changing value detrended cross correlation coefficient over time between crude oil and crop prices abstract in this paper we analyzed changing comovement relationship between prices of crude oil and food crops food index using a detrended cross correlation analysis dcca approach proposed by podobnik and stanley 2008 in order to detect the changing nature of cross correlation coefficient over time we estimated the detrended cross correlation coefficient on a rolling window and found that cross correlations were negative before 2004 for most of the items but they increased considerably after the surge in crude oil price in 2007 that caused diversion of food grains for production of biofuels

dcca cross correlation coefficient quantifying level of cross correlation abstract in this paper a new coefficient is proposed with the objective of quantifying the level of cross correlation between nonstationary time series this cross correlation coefficient is defined in terms of the dfa method and the dcca method the implementation of this cross correlation coefficient will be illustrated with selected time series

corrigendum corrigendum to the explicit linear quadratic regulator for constrained systems automatica 38 1 2002 3 20 we apologize that example 7 1 as publishedin bemporad morari dua andpistikopoulos 2002 is incorrect due to a miscalculation of the weight matrix p on the terminal state

multifractal detrended cross correlation analysis for two nonstationary signals we propose a method called multifractal detrended cross correlation analysis to investigate the multifractal behaviors in the power law cross correlations between two time series or higher dimensional quantities recorded simultaneously which can be applied to diverse complex systems such as turbulence finance ecology physiology geophysics and so on the method is validated with cross correlated one and two dimensional binomial measures and multifractal random walks as an example we illustrate the method by analyzing two financial time series

multifractal detrended cross correlations between the csi 300 index futures and the spot markets based on high frequency data abstract the cross correlation between the china securities index 300 csi 300 index futures and the spot markets based on high frequency data is discussed in this paper we empirically analyze the cross correlation by using the multifractal detrended cross correlation analysis mf dcca and investigate further the characteristics of asymmetry frequency difference and transmission direction of the cross correlation the results indicate that the cross correlation between the two markets is significant and multifractal meanwhile weak asymmetries exist in the cross correlation and higher data frequency results in a lower multifractality degree of the cross correlation the causal relationship between the two markets is bidirectional but the csi 300 index futures market has greater impact on the spot market

can the bivariate hurst exponent be higher than an average of the separate hurst exponents abstract in this note we investigate possible relationships between the bivariate hurst exponent h x y and an average of the separate hurst exponents 1 2 h x h y we show that two cases are well theoretically founded these are the cases when h x y 1 2 h x h y and h x y 1 2 h x h y however we show that the case of h x y 1 2 h x h y is not possible regardless of stationarity issues further discussion of the implications is provided as well together with a note on the finite sample effect

a new correlation coefficient for bivariate time series data abstract the correlation in time series has received considerable attention in the literature its use has attained an important role in the social sciences and finance for example pair trading in finance is concerned with the correlation between stock prices returns etc in general pearson s correlation coefficient is employed in these areas although it has many underlying assumptions which restrict its use here we introduce a new correlation coefficient which takes into account the lag difference of data points we investigate the properties of this new correlation coefficient we demonstrate that it is more appropriate for showing the direction of the covariation of the two variables over time we also compare the performance of the new correlation coefficient with pearson s correlation coefficient and detrended cross correlation analysis dcca via simulated examples

measuring correlations between non stationary series with dcca coefficient abstract in this short report we investigate the ability of the dcca coefficient to measure correlation level between non stationary series based on a wide monte carlo simulation study we show that the dcca coefficient can estimate the correlation coefficient accurately regardless the strength of non stationarity measured by the fractional differencing parameter d for a comparison we also report the results for the standard pearson correlation coefficient the dcca coefficient dominates the pearson coefficient for non stationary series

cross correlations between brazilian biofuel and food market ethanol versus sugar abstract we investigate intrinsic correlations between brazilian energy ethanol and food market sugar by applying recently introduced method detrended partial cross correlation analysis dpcca on returns and volatility series of sugar ethanol and crude oil prices the results show that intrinsic cross correlations between ethanol and sugar are positive and increase with time scale for both returns and volatility indicating that the diversion of sugar cane for biofuel production due to the variations in ethanol prices affects more sugar prices than the price movements in external energy market ethanol oil volatility series and sugar oil return series do not show correlations for small scales while at larger scales intrinsic correlations become negative the intrinsic correlations in oil ethanol return series and oil sugar volatility series show similar behavior as corresponding ethanol sugar series indicating the existence of strong correlations between sugar and ethanol price variations

detrending moving average algorithm for multifractals the detrending moving average dma algorithm is a widely used technique to quantify the long term correlations of nonstationary time series and the long range correlations of fractal surfaces which contains a parameter ensuremath theta determining the position of the detrending window we develop multifractal detrending moving average mfdma algorithms for the analysis of one dimensional multifractal measures and higher dimensional multifractals which is a generalization of the dma method the performance of the one dimensional and two dimensional mfdma methods is investigated using synthetic multifractal measures with analytical solutions for backward ensuremath theta 0 centered ensuremath theta 0 5 and forward ensuremath theta 1 detrending windows we find that the estimated multifractal scaling exponent ensuremath tau q and the singularity spectrum f ensuremath alpha are in good agreement with the theoretical values in addition the backward mfdma method has the best performance which provides the most accurate estimates of the scaling exponents with lowest error bars while the centered mfdma method has the worse performance it is found that the backward mfdma algorithm also outperforms the multifractal detrended fluctuation analysis the one dimensional backward mfdma method is applied to analyzing the time series of shanghai stock exchange composite index and its multifractal nature is confirmed

multifractal analysis of stock exchange crashes abstract we analyze the complexity of rare events of the djia index we reveal that the returns of the time series exhibit strong multifractal properties meaning that temporal correlations play a substantial role the effect of major stock market crashes can be best illustrated by the comparison of the multifractal spectra of the time series before and after the crash aftershock periods compared to foreshock periods exhibit richer and more complex dynamics compared to an average crash calculated by taking into account the larger 5 crashes of the djia index the 1929 event exhibits significantly more increase in multifractality than the 1987 crisis

power law cross correlations between price change and volume change of indian stocks abstract we study multifractal long range correlations and cross correlations of daily price change and volume change of 50 stocks that comprise nifty index of national stock exchange mumbai using mf dfa and mf dcca methods we find that the time series of price change are uncorrelated whereas anti persistent long range multifractal correlations are found in volume change series we also find antipersistent long range multifractal cross correlations between the time series of price change and volume change as multifractality is a signature of complexity we estimate complexity parameters of the time series of price change volume change and cross correlated price volume change by fitting the fourth degree polynomials to their multifractal spectra our results indicate that the time series of price change display high complexity whereas the time series of volume change and cross correlated price volume change display low complexity

multifractal characterization of brazilian market sectors abstract we study auto correlations and cross correlations of daily price returns for seven brazilian market bovespa sectors using multifractal detrended fluctuation analysis mf dfa and multifractal detrended cross correlation analysis mf dxa we discover rather distinct multifractal behavior for different market sectors which indicates that individual sectors follow different dynamics from the entire market our analysis reveals that most sectors are market efficient due to the lack of long term correlations shuffling the series suggests that multifractality in the auto correlations arises both from a broad probability density function and from different long term correlations comparisons of multifractal cross correlations between bovespa and market sectors reveals that some sectors are more affected by multifractality of the entire market while others are more affected by multifractality of the sectors themselves a multifractal analysis of cross correlations between different market sectors provides a multifractal description of the brazilian sectors

multifractal analysis of indian public sector enterprises abstract in this paper we apply the methods multifractal detrended fluctuation analysis mf dfa and multifractal detrended cross correlation analysis mf dxa to study the auto correlation cross correlation behaviour and multifractal characteristics on twenty three stock market indices of department of public enterprises dpe india the auto correlation and cross correlation have been measured from the hurst scaling exponents and the singularity spectrum quantitatively from the calculated power law scaling exponents we observe the volume and price volume change time series possess strong anti persistent behaviour the price change of different time series shows persistent stochastic and anti persistent behaviour we also observe the existence of multifractal characteristics in all price volume and price volume change time series the price changes in the time series shows high complexity compared to volume and cross correlated price volume

detecting and quantifying cross correlations by analogous multifractal height cross correlation analysis abstract a new algorithm analogous multifractal height cross correlation analysis amf hxa is proposed in this paper our novel method takes into consideration of both the fluctuation information and the sign information in the corresponding cross covariance function numerical tests on artificially simulated series and real world series are performed to demonstrate that our method can accurately detect long range cross correlations for two simultaneously recorded series a new cross correlation coefficient is also defined to quantify the levels of cross correlation between two series

chaos based nonlinear analysis to study cardiovascular responses to changes in posture abstract cardiovascular responses to changes in posture have been the focus of numerous investigations in the past analysis of ecg and arterial blood pressure abp data for different postures obtained from physionet was done from a new perspective of analyzing nonlinear time series having multifractal features multifractal detrended fluctuation analysis mfdfa and also the cross correlation between ecg and bp with another technique multifractal detrended cross correlation analysis mfdxa reveals ecg and abp time series of different subjects to be multifractal in nature with different degree of complexity different degree of auto and cross correlation for both ecg and abp signals is also observed for all subjects further significant information obtained from the cross correlation parameters obtained from mfdxa analysis is very important and relevant particularly for understanding the dynamics of orthostatic stress

transfer entropy coefficient quantifying level of information flow between financial time series abstract in this paper a new coefficient is proposed with the objective of quantifying the level of information flow between financial time series this transfer entropy coefficient which provides an assessment on the multiscale information flow between measurements is defined in terms of the transfer entropy method and the multiscale method the implementation of this transfer entropy coefficient is illustrated with simulated time series and financial time series examples taken from simulated and financial data demonstrate that the dynamic mechanism of a complex system cannot be detected solely on the basis of transfer entropy of single scale

characterization of flow pattern transitions for horizontal liquid liquid pipe flows by using multi scale distribution entropy in coupled 3d phase space abstract horizontal oil water two phase flows often exist in many industrial processes uncovering the dynamic mechanism of the flow pattern transition is of great significance for modeling the flow parameters in this study we propose a method called multi scale distribution entropy msde in a coupled 3d phase space and use it to characterize the flow pattern transitions in horizontal oil water two phase flows firstly the proposed msde is validated with lorenz system and arfima processes interestingly it is found that the msde is dramatically associated with the cross correlations of the coupled time series then through conducting the experiment of horizontal oil water two phase flows the upstream and downstream flow information is collected using a conductance cross correlation velocity probe the coupled cross correlated signals are investigated using the msde method and the results indicate that the msde is an effective tool uncovering the complex dynamic behaviors of flow pattern transitions

measuring multifractality of stock price fluctuation using multifractal detrended fluctuation analysis abstract analyzing the shanghai stock price index daily returns using mf dfa method it is found that there are two different types of sources for multifractality in time series namely fat tailed probability distributions and non linear temporal correlations based on that a sliding window of 240 frequency data in 5 trading days was used to study stock price index fluctuation it is found that when the stock price index fluctuates sharply a strong variability is clearly characterized by the generalized hurst exponents h q therefore two measures h and based on generalized hurst exponents were proposed to compare financial risks before and after price limits and reform of non tradable shares the empirical results verify the validity of the measures and this has led to a better understanding of complex stock markets

nonlinear stochastic exclusion financial dynamics modeling and time dependent intrinsic detrended cross correlation abstract in attempt to reproduce price dynamics of financial markets a stochastic agent based financial price model is proposed and investigated by stochastic exclusion process the exclusion process one of interacting particle systems is usually thought of as modeling particle motion with the conserved number of particles in a continuous time markov process in this work the process is utilized to imitate the trading interactions among the investing agents in order to explain some stylized facts found in financial time series dynamics to better understand the correlation behaviors of the proposed model a new time dependent intrinsic detrended cross correlation tdi dcc is introduced and performed also the autocorrelation analyses are applied in the empirical research furthermore to verify the rationality of the financial price model the actual return series are also considered to be comparatively studied with the simulation ones the comparison results of return behaviors reveal that this financial price dynamics model can reproduce some correlation features of actual stock markets

constrained infinite horizon linear quadratic regulation of discrete time systems we are concerned with the output norm constrained infinite horizon linear quadratic regulation problem where the underlying state control constraints are specified by curved rather than polyhedral surfaces each suboptimal problem admits an exact convex synthesis condition expressed by an increasing union of linear matrix inequalities and results in an eventually time invariant controller satisfying the desired performance level subject to given constraints and closed loop stability the output norm constrained minimum time control problem is also dealt with as a corollary

autocorrelation and cross correlation in time series of homicide and attempted homicide abstract we propose in this paper to establish the relationship between homicides and attempted homicides by a non stationary time series analysis this analysis will be carried out by detrended fluctuation analysis dfa detrended cross correlation analysis dcca and dcca cross correlation coefficient d c c a n through this analysis we can identify a positive cross correlation between homicides and attempted homicides at the same time looked at from the point of view of autocorrelation dfa this analysis can be more informative depending on time scale for short scale days we cannot identify auto correlations on the scale of weeks dfa presents anti persistent behavior and for long time scales n 90 days dfa presents a persistent behavior finally the application of this new type of statistical analysis proved to be efficient and in this sense this paper can contribute to a more accurate descriptive statistics of crime

multifractal fourier detrended cross correlation analysis of traffic signals abstract multifractal detrended cross correlation analysis mf dxa has been developed to detect the long range power law cross correlation of considered signals in the presence of non stationarity however crossovers arising from extrinsic periodic trends make the scaling behavior difficult to analyze we introduce a fourier filtering method to eliminate the trend effects and systematically investigate the multifractal cross correlation of simulated and real traffic signals the crossover locations are found approximately corresponding to the periods of underlying trend traffic velocity on one road and flows on adjacent roads show strong cross correlation they also present weak multifractality after periodic trends are removed the traffic velocity and flow are cross correlated in opposite directions which is accordant to their actual evolution

multifractal analysis of shanghai and hong kong stock markets before and after the connect program abstract in this paper we study the multifractal scaling behaviour in shanghai and hong kong stock markets by means of multifractal detrended fluctuation analysis mf dfa and multifractal detrended cross correlation analysis mf dcca the results show that the multifractal degrees of each stock market are larger after the shanghai hong kong stock connect program shscp than before scaling analysis demonstrates that multifractality exists in cross correlations and the cross correlation coefficients after the shscp are larger than those before the shscp moreover an analysis of the origin of multifractality indicates that long range correlation and fat tailed distribution play important roles in the contributions of multifractality finally the results via the sliding window procedure indicate that the multifractal degrees after the shscp are not significantly affected by the stock market turbulence in 2015

modified multifractal large deviation spectrum based on cid for financial market system abstract we modify the basic roughness grain exponent only available for application of one single series to complexity invariant distance c i d for studying multifractal features between two time series c i d is taken into consideration as a new roughness grain exponent with the large deviation spectrum to detect the similarity and correlation between different stock markets in this work the new method is firstly applied to artificial series in order to test the scale invariance hypothesis with both the legendre spectrum and large deviation spectrum results show that the large deviation spectrum is better in the detection of multifractal analysis between two time series as it exhibit plentiful scaling structures then we investigate the scaling behavior between financial time series so as to test whether there is scale invariance of stock markets in china and the us besides from the values responding to the maximal f in the 5 pair series and the widths of the spectrum a new way of measurement of the similarity and correlation has been found to overcome the limitation of q we then compute the surface area of the large deviation spectrum under each scale and further detect the evolution of the slope by a scaling non scaling criterion which helps in the measurement of scaling behavior moreover the proposed method can give us more information between different markets and distinguish them from different angles

statistical test for δρdcca cross correlation coefficient abstract in this paper we propose a new statistical test for d c c a detrended cross correlation coefficient difference a tool to measure contagion interdependence effect in time series of size n at different time scale n for this proposition we analyzed simulated and real time series the results showed that the statistical significance of d c c a depends on the size n and the time scale n and we can define a critical value for this dependency in 90 95 and 99 of confidence level as will be shown in this paper

finite sample properties of power law cross correlations estimators abstract we study finite sample properties of estimators of power law cross correlations detrended cross correlation analysis dcca height cross correlation analysis hxa and detrending moving average cross correlation analysis dmca with a special focus on short term memory bias as well as power law coherency we present a broad monte carlo simulation study that focuses on different time series lengths specific methods parameter setting and memory strength we find that each method is best suited for different time series dynamics so that there is no clear winner between the three the method selection should be then made based on observed dynamic properties of the analyzed series

long memory of abnormal investor attention and the cross correlations between abnormal investor attention and trading volume volatility respectively abstract taking baidu index as a proxy for abnormal investor attention aia the long memory property in the aia of shanghai stock exchange sse 50 index component stocks was empirically investigated using detrended fluctuation analysis dfa method the results show that abnormal investor attention is power law correlated with hurst exponents between 0 64 and 0 98 furthermore the cross correlations between abnormal investor attention and trading volume volatility respectively are studied using detrended cross correlation analysis dcca and the dcca cross correlation coefficient d c c a the results suggest that there are positive correlations between aia and trading volume volatility respectively in addition the correlations for trading volume are in general higher than the ones for volatility by carrying on rescaled range analysis r s and rolling windows analysis we find that the results mentioned above are effective and significant

multiscale multifractal dcca and complexity behaviors of return intervals for potts price model abstract to investigate the characteristics of extreme events in financial markets and the corresponding return intervals among these events we use a potts dynamic system to construct a random financial time series model of the attitudes of market traders we use multiscale multifractal detrended cross correlation analysis mm dcca and lempel ziv complexity lzc perform numerical research of the return intervals for two significant china s stock market indices and for the proposed model the new mm dcca method is based on the hurst surface and provides more interpretable cross correlations of the dynamic mechanism between different return interval series we scale the lzc method with different exponents to illustrate the complexity of return intervals in different scales empirical studies indicate that the proposed return intervals from the potts system and the real stock market indices hold similar statistical properties

cross correlations between crude oil and agricultural commodity markets abstract in this paper we investigate cross correlations between crude oil and agricultural commodity markets based on a popular statistical test proposed by podobnik et al 2009 we find that the linear return cross correlations are significant at larger lag lengths and the volatility cross correlations are highly significant at all of the lag lengths under consideration using a detrended cross correlation analysis dcca we find that the return cross correlations are persistent for corn and soybean and anti persistent for oat and soybean the volatility cross correlations are strongly persistent using a nonlinear cross correlation measure our results show that cross correlations are relatively weak but they are significant for smaller time scales for larger time scales the cross correlations are not significant the reason may be that information transmission from crude oil market to agriculture markets can complete within a certain period of time finally based on multifractal extension of dcca we find that the cross correlations are multifractal and high oil prices partly contribute to food crisis during the period of 2006 mid 2008

random matrix theory analysis of cross correlations in the us stock market evidence from pearson s correlation coefficient and detrended cross correlation coefficient abstract 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 marcenko pastur distribution

a new approach to quantify power law cross correlation and its application to commodity markets abstract we proposed a new method detrended moving average cross correlation analysis dmca to detect the power law cross correlation between two correlated non stationary time series by combining detrended cross correlation analysis dcca and detrended moving average dma in order to compare the performance of dmca and dcca in the detection of cross correlation and to estimate the influence of periodic trend we generate two cross correlated time series x i and y i by a periodic two component fractionally autoregressive integrated moving average arfima process then we apply both methods to quantify the cross correlations of the generated series whose theoretical values are already known to us by comparing the results we obtained we find that the performance of this new approach is comparable to dcca with less calculating amounts our method can also reduce the impact of trends furthermore dmca for background and forward moving average case outperforms dcca in more accurate estimation when the analyzed times series are short in length to provide an example we also apply this new method to the time series of the real world data from brent and wti crude oil spot markets to investigate the complex cross market correlation between these commodity markets in all our method is another practical choice to detect the cross correlation between two short period non stationary time series and has potential application to real world problems

dcca cross correlation coefficient with sliding windows approach abstract we have implemented in this paper the dcca cross correlation coefficient d c c a with sliding windows approach to measure cross correlation as a function of time thereby from two non stationary time series a fixed size window will be defined by w and the coefficients d c c a calculated for different time scales 4 n w 4 following this procedure it was possible to set up a cross correlation color map of d c c a which was tested in this paper for a simulated random and an empirical econometric case this new color map with sliding windows shows the time scale and the current time for a cross correlation analysis in this way it is possible to analyze the complete cross correlation between two variables in different areas of knowledge such as economics our case of study

optimal portfolio strategy with cross correlation matrix composed by dcca coefficients evidence from the chinese stock market abstract in this paper a new estimator of correlation matrix is proposed which is composed of the detrended cross correlation coefficients dcca coefficients to improve portfolio optimization in contrast to pearson s correlation coefficients pcc dcca coefficients acquired by the detrended cross correlation analysis dcca method can describe the nonlinear correlation between assets and can be decomposed in different time scales these properties of dcca make it possible to improve the investment effect and more valuable to investigate the scale behaviors of portfolios the minimum variance portfolio mvp model and the mean variance mv model are used to evaluate the effectiveness of this improvement stability analysis shows the effect of two kinds of correlation matrices on the estimation error of portfolio weights the observed scale behaviors are significant to risk management and could be used to optimize the portfolio selection

modeling long range cross correlations in two component arfima and fiarch processes we investigate how simultaneously recorded long range power law correlated multivariate signals cross correlate to this end we introduce a two component arfima stochastic process and a two component fiarch process to generate coupled fractal signals with long range power law correlations which are at the same time long range cross correlated we study how the degree of cross correlations between these signals depends on the scaling exponents characterizing the fractal correlations in each signal and on the coupling between the signals our findings have relevance when studying parallel outputs of multiple component of physical physiological and social systems

dynamical mechanism in aero engine gas path system using minimum spanning tree and detrended cross correlation analysis abstract identifying the mutual interaction in aero engine gas path system is a crucial problem that facilitates the understanding of emerging structures in complex system by employing the multiscale multifractal detrended cross correlation analysis method to aero engine gas path system the cross correlation characteristics between gas path system parameters are established further we apply multiscale multifractal detrended cross correlation distance matrix and minimum spanning tree to investigate the mutual interactions of gas path variables the results can infer that the low spool rotor speed n1 and engine pressure ratio epr are main gas path parameters the application of proposed method contributes to promote our understanding of the internal mechanisms and structures of aero engine dynamics

universal and nonuniversal properties of cross correlations in financial time series we use methods of random matrix theory to analyze the cross correlation matrix c of stock price changes of the largest 1000 u s companies for the 2 year period 1994 1995 we find that the statistics of most of the eigenvalues in the spectrum of c agree with the predictions of random matrix theory but there are deviations for a few of the largest eigenvalues we find that c has the universal properties of the gaussian orthogonal ensemble of random matrices furthermore we analyze the eigenvectors of c through their inverse participation ratio and find eigenvectors with large ratios at both edges of the eigenvalue spectrum a situation reminiscent of localization theory results

the effects of common risk factors on stock returns a detrended cross correlation analysis abstract in this paper we investigate the cross correlations between fama and french three factors and the return of american industries on the basis of cross correlation statistic test and multifractal detrended cross correlation analysis mf dcca qualitatively we find that the return series of fama and french three factors and american industries were overall significantly cross correlated based on the analysis of a statistic quantitatively we find that the cross correlations between three factors and the return of american industries were strongly multifractal and applying mf dcca we also investigate the cross correlation of industry returns and residuals we find that there exists multifractality of industry returns and residuals the result of correlation coefficients we can verify that there exist other factors which influence the industry returns except fama three factors

minimum spanning tree filtering of correlations for varying time scales and size of fluctuations based on a recently proposed q dependent detrended cross correlation coefficient ensuremath rho q j kwapie ifmmode acute n else n fi p o ifmmode acute s else s fi wi ifmmode mbox k e else k e fi cimka and s dro ifmmode dot z else z fi d ifmmode dot z else z fi phys rev e 92 052815 2015 we generalize the concept of the minimum spanning tree mst by introducing a family of q dependent minimum spanning trees q mathrm mst mathrm s that are selective to cross correlations between different fluctuation amplitudes and different time scales of multivariate data they inherit this ability directly from the coefficients ensuremath rho q which are processed here to construct a distance matrix being the input to the mst constructing kruskal s algorithm the conventional mst with detrending corresponds in this context to q 2 in order to illustrate their performance we apply the q mathrm msts to sample empirical data from the american stock market and discuss the results we show that the q mathrm mst graphs can complement ensuremath rho q in disentangling hidden correlations that cannot be observed in the mst graphs based on ensuremath rho mathrm dcca and therefore they can be useful in many areas where the multivariate cross correlations are of interest as an example we apply this method to empirical data from the stock market and show that by constructing the q mathrm msts for a spectrum of q values we obtain more information about the correlation structure of the data than by using q 2 only more specifically we show that two sets of signals that differ from each other statistically can give comparable trees for q 2 while only by using the trees for q ensuremath ne 2 do we become able to distinguish between these sets we also show that a family of q mathrm msts for a range of q expresses the diversity of correlations in a manner resembling the multifractal analysis where one computes a spectrum of the generalized fractal dimensions the generalized hurst exponents or the multifractal singularity spectra the more diverse the correlations are the more variable the tree topology is for different q s as regards the correlation structure of the stock market our analysis exhibits that the stocks belonging to the same or similar industrial sectors are correlated via the fluctuations of moderate amplitudes while the largest fluctuations often happen to synchronize in those stocks that do not necessarily belong to the same industry

detrended fluctuation analysis as a regression framework estimating dependence at different scales we propose a framework combining detrended fluctuation analysis with standard regression methodology the method is built on detrended variances and covariances and it is designed to estimate regression parameters at different scales and under potential nonstationarity and power law correlations the former feature allows for distinguishing between effects for a pair of variables from different temporal perspectives the latter ones make the method a significant improvement over the standard least squares estimation theoretical claims are supported by monte carlo simulations the method is then applied on selected examples from physics finance environmental science and epidemiology for most of the studied cases the relationship between variables of interest varies strongly across scales

an analysis of the intrinsic cross correlations between api and meteorological elements using dpcca abstract in order to reveal the intrinsic cross correlations between air pollution index api records and synchronously meteorological elements data the detrended partial cross correlation dpcc coefficients are analyzed using a detrended partial cross correlation analysis dpcca dpcc coefficients for different spatial locations and seasons are calculated and compared the results show that dpcca can uncover intrinsic cross correlations between api and meteorological elements and most of their interactional mechanisms can be explained dpcc coefficients are either positive or negative and vary with spatial locations and seasons with consistently interactional mechanisms more remarkable we find that detrended cross correlation analysis can present the cross correlations between the fluctuations in two nonstationary time series but this cross correlation does not always fully reflect the interactional mechanism for the original time series despite this dpcca is recommended as a comparatively reliable method for revealing intrinsic cross correlations between api and meteorological elements and it can also be useful for our understanding of their interactional mechanisms

assessment of 48 stock markets using adaptive multifractal approach abstract 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 2 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 h x y h x x h y y 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 x x 0 304 0 905 and x y 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 d c c a indicates that all pairs of stock market studied in this time interval belong to cross correlated processes

a new methodology for local cross correlation between two nonstationary time series abstract to measure the degree of local cross correlation between two nonstationary time series a new approach with a locally weighted pearson correlation coefficient based on a simple locally weighted linear regression model was proposed in this approach a gaussian decay based function is selected as a weighting function an appropriate bandwidth is selected using an alternative criterion some factors influencing the local cross correlation degree including long range exponent estimated by means of a detrended fluctuation analysis dfa and seasonal change in the series are discussed artificial and real world datasets are analyzed the results show that the proposed method can measure the degree of a locally intrinsic cross correlation between two series the contribution of this locally intrinsic cross correlation is attributed to original input excitation sources and dfa scaling exponents the effects of seasonal change with a high frequency in the series on a locally intrinsic cross correlation are significant the effects of a low frequency seasonal change are insignificant a positive local cross correlation between a synchronous wind speed and air pollution index series in nanjing china is observed which is related to externally imported air pollution sources consistent results are obtained by comparing the new method with the detrended cross correlation coefficient d c c a therefore the proposed approach is reliable reasonable and applicable and can examine the degree of the local intrinsic cross correlation between two nonstationary time series

time varying lead lag structure between the crude oil spot and futures markets abstract the linkages between crude oil spot and futures markets are widely studied in previous literatures most of these conventional methods are static linear and parametric in order to overcome this difficulty we employ the nonparametric and nonlinear symmetric thermal optimal path tops method to determine the time dependent lead lag relationship between two time series based on the daily weekly monthly spot and futures returns for maturities of one two three and four months of the west texas intermediate wti crude oil benchmark we apply the tops method together with self consistent test to investigate the time varying lead lag dependences between spot and futures markets from 1987 to 2017 we find that for total three data sets with different frequencies the tops paths indicate an alternate lead lag structure instead of a dominance between spot and futures markets in most of the time periods for the daily data the lead lag relationship between the two markets exists within one day except on some specific days moreover without considering the units of time on average the lead lag steps between the two markets are diminishing with the increasing frequency roughly speaking these periods with strong lead lag signals coincide with major influential changes in the oil and stock markets and the geopolitics which can reflect real economic financial and geopolitical regime changes all in all the results show that the lead lag relationship between the spot and futures oil markets exists only temporarily

multifractal detrending moving average cross correlation analysis there are a number of situations in which several signals are simultaneously recorded in complex systems which exhibit long term power law cross correlations the multifractal detrended cross correlation analysis mfdcca approaches can be used to quantify such cross correlations such as the mfdcca based on the detrended fluctuation analysis mfxdfa method we develop in this work a class of mfdcca algorithms based on the detrending moving average analysis called mfxdma the performances of the proposed mfxdma algorithms are compared with the mfxdfa method by extensive numerical experiments on pairs of time series generated from bivariate fractional brownian motions two component autoregressive fractionally integrated moving average processes and binomial measures which have theoretical expressions of the multifractal nature in all cases the scaling exponents h xy extracted from the mfxdma and mfxdfa algorithms are very close to the theoretical values for bivariate fractional brownian motions the scaling exponent of the cross correlation is independent of the cross correlation coefficient between two time series and the mfxdfa and centered mfxdma algorithms have comparative performances which outperform the forward and backward mfxdma algorithms for two component autoregressive fractionally integrated moving average processes we also find that the mfxdfa and centered mfxdma algorithms have comparative performances while the forward and backward mfxdma algorithms perform slightly worse for binomial measures the forward mfxdma algorithm exhibits the best performance the centered mfxdma algorithms performs worst and the backward mfxdma algorithm outperforms the mfxdfa algorithm when the moment order q 0 we apply these algorithms to the return time series of two stock market indexes and to their volatilities for the returns the centered mfxdma algorithm gives the best estimates of h xy q since its h xy 2 is closest to 0 5 as expected and the mfxdfa algorithm has the second best performance for the volatilities the forward and backward mfxdma algorithms give similar results while the centered mfxdma and the mfxdfa algorithms fail to extract rational multifractal nature

long range correlation and market segmentation in bond market abstract this paper investigates the long range auto correlations and cross correlations in bond market based on detrended moving average dma method empirical results present a clear evidence of long range persistence that exists in one year scale the degree of long range correlation related to maturities has an upward tendency with a peak in short term these findings confirm the expectations of fractal market hypothesis fmh furthermore we have developed a method based on a complex network to study the long range cross correlation structure and applied it to our data and found a clear pattern of market segmentation in the long run we also detected the nature of long range correlation in the sub period 2007 2012 and 2011 2016 the result from our research shows that long range auto correlations are decreasing in the recent years while long range cross correlations are strengthening

cross correlations between volume change and price change in finance one usually deals not with prices but with growth rates r defined as the difference in logarithm between two consecutive prices here we consider not the trading volume but rather the volume growth rate r the difference in logarithm between two consecutive values of trading volume to this end we use several methods to analyze the properties of volume changes r and their relationship to price changes r we analyze 14 981 daily recordings of the standard and poor s s p 500 index over the 59 year period 1950 2009 and find power law cross correlations between r and r by using detrended cross correlation analysis dcca we introduce a joint stochastic process that models these cross correlations motivated by the relationship between r and r we estimate the tail exponent of the probability density function p r r 1 for both the s p 500 index as well as the collection of 1819 constituents of the new york stock exchange composite index on 17 july 2009 as a new method to estimate we calculate the time intervals q between events where r q we demonstrate that q the average of q obeys q q we find 3 furthermore by aggregating all q values of 28 global financial indices we also observe an approximate inverse cubic law

price volume multifractal analysis and its application in chinese stock markets abstract an empirical research on chinese stock markets is conducted using statistical tools first the multifractality of stock price return series r i r i ln p t 1 ln p t and trading volume variation series v i v i ln v t 1 ln v t is confirmed using multifractal detrended fluctuation analysis furthermore a multifractal detrended cross correlation analysis between stock price return and trading volume variation in chinese stock markets is also conducted it is shown that the cross relationship between them is also found to be multifractal second the cross correlation between stock price p i and trading volume v i is empirically studied using cross correlation function and detrended cross correlation analysis it is found that both shanghai stock market and shenzhen stock market show pronounced long range cross correlations between stock price and trading volume third a composite index r based on price and trading volume is introduced compared with stock price return series r i and trading volume variation series v i r variation series not only remain the characteristics of original series but also demonstrate the relative correlation between stock price and trading volume finally we analyze the multifractal characteristics of r variation series before and after three financial events in china namely price limits reform of non tradable shares and financial crisis in 2008 in the whole period of sample to study the changes of stock market fluctuation and financial risk it is found that the empirical results verified the validity of r

effect of trends on detrended fluctuation analysis scaling behavior we find that crossovers result from the competition between the scaling of the noise and the apparent scaling of the trend we study how the characteristics of these crossovers depend on i the slope of the linear trend ii the amplitude and period of the periodic trend iii the amplitude and power of the power law trend and iv the length as well as the correlation properties of the noise surprisingly we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws i e long range power law dependence of the position of the crossover on the parameters of the trends we show that the dfa result of noise with a trend can be exactly determined by the superposition of the separate results of the dfa on the noise and on the trend assuming that the noise and the trend are not correlated if this superposition rule is not followed this is an indication that the noise and the superposed trend are not independent so that removing the trend could lead to changes in the correlation properties of the noise in addition we show how to use dfa appropriately to minimize the effects of trends how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation or if the crossover is due to a trend without any transition in the dynamical properties of the noise

multifractal detrended cross correlation analysis of the oil dependent economies evidence from the west texas intermediate crude oil and the gcc stock markets abstract 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 q c c 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 h x y q in addition we explore the relationship between the cross correlation exponents h x y q and the average scaling exponents h x x q h y y q 2

time dependent cross correlations between different stock returns a directed network of influence we study the time dependent cross correlations of stock returns i e we measure the correlation as the function of the time shift between pairs of stock return time series using tick by tick data we find a weak but significant effect showing that in many cases the maximum correlation appears at nonzero time shift indicating directions of influence between the companies due to the weakness of this effect and the shortness of the characteristic time of the order of a few minutes our findings are compatible with market efficiency the interaction of companies defines a directed network of influence

price volume cross correlation analysis of csi300 index futures abstract 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

division algebras with psl 2 q galois maximal subfields abstract if g is a finite group and k is a field then g is k admissible if there exists a g galois extension l k such that l is a maximal subfield of a k division algebra we prove that psl 2 7 is k admissible for any number field which either fails to contain 1 or which has two primes lying over the dyadic prime in addition psl 2 11 is shown to be admissible over q or any number field k with at least two extensions of the dyadic prime indeed there exist infinitely many linearly disjoint admissible extensions for these groups

multifractal cross correlation spectra analysis on chinese stock markets abstract in this paper the long range cross correlation of chinese stock indices is systematically studied the multifractal detrended cross correlation analysis mf dxa appears to be one of the most effective methods in detecting long range cross correlation of two non stationary variables the legendre spectrum and the large deviations spectrum are extended to the cross correlation case so as to present multifractal structure of stock return and volatility series it is characterized of the multifractality in chinese stock markets partly due to clusters of local detrended covariance with large and small magnitudes

power law correlations in finance related google searches and their cross correlations with volatility and traded volume evidence from the dow jones industrial components abstract we study power law correlations properties of the google search queries for dow jones industrial average djia component stocks examining the daily data of the searched terms with a combination of the rescaled range and rescaled variance tests together with the detrended fluctuation analysis we show that the searches are in fact power law correlated with hurst exponents between 0 8 and 1 1 the general interest in the djia stocks is thus strongly persistent we further reinvestigate the cross correlation structure between the searches traded volume and volatility of the component stocks using the detrended cross correlation and detrending moving average cross correlation coefficients contrary to the universal power law correlations structure of the related google searches the results suggest that there is no universal relationship between the online search queries and the analyzed financial measures even though we confirm positive correlation for a majority of pairs there are several pairs with insignificant or even negative correlations in addition the correlations vary quite strongly across scales

a dfa approach for assessing asymmetric correlations abstract here we propose a method based on detrended fluctuation analysis to investigate asymmetric correlations in nonstationary time series the aim is to show that for a certain range of time scales different scaling properties are found if signal trending is either positive and negative we illustrate the method by selected examples from physics and finance

the explicit linear quadratic regulator for constrained systems we present a technique to compute the explicit state feedback solution to both the finite and infinite horizon linear quadratic optimal control problem subject to state and input constraints we show that this closed form solution is piecewise linear and continuous as a practical consequence of the result constrained linear quadratic regulation becomes attractive also for systems with high sampling rates as on line quadratic programming solvers are no more required for the implementation

multifractal detrended cross correlation analysis of gold price and sensex abstract this paper studies the variation of autocorrelation and cross correlation coefficients of gold price and sensex fluctuations with time the paper uses mfdfa and mfdxa methodologies sensex plays a more dominant role in the variation of cross correlations it is observed that the cross correlation coefficients can be linked with the stability of the market the market is most stable when the two series are most correlated

cross correlation analysis between chinese tf contracts and treasury etf based on high frequency data abstract in this paper we investigate the high frequency cross correlation relationship between chinese treasury futures contracts and treasury etf we analyze the logarithmic return of these two price series from which we can conclude that both return series are not normally distributed and the futures markets have greater volatility we find significant cross correlation between these two series we further confirm the relationship using the dcca coefficient and the dmca coefficient we quantify the long range cross correlation with dcca method and we further show that the relationship is multifractal an arbitrage algorithm based on dfa regression with stable return is proposed in the last part

detrended minimum variance hedge ratio a new method for hedge ratio at different time scales abstract in this paper based on the detrended fluctuation analysis dfa method and the detrended cross correlation analysis dcca method we propose an improved method of minimum variance mv hedge ratio i e the detrended minimum variance d mv hedge ratio which can measure the hedge ratio at different time scales the proposed d mv hedge ratio is defined as the detrended covariance function between spot and futures returns divided by the detrended variance function of futures returns through the simulated and empirical analysis we find that i the outcomes of the hedge ratio and the corresponding hedging effectiveness for the d mv hedge ratio are diverse at different time scales which can meet needs of various hedging participants with different hedging horizons ii our proposed d mv hedge ratio has a better hedging performance and a greater potential to determine the hedge ratio because its results of hedging effectiveness at most of time scales are better than those of the traditional mv hedge ratio and iii as for the method of d mv hedge ratio for different polynomial orders m in the fitting procedure the d mv 1 hedge ratio i e the linear polynomial in the fitting procedure has the best hedging capability for determining the hedge ratio

detrending moving average cross correlation coefficient measuring cross correlations between non stationary series abstract in the paper we introduce a new measure of correlation between possibly non stationary series as the measure is based on the detrending moving average cross correlation analysis dmca we label it as the dmca coefficient d m c a with a moving average window length we analytically show that the coefficient ranges between 1 and 1 as a standard correlation does in the simulation study we show that the values of d m c a very well correspond to the true correlation between the analyzed series regardless the non stationarity level dependence of the newly proposed measure on other parameters correlation level moving average window length and time series length is discussed as well

effect of nonstationarities on detrended fluctuation analysis detrended fluctuation analysis dfa is a scaling analysis method used to quantify long range power law correlations in signals many physical and biological signals are noisy heterogeneous and exhibit different types of nonstationarities which can affect the correlation properties of these signals we systematically study the effects of three types of nonstationarities often encountered in real data specifically we consider nonstationary sequences formed in three ways i stitching together segments of data obtained from discontinuous experimental recordings or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts a cutting procedure commonly used in preparing data prior to signal analysis ii adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitudes and iii generating a signal comprised of segments with different properties e g different standard deviations or different correlation exponents we compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities we find that introducing nonstationarities to stationary correlated signals leads to the appearance of crossovers in the scaling behavior and we study how the characteristics of these crossovers depend on a the fraction and size of the parts cut out from the signal b the concentration of spikes and their amplitudes c the proportion between segments with different standard deviations or different correlations and d the correlation properties of the stationary signal we show how to develop strategies for preprocessing raw data prior to analysis which will minimize the effects of nonstationarities on the scaling properties of the data and how to interpret the results of dfa for complex signals with different local characteristics

dcca cross correlation analysis in time series with removed parts abstract in this paper we analyze the effect of removing pieces in time series with long range memory by dfa method and detrended cross correlation coefficient to achieve this purpose initially simulated time series are produced by arfima process long time dependence from these simulated time series cuts and removals are produced the results show that for up to 50 of removed parts compared to the original time series there is no change in the final results for detrended auto and cross correlations therefore with this paper we show that the dfa method and the detrended cross correlation coefficient are robust for time series analysis even for time series with removed parts this result ensures that these methods can be applied to real time series which in many cases lacks measurement for a variety of reasons and causes

cross correlation analysis of stock markets using emd and eemd abstract empirical mode decomposition emd is a data driven signal analysis method for nonlinear and nonstationary data since it is intuitive direct posterior and adaptive emd is widely applied to various fields of study in this paper emd and ensemble empirical mode decomposition eemd a modified method of emd are applied to financial time series through analyzing the intrinsic mode functions imfs of emd and eemd we find eemd method performs better on the orthogonality of imfs than emd with clustering the ordered frequencies of imfs the imfs obtained from eemd method are grouped into high medium and low frequency components representing the short medium and long term volatilities of the index sequences respectively with the cross correlation analysis of dcca cross correlation coefficient our findings allow us to gain further and detailed insight into the cross correlations of stock markets

cross correlation between crude oil and refined product prices abstract in this paper we investigate cross correlations between crude oil and refined product prices based on the well known detrended cross correlation analysis dcca our findings indicate that the cross correlations are significant and strong furthermore the multifractality in cross correlations is also revealed the cross correlation coefficients are as high as 0 9 for larger time scales and are greater than those for smaller time scales two popular models vector error correction model and bivariate bekk volatility model are found to have very limited power in capturing long range cross correlations suggesting the drawbacks of these conventional models in actual applications long term cross correlations are stronger in recent ten years than those in the past decades

a non split torsor with trivial fixed point obstruction abstract let g be a linear algebraic group and x be an irreducible algebraic variety with a generically free g action all defined over an algebraically closed base field of characteristic zero it is well known that x can be viewed as a g torsor representing a class x in h 1 k g where k is the field of g invariant rational functions on x we have previously shown that if x has a smooth h fixed point for some non toral diagonalizable subgroup h of g then x 1 it is natural to ask if the converse is true assuming g is connected and x is projective and smooth in this note we show that the answer is no

price volume multifractal analysis of the moroccan stock market abstract in this paper we analyzed price volume multifractal cross correlations of moroccan stock exchange we chose the period from january 1st 2000 to january 20th 2017 to investigate the multifractal behavior of price change and volume change series then we used multifractal detrended cross correlations analysis method mf dcca and multifractal detrended fluctuation analysis mf dfa to analyze the series we computed bivariate generalized hurst exponent renyi exponent and spectrum of singularity for each pair of indices to measure quantitatively cross correlations furthermore we used detrended cross correlations coefficient dcca and cross correlation test q m to analyze cross correlation quantitatively and qualitatively by analyzing results we found existence of price volume multifractal cross correlations the spectrum width has a strong multifractal cross correlation we remarked that volume change series is anti persistent when we analyzed the generalized hurst exponent for all moments q the cross correlation test showed the presence of a significant cross correlation however dcca coefficient had a small positive value which means that the level of correlation is not very significant finally we analyzed sources of multifractality and their degree of contribution in the series

detrended multiple cross correlation coefficient abstract based on the detrended cross correlation coefficient x a x b we propose in this paper to establish a detrended multiple cross correlation coefficient d m c x 2 to be applied in order to quantify the relations between non stationary signals on different time scales this detrended multiple cross correlation coefficient will be the measure of the total association between the dependent variable y with the others i independent variables x it will be the generalization of x a x b for more than two independent variables to validate d m c x 2 we set up a cross correlation table ranging from 0 to 1 and we determined the detrended multiple cross correlation coefficient into simulated and real time series the results of this analysis show that the detrended multiple cross correlation coefficient may be suitable and useful to measure multiple cross correlations as we will see in this paper

backcasting and forecasting time series using detrended cross correlation analysis abstract in this paper we addressed the problem of backcasting and forecasting non stationary time series given that traditional backcasting are based on the classical cross correlation function assuming two stationary time series assumptions based on two non stationary time series need a new approach thus detrended cross correlation analysis dcca provides a fanned estimator for a correlation between two non stationary time series providing then the stationary time series therefore we developed a backcaster estimator and a predictor for the obtained stationary time series the practical example of a chilean cement production time series 1991 2015 illustrates our results

dcca cross correlation coefficient differentiation theoretical and practical approaches abstract we propose in this paper to establish a well defined relationship between d f a the long range auto correlation exponent and 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 d c c a n also for some specific times series we apply this theory in order to establish its validity