Detrended Cross-correlation Analysis Research Articles

Analysis of the human gait rhythm in Neurodegenerative disease: A multifractal approach using Multifractal detrended cross correlation analysis

In this paper the human gait rhythm of the healthy individuals and the patients suffering from a neurological disorder, Amyotrophic lateral sclerosis (ALS) disease has been studied applying a non-linear technique, Multifractal detrended cross correlation analysis (MF-DXA). The autocorrelation and cross correlation of the stride-interval fluctuations between the left foot and the right foot were studied. The results obtained reflect the fact that the degree of multifractality (W) and the degree of correlation (γ) are greater for the Control group compared to the diseased group. It is evident that the gait pattern of an individual becomes less steady and temporarily more disorganized in neural diseases due to the neuronal deterioration. The results obtained from the autocorrelation study for the left and the right foot are almost identical. It was also observed that the study of the autocorrelation is not always enough to distinguish between the Controlled and the diseased group. The study of the cross correlation between the left and the right foot can then help to recognize the diseased group. The present analysis shows that the cross correlation between the stride-interval fluctuations between the left and the right foot was greater for the healthy individuals compared to the patients with neurodegenerative disease.

Dynamical behavior of combined detrended cross-correlation analysis methods in random walks and Lévy flights

In this paper, the utility and the correlation technique of the detrended cross-correlation analysis and the combined detrended cross-correlation analysis methods are treated for the stochastic properties of the random walk and the Lévy flight via nucleotide sequence data. Data are extracted definitely from twelve genomic DNA sequences (HUMHBB 1-6, Amazonmolly, Bushbaby, Cow, Dolphin, Elephant, and Tarsier) of the GenBank databank. We mainly simulate and analyze scaling exponents for three methods in 1D and 2D random walks and Lévy flights. To compare each other between one gene and the other gene in the twelve genomic DNA sequences, the value of the detrended cross-correlation coefficient ρDCCA in {HUMHBB3} and {Dolphin} genes is shown the largest value 0.214 in the 1D Lévy flight with μ=1.5 compared to other sets. The detrended cross-correlation coefficient ρDCCA in {HUMHBB4} and {HUMHBB6} genes is shown the smallest value -0.231 in the 1D Lévy flight with μ=1.5. We particularly find that the combined detrended cross-correlation coefficient ρCDCCA in the two cases of {HUMHBB3}+{Bushbaby} and {HUMHBB6}+{Dolphin} has the largest value 0.331 in the 1D random walk compared to other sets, while that in {HUMHBB3}+{Tarsier} and {HUMHBB4}+{Elephant} has the smallest value -0.295 in the 1D Lévy flight with μ=1.5.

Financial stability and real estate price fluctuation in China

The relationship between financial stability and the real estate market has received increasing attention. Understanding the interaction between them may monitor financial risk and real estate price fluctuation. This paper aims at examining the cross-correlation between financial stability and real estate price fluctuation in China. A measure of financial stability is constructed and the cross-correlation between financial stability and the real estate market is demonstrated by using detrended cross-correlation analysis (DCCA). Furthermore, multifractal asymmetric detrended cross-correlation analysis (MF-ADCCA) is used to evaluate the scaling properties of the cross-correlation among financial stability and real estate price fluctuation. Empirical results indicate that asymmetries exist in the cross-correlation and that the asymmetric cross-correlation is multifractal. The cross-correlation is related to the fluctuation magnitude if the financial stress index (or the growth rate in house prices) is in a different trend. Finally, DCCA analysis based on time-delay is employed to investigate transmission direction of the cross-correlation. Our findings indicate the transmission direction is bidirectional, but the impact of financial stability on real estate price fluctuation is larger than the impact in the reverse direction.

Asymmetric MF-DCCA Method Based on Fluctuation Conduction and its Application in Air Pollution in Hangzhou

The study of the relationship between the concentration of PM2.5 and the local air quality index (AQI) is significant for the improvement of urban air quality. This study not only considered multifractal cross-correlation but also the fluctuation conduction mechanism. An asymmetric multifractal detrended cross-correlation analysis (MF-DCCA) method based on fluctuation conduction is introduced here to empirically explore the causality and conduction time between air quality factors and PM2.5 concentration. The empirical results indicate the existence of a bidirectional fluctuation conduction effect between PM2.5 and PM10, SO2, and NO2 in Hangzhou, China, with a conduction time of 30 hours; this effect is non-existent between PM2.5 and O3. In addition, there is a unidirectional fractal fluctuation conduction between PM2.5 and CO with a conduction time of 21 hours.

Long-Range Behaviour and Correlation in DFA and DCCA Analysis of Cryptocurrencies

In recent years, increasing attention has been devoted to cryptocurrencies, owing to their great development and valorization. In this study, we propose to analyse four of the major cryptocurrencies, based on their market capitalization and data availability: Bitcoin, Ethereum, Ripple, and Litecoin. We apply detrended fluctuation analysis (the regular one and with a sliding windows approach) and detrended cross-correlation analysis and the respective correlation coefficient. We find that Bitcoin and Ripple seem to behave as efficient financial assets, while Ethereum and Litecoin present some evidence of persistence. When correlating Bitcoin with the other cryptocurrencies under analysis, we find that for short time scales, all the cryptocurrencies have statistically significant correlations with Bitcoin, although Ripple has the highest correlations. For higher time scales, Ripple is the only cryptocurrency with significant correlation.

Multifractal detrended cross-correlation analysis of the relation between price and volume in European carbon futures markets

Recently, with the development of European carbon futures markets, the complex dynamic relationship between price and volume has become the focus of energy research area. In our research, we applied multifractal detrended cross-correlation analysis method (MF-DCCA) to investigate the cross-correlation and multifractality between price and volume in European carbon futures markets. Firstly, the analysis of basic statistics show that the European carbon futures market has obvious non-normal, peak-heavy-tailed distribution, which does not satisfy the normal distribution hypothesis in the efficient market. Secondly, through multifractal detrended cross-correlation analysis, we conclude that trading price and volume relationship in European carbon futures markets has a non-linear dependence. Thirdly, we find the existence of power-law cross-correlations between price and volume in European carbon futures markets. Finally, the relationship between price and volume is non-linear. After random rearrangement and phase treatment of correlation coefficients, the long-range correlation of small fluctuations and large fluctuations and the fat tail distribution of series are the reasons for the formation of multifractality.

Multiscale optimal portfolios using CAPM fractal regression: estimation for emerging stock markets

ABSTRACTBased on the mean-variance portfolio model and on the capital asset pricing model, we propose the construction of multiscale optimal portfolios, for four emerging stock markets: China, the Czech Republic, Hungary and Russia. We compare the results with the German market, in order to understand possible differences. We use fractal regressions based on detrended cross-correlation analysis, allowing us to study portfolios for different time scales. This feature helps us to identify whether investors are homogeneous or heterogeneous in their expectations and if they have common or different investment horizons. Results show that for most shares, a unique CAPM parameter explains asset pricing well. However, for some shares, behaviour is different between short and long run scales, consistent with the fractal market hypothesis. Moreover, Chinese and Czech markets are closer to what happens in the German market, while Russian and Hungarian investors behave differently, with investors preferring risk-free assets.

The informativeness of options-trading activities: Non-linear analysis based on MF-DCCA and Granger test

Using both Put–Call ratio (P/C) and Option-to-Stock Volume ratio (O/S) as measures of options-trading activities, this paper investigates the information content of SSE 50 ETF options. We begin by using detrended fluctuation analysis (MF-DFA) method to examine the multifractal properties of P/C ratio change series, O/S ratio change series and ETF returns, and find that these time series exhibit strong multifractality. Moreover, employing multifractal detrended cross-correlation analysis (MF-DCCA), we show that there exists strong anti-persistent cross-correlation between P/C ratios and 50 ETF returns, but no significant cross-correlation between O/S ratios and 50 ETF returns, suggesting that P/C ratio is more pronounced detecting the information content of options. Furthermore, we use nonlinear Granger causality test and show that the Granger causality relationships between P/C ratio and 50 ETF return series is more significant and stronger than that between O/S ratio and 50 ETF return series. Our findings imply that P/C ratio can better capture the informativeness of options.

Multiscale Multifractal Detrended Cross-Correlation Analysis of High-Frequency Financial Time Series

In order to obtain richer information on the cross-correlation properties between two time series, we introduce a method called multiscale multifractal detrended cross-correlation analysis (MM-DCCA). This method is based on the Hurst surface and can be used to study the non-linear relationship between two time series. By sweeping through all the scale ranges of the multifractal structure of the complex system, it can present more information than the multifractal detrended cross-correlation analysis (MF-DCCA). In this paper, we use the MM-DCCA method to study the cross-correlations between two sets of artificial data and two sets of 5[Formula: see text]min high-frequency stock data from home and abroad. They are SZSE and SSEC in the Chinese market, and DJI and NASDAQ in the US market. We use Hurst surface and Hurst exponential distribution histogram to analyze the research objects and find that SSEC, SZSE and DJI, NASDAQ all show multifractal properties and long-range cross-correlations. We find that the fluctuation of the Hurst surface is related to the positive and negative of [Formula: see text], the change of scale range, the difference of national system, and the length of time series. The results show that the MM-DCCA method can give more abundant information and more detailed dynamic processes.

Contagion Effect in Cryptocurrency Market

The rapid development of cryptocurrencies has drawn attention to this particular market, with investors trying to understand its behaviour and researchers trying to explain it. The evolution of cryptocurrencies’ prices showed a kind of bubble and a crash at the end of 2017. Based on this event, and on the fact that Bitcoin is the most recognized cryptocurrency, we propose to evaluate the contagion effect between Bitcoin and other major cryptocurrencies. Using the Detrended Cross-Correlation Analysis correlation coefficient (ΔρDCCA) and comparing the period after and before the crash, we found evidence of a contagion effect, with this particular market being more integrated now than in the past—something that should be taken into account by current and potential investors.

Assessing the Wet Deposition Mechanism of Benzo(a)pyrene in the Atmosphere by MF-DCCA

Based on the 19 year observation from 1998 to 2016 at the Tsuan Wan and Central/Western District monitoring stations in Hong Kong, the aim of this paper was to assess the wet deposition pathway of Benzo(a)pyrene (BaP) on a large time-scale. In order to achieve this goal, multi-fractal detrended cross-correlation analysis (MF-DCCA) was used to characterize the long-term cross-correlations behaviors and multi-fractal temporal scaling properties between BaP (or PM2.5) and precipitation. The results showed that the relationships between BaP and precipitation (or PM2.5) displayed long-term cross-correlation at the time-scale ranging from one month to one year; no cross-correlation between each other was observed in longer temporal scaling regimes (greater than one year). These results correspond to the atmospheric circulation of the Asian monsoon system and are explained in detail. Similar dynamic processes of the wet deposition of BaP and PM2.5 suggested that the main removal process of atmospheric BaP was rainfall deposits of PM2.5-bound BaP. Furthermore, cross-correlations between BaP (or PM2.5) and precipitation at the long time-scale have a multi-fractal nature and long-term persistent power-law decaying behavior. The temporal evolutions of the multi-fractality were investigated by the approach of a sliding window. Based on the evolution curves of multi-fractal parameters, the wet deposition pathway of PM2.5-bound BaP is discussed. Finally, the contribution degree of wet deposition to PM2.5-bound BaP was derived from the coefficient of determination. It was demonstrated that about 45% and 60% of atmospheric BaP removal can be attributed to the wet deposition pathway of PM2.5-bound BaP for the Tsuan Wan and Central/Western District areas, respectively. The findings in this paper are of great significance for further study on the removal mechanism of atmospheric BaP in the future. The MF-DCCA method provides a novel approach to assessing the geochemical cycle dynamics of BaP.

Multifractal detrended partial cross-correlation analysis on Asian markets

The impact of the recession on global markets motivates us to explore the effect of the stock market on the economic stability of a country. The growth of a stock market depends on various factors such as inter-dependency, globalization, economic policies etc. In this paper, we apply the recently developed multifractal detrended partial cross-correlation analysis method on some Asian markets by assuming NASDAQ composite index commonly influences these markets. For this purpose, we analyze the daily returns of three Asian markets such as China’s Shanghai composite index (SHCOMP), Japan’s Nikkei stock average index (NIKKEI 225), and India’s Bombay stock exchange (BSE) sensex index over a period of 18 years (2000–2018). The analysis was performed between all bivariate time series after removing the external influence factor and the results indicate that there exists long-range partial cross-correlation behavior and multifractal nature. For comparison, we also performed analysis without removal of external influence factor i.e. multifractal detrended cross-correlation analysis. From the calculated Hurst scaling exponents, we found that the NASDAQ composite index shows significant influence on these analyzed Asian stock markets.

PID: a PDF-induced distance based on permutation cross-distribution entropy

In this paper, a PDF-induced distance (PID) based on permutation cross-distribution entropy is proposed to measure the dissimilarity between complex time series. It overcomes the effects of spatial distance by focusing on similar local fluctuation patterns. It also corrects the disadvantage of being insensitive to symmetric skewness distributions. We have applied PID to synthetic data and financial time series. The Euclidean distance is employed as a reference. In simulated experiments, eight signals generated from four models are detected, and results are presented by hierarchical clustering analysis via PID, which is correctly clustered and superior to other methods. Then, PID is applied to the real-world financial time series. Eight stocks in the global financial markets are employed. It reveals that they are clearly divided based on their financial backgrounds. The cophenetic correlation coefficient is used to measure the quality of solutions. It reveals that the PID is convincing and superior to the Euclidean distance. In addition, as a classic method for non-stationary time series, detrended cross-correlation analysis (DCCA) is adopted to compare the superiority of PID. Although experiments show that DCCA does perform well, it is inferior to PID. Also, we conduct additional experiments on the effects of non-Gaussian noises. Excitingly, PID can still cluster signals accurately after adding uniformly distributed noises, and the cophenetic correlation coefficient reaches 0.9788.

Application of an Improved Correlation Method in Electrostatic Gait Recognition of Hemiparetic Patients.

Hemiparesis is one of the common sequelae of neurological diseases such as strokes, which can significantly change the gait behavior of patients and restrict their activities in daily life. The results of gait characteristic analysis can provide a reference for disease diagnosis and rehabilitation; however, gait correlation as a gait characteristic is less utilized currently. In this study, a new non-contact electrostatic field sensing method was used to obtain the electrostatic gait signals of hemiplegic patients and healthy control subjects, and an improved Detrended Cross-Correlation Analysis cross-correlation coefficient method was proposed to analyze the obtained electrostatic gait signals. The results show that the improved method can better obtain the dynamic changes of the scaling index under the multi-scale structure, which makes up for the shortcomings of the traditional Detrended Cross-Correlation Analysis cross-correlation coefficient method when calculating the electrostatic gait signal of the same kind of subjects, such as random and incomplete similarity in the trend of the scaling index spectrum change. At the same time, it can effectively quantify the correlation of electrostatic gait signals in subjects. The proposed method has the potential to be a powerful tool for extracting the gait correlation features and identifying the electrostatic gait of hemiplegic patients.

Cross-correlations between the CSI300 index and commodity markets: Non-stationary principal component analysis (NSPCA)

The categorization of high dimensional data present a fascinating challenge to statistical models as frequent number of highly correlated dimensions or attributes can affect the accuracy of model. When the underlying time series present non-stationarity, typically when the series are contaminated by external trends, the strength of cross-correlations among variables is often overestimated or underestimated, and therefore, the traditional PCA method fails to rely on reliable cross-correlations to guide for the linear transformation of original variables. In this study, we apply the non-stationary principal component analysis (NSPCA) introduced by Zhao and Shang (2015) to analysis cross-correlations between the CSI300 Index and commodity markets. The main result of this paper is that for commodity markets, utilization of the non-stationary principal component analysis (NSPCA) can improve the efficiency, with more proportion of total population variance (information) due to an equal number of principal components than the traditional PCA. Meanwhile, as the increasing of time scales, this efficiency of NSPCA has a trend to increase. To check that whether the first several principal components can preserve some important information of original data or not, we apply detrended cross-correlation analysis (DCCA) to examine cross-correlation relationship between the CSI300 Index and the selected first five principal components and conclude that the information of long-range dependence measured by Hurst exponent has not been lost.

Multifractal Detrended Cross-Correlation Analysis of Electricity and Carbon Markets in China

With the development of carbon market, the complex dynamic relationship between electricity and carbon market has become the focus of energy research area. In this paper, we applied a new developed multifractal detrended cross-correlation analysis method to investigate the cross-correlation and multifractality between electricity and carbon markets. We analyze the daily return of electricity and carbon prices over a period of 6 years to do the research. The results show that, firstly, we find that there is a strong negative correlation between domestic carbon price and electricity price and a significant cross-correlation between the return series of electricity and carbon markets. Secondly, through multifractal detrended fluctuation analysis, it is proven that there are obvious multifractal characteristics in the return series of electricity and carbon markets, and the results of traditional linear analysis are unreliable. We also find that, based on multifractal detrended cross-correlation analysis, the law cross-correlation between electricity and carbon markets exists significantly. The long-range correlation of small fluctuations and large fluctuations and the fat tail distribution of return series are the reasons for the formation of multifractality.

Traces of the Multifractal Nature of the Financial Crises in Turkey: Co-Movement of the Hölder Exponents and Large-Scale Forecast

This paper investigates the multifractal behavior of the probability of default (PD) of real sector firms and Turkey sovereign credit default swap (CDS). Moreover, we emphasize the co-movements of Hölder exponents during the financial crisis periods. For this reason, first, it is necessary to figure out the default probabilities of real sector firms. The default probability is evaluated weekly by the methodology of Moody’s Analytics, which is a commonly used approach, in which the market value of a firm is a call option written on its total assets. Multifractal detrended fluctuation analysis (MF-DFA), multifractal detrended cross-correlation analysis (MF-DCCA) and multifractal detrended moving average cross-correlation analysis (MF-X-DMA) techniques are applied to identify the multifractal behavior of the large-scale fluctuations of PDs and CDSs. In this way, we can evaluate the local Hurst exponents. Besides, the oscillation method is employed to estimate the pointwise and local Hölder exponents. In the period between January 2001 and March 2018, the structure of dynamic co-movements of Hölder exponents is determined by applying wavelet coherency methodology and the relations in crisis period are revealed. The selected period covers the crises with structural differences: Turkey banking crisis, the US sub-prime mortgage crisis and the European sovereign debt crisis that occurred in 2001, 2008 and 2009, respectively. Besides, during the periods of financial crises, among the local Hölder exponents, severely correlated large scales show multifractal features, and hence vector fractionally autoregressive integrated moving average (VFARIMA) forecasting provides better results than scalar models.

Relationship between onshore and offshore renminbi exchange markets: Evidence from multiscale cross-correlation and nonlinear causal effect analyses

Through multifractal detrended moving-average cross-correlation analysis (MF-X-DMA) and partial moving-average cross-correlation coefficient analysis (PDMCA), this paper studies power-law cross-correlations between renminbi (RMB) onshore and offshore markets (2013–2018). The interaction between CNY and CNH market pairs was examined with attention to how the floating exchange rate regime reform of August 11, 2015 affects their interactions. The obtained results suggest that net power-law cross-correlations exist between the CNY and CNH exchange markets (with influences of autocorrelation, interest rate difference, US Dollar, and Oil signals removed) and that the August 11, 2015 (referred to as “811”) exchange reform significantly affects the trend of multiscale cross-correlation coefficient curves. This study also verifies that the risk of offshore RMB markets in Europe and the UK is larger than in Hong Kong and the US when facing a large shock. The nonlinear causal effect analysis reveals that asymmetric bidirectional nonlinear causality exists between any market pair, and the degree of asymmetry appears to have declined after the 811 exchange rate regime reform. For the offshore RMB markets in the US, Europe, and UK, there is evidence of stronger causality running from the CNH to CNY than vice versa, which implies that the foreign impulses have had an influence on the domestic market, and the floating exchange rate reform effectively improves the RMB exchange rate formation mechanism.

European union effect on financial correlation dynamics

How social events affect stock markets is a central problem in financial dynamics. In this article, European union effect on correlation dynamics is investigated for European stock markets, based on their daily market data. According to the time the countries enter the European Union(EU), the stock markets are distinguished as the formerly joining the European Union(F-EU) markets, later joining the EU(L-EU) markets, and not joining the EU(N-EU) markets. Based on correlation analysis, Detrended Cross-Correlation Analysis and partial correlation analysis, the union is found to have a great impact on the correlations of F-EU markets, but show little influence on those of the L-EU and N-EU markets. Among the worldwide stock markets, the influence of the F-EU and American stock markets on the Eurostoxx50 index is stronger than that of the L-EU, N-EU markets, and Asian stock markets present weak influence on the Eurostoxx50 index. However, financial crisis would increase the correlations of the L-EU and N-EU stock markets, as well as their influence on the Eurostoxx50 index.

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.