC stock markets in the different phases according to these break points. At last, we employ the technique of the rolling window to investigate the dynamic of the scaling exponent Hxy(q). In addition, we explore the relationship between the cross-correlation exponents Hxy(q) and the average scaling exponents [Hxx(q)+Hyy(q)]/2].

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) 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)) and the generalized Hurst exponents.

Cross-correlations between the CSI 300 spot and futures markets

Financial markets are complex dynamical systems. One of the important features of market dynamics is the existence of cross-correlations between financial variables. Based on the high-frequency transaction prices (every 5 min) data, in this study, we investigate the cross-correlations between China Securities Index 300 (CSI 300) spot and futures markets. Qualitatively, employing a statistical test in analogy to the Ljung-Box test, we find that the cross-correlations are significant at the 1 % level. Quantitatively, using the multifractal detrending moving-average cross-correlation analysis (MF-XDMA) method, we find that the cross-correlations are strongly multifractal. An interesting finding is that the cross-correlation exponent is larger than the averaged generalized scaling exponent for different q, which is different from the general conclusion. Using the method of rolling windows, we find that the cross-correlations are positive over time, which suggests that China’s securities markets are not mature and efficient markets at present.

Using Detrended Cross-Correlation Analysis in geophysical data

Detrended cross correlation analysis (DCCA) is used to identify and characterize correlated data obtained in drilled oil wells. The investigation is focused on different petro-physical measurements within the same well, and of the same measurement from two wells in the same oil field. The evaluation of cross correlation exponents indicates if scaling properties in two measurements are alike. The work considers also the values of cross correlated coefficients, which provide an assessment on the local correlation between measurements. The existence of several highly correlated events provides information on the continuity of geological structures, including partial and global dislocations of deposited layers.

DCCA cross-correlation coefficient differentiation: Theoretical and practical approaches

Abstract We propose in this paper to establish a well-defined relationship between α D F A (the long range auto-correlation exponent) and λ D C C A (the long range cross-correlation exponent), respectively described by the DFA and DCCA methods. This relationship will be accomplished theoretically by differentiating the DCCA cross-correlation coefficient, ρ D C C A ( n ) . Also, for some specific times series, we apply this theory in order to establish its validity.

Multifractal detrended cross-correlation analysis for power markets

Multifractal theory has been widely used in kinds of field. In this paper, methods were proposed to study in the power-law auto-correlation and cross-correlation of power operating data based on multifractal detrended analysis (MF-DFA) and multifractal detrended cross-correlation analysis (MF-DXA). We find that both the price and the load time series in California power market and PJM power market exhibit long-term correlation. And the cross-correlation behaviors of the two series in each power market and between the two markets are also analyzed by the method MF-DXA after testing the existence of the cross-correlation of the above power operating data. However, there are some differences in the cross-correlation behaviors between the two markets. It shows that the cross-correlation of the price and the load is significant in every time periods in California 1999 power market, but in the year of 2000 in the same region market, the cross-correlation is insignificant in most time periods. Meanwhile, we conclude that cross-correlation is weaker in the California market than in the PJM market by studying the two consecutive years of the California 1999–2000 and PJM 2001–2002 power markets. We also discuss how the time intervals affect the cross-correlation exponents of the power operating data based on time-delay MF-DXA. An interesting finding is that the biggest cross-correlation exponent of the two series appeared in about 12 days time delay for the PJM 2001 power market and strongest cross-correlation in the California 1999 power market is found in lots of cyclical time intervals.

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 and more than the averaged generalized Hurst exponent when q>0 in the short term, while in the long term they are almost the same.