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

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

non linear approach to study the dynamics of neurodegenerative diseases by multifractal detrended cross correlation analysis a quantitative assessment on gait disease abstract this paper studies the human gait pattern of normal people and patients suffering from parkinson s disease using the mfdxa multifractal detrended cross correlation analysis methodology the auto correlation and cross correlation of the time series of the total force under the left foot and right foot were studied the study reveals that the degree of multifractality w and degree of correlation are generally more for normal patients than the diseased set it is also observed that the values of w and are nearly same for left foot and right it is also observed that the study of autocorrelation alone is not sufficient cross correlations should also be studied to get a better concept of neurodegenerative diseases

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

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

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

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

a decomposition technique for integrable functions with applications to the divergence problem abstract let r n be a bounded domain that can be written as t t where t t is a countable collection of domains with certain properties in this work we develop a technique to decompose a function f l 1 with vanishing mean value into the sum of a collection of functions f t f t t subordinated to t t such that supp f t f t t and f t f t 0 as an application we use this decomposition to prove the existence of a solution in weighted sobolev spaces of the divergence problem div u f and the well posedness of the stokes equations on holder domains and some other domains with an external cusp arbitrarily narrow we also consider arbitrary bounded domains the weights used in each case depend on the type of domain

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

how long the singular value decomposed entropy predicts the stock market evidence from the dow jones industrial average index in this paper a new concept of multi scales singular value decomposition entropy based on dcca cross correlation analysis is proposed and its predictive power for the dow jones industrial average index is studied using granger causality analysis with different time scales it is found that the singular value decomposition entropy has predictive power for the dow jones industrial average index for period less than one month but not for more than one month this shows how long the singular value decomposition entropy predicts the stock market that extends caraiani s result obtained in caraiani 2014 on the other hand the result also shows an essential characteristic of stock market as a chaotic dynamic system

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

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

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

tail probability approximations in the first order noncircular autoregression a saddlepoint expansion is derived for the cumulative distribution function of the least squares estimator of the autoregressive coefficient the new method is shown to be superior both analytically and numerically to many existing approximations unlike other methods the new approximation performs uniformly well over the whole range of the distribution including the extreme tail even when the sample size is as small as 10

dcca and dmca correlations of cryptocurrency markets abstract we examine the serial correlation structure of six liquid cryptocurrencies with a long data record bitcoin dash stellar litecoin monero and ripple with a use of the detrended cross correlation dcca and detrending moving average cross correlation dmca correlation coefficients we find that these cryptocurrencies behave differently from the stock markets which are much closer to the random walk efficient dynamics we further discuss issues connected to strong statements about cryptocurrency markets practical inefficiency

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

solvability of the divergence equation implies john via poincare inequality abstract let r 2 be a bounded simply connected domain we show that for a fixed every p 1 the divergence equation div v f is solvable in w 0 1 p 2 for every f l 0 p if and only if is a john domain if and only if the weighted poincare inequality u x u q d x c u x q dist x q d x holds for some every q 1 this gives a positive answer to a question raised by russ 2013 in the case of bounded simply connected domains in higher dimensions similar results are proved under some additional assumptions on the domain in question

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

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

solutions of the divergence operator on john domains if rn is a bounded domain the existence of solutions u w01 p of divu f for f lp with vanishing mean value and 1 p is a basic result in the analysis of the stokes equations it is known that the result holds when is a lipschitz domain and that it is not valid for domains with external cusps in this paper we prove that the result holds for john domains our proof is constructive the solution u is given by an explicit integral operator acting on f to prove that u w01 p we make use of the calderon zygmund singular integral operator theory and the hardy littlewood maximal function for domains satisfying the separation property introduced in s buckley p koskela sobolev poincare implies john math res lett 2 5 1995 577 593 and 1 p n we also prove a converse result thus characterizing in this case the domains for which a continuous right inverse of the divergence exists in particular our result applies to simply connected planar domains because they satisfy the separation property

quantifying the cross correlations between online searches and bitcoin market abstract in this paper we quantify the cross correlations between google trends and bitcoin market by employing the multifractal detrended cross correlation analysis mf dcca method we find that the change of google trends cgt and bitcoin market i e returns and changes of volume are overall significantly cross correlated based on the cross correlation test in particular the empirical results show that 1 there exist power law cross correlations between cgt and bitcoin returns as well as cgt and changes of volume 2 the cross correlations between cgt and returns have a higher degree of multifractal in the long term and weak multifractal in the short term while the cross correlations between cgt and change of volume show the opposite trend 3 with the rolling window analysis we further find that there is a decrease trend for the cross correlations between cgt and bitcoin returns over time and the cross correlations scaling exponents are less than 0 5 which indicate that they are both anti persistent cross correlated

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

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

uniformly fat sets in this paper we study closed sets e which are locally uniformly fat with respect to a certain nonlinear riesz capacity we show that e is actually locally uniformly fat with respect to a weaker riesz capacity two applications of this result are given the first application is concerned with proving sobolev type inequalities in domains whose complements are uniformly fat the second application is concerned with the fekete points of e introduction let x x x2 x be a point in euclidean n space rn with jxl the norm of x for a 0 let i x ixi a n denote the riesz kernel of order a and put i f x f ix y f n f y dy x e r rn ic u x fr yj c n d u y x e r rn when f is a lebesgue integrable function and u a borel measure on rn here dy denotes lebesgue measure on rn if e c rn 0 1 define the a p outer riesz capacity of e by ra p e inf jfllfp ia f 1 on el where if lip is the lebesgue p norm of f we note that a 1 p 2 is the classical newtonian capacity if ap n we let rc p e inf jfjjf j f 1 on el where jc is the truncated riesz kernel defined by je x ixi a n 100 a n x 100 0 lxl 100 we shall say that a property holds a p quasi everywhere abbreviated a p q e on a set e if it holds on e except perhaps for a set of rop capacity zero next we list some properties of riesz capacities to simplify the writing we state these properties only for 0 u l p l 1 a p q e on e and p 1 a p q e on supp u c e moreover e jjli pi ujj rop e received by the editors march 11 1987 1980 mathematic3 subject cla33ification 1985 revi3ion primary 31c15 31b15 1988 american mathematical society 0002 9947 88 1 00 25 per page

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

multifractal detrended cross correlation analysis in the mena area abstract in this paper we investigated multifractal cross correlations qualitatively and quantitatively using a cross correlation test and the multifractal detrended cross correlation analysis method mf dcca for markets in the mena area we used cross correlation coefficients to measure the level of this correlation the analysis concerns four stock market indices of morocco tunisia egypt and jordan the countries chosen are signatory of the agadir agreement concerning the establishment of a free trade area comprising arab mediterranean countries we computed the bivariate generalized hurst exponent renyi exponent and spectrum of singularity for each pair of indices to measure quantitatively the cross correlations by analyzing the results we found the existence of multifractal cross correlations between all of these markets we compared the spectrum width of these indices we also found which pair of indices has a strong multifractal cross correlation

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

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

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

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

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

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 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

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

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

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

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

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

saddlepoint approximations for short and long memory time series a frequency domain approach abstract saddlepoint techniques provide numerically accurate small sample approximations to the distribution of estimators and test statistics except for a few simple models these approximations are not available in the framework of stationary time series we contribute to fill this gap under short or long range serial dependence for gaussian and non gaussian processes we show how to derive and implement saddlepoint approximations for two relevant classes of frequency domain statistics ratio statistics and whittle s estimator we compare our new approximations to the ones obtained by the standard asymptotic theory and by two widely applied bootstrap methods the numerical exercises for whittle s estimator show that our approximations yield accuracy s improvements while preserving analytical tractability a real data example concludes the paper

the inefficiency of cryptocurrency and its cross correlation with dow jones industrial average abstract as a form of cryptocurrency the issue of informational efficiency of bitcoin has received much attention recently we add to the literature by investigating nine forms of cryptocurrencies i e bitcoin ripple ethereum nem stellar litecoin dash monero and verge with a battery of efficiency tests and the empirical results indicate that all these cryptocurrencies are inefficient markets what is more we further construct a value weighted cryptocurrency composite index cci and show that cci and dow jones industrial average are persistently cross correlated

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

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

chaotic svd method for minimizing the effect of exponential trends in detrended fluctuation analysis abstract the detrended fluctuation analysis dfa and its extensions mf dfa have been used extensively to determine possible long range correlations in self affine signals however recent studies have reported the susceptibility of dfa to trends which give rise to spurious crossovers and prevent reliable estimation of the scaling exponents in this study a smoothing algorithm based on the chaotic singular value decomposition csvd is proposed to minimize the effect of exponential trends and distortion in the log log plots obtained by dfa techniques the effectiveness of the technique is demonstrated on monofractal and multifractal data corrupted with exponential trends

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

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

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

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

recurrence duration statistics and time dependent intrinsic correlation analysis of trading volumes a study of chinese stock indices abstract the trading volume in stock markets is known as an important variable which reflects the liquidity of the financial markets and therefore is regarded to be greatly important for the measurement of market liquidity risk in this work a new concept called recurrence duration is introduced for study of daily trading volumes which is inspired by idea of the volatility duration that was proposed and studied in our previous work the recurrence duration is thought as the shortest passing time that the following days trading volume takes to exceed or go below the current trading volume which is time varying similar to the volatility duration distribution of the price returns the power law function could describe the empirical probability distribution of recurrence durations of trading volumes and their tail distributions can be fitted by two stretched exponential functions further the correlation relationships of trading volumes between chinese stock indices as well as the correlations of recurrence durations are investigated one approach employed is a recently proposed method time dependent intrinsic correlation tdic which is based on the empirical mode decomposition emd to decompose nonlinear and nonstationary signals into the intrinsic mode functions imfs the instantaneous periods of which are used then in determination of the sizes of sliding windows to compute the running correlation coefficients for the multiscale signals the empirical results reveal rich patterns of correlations for both trading volumes and recurrence durations at different scales for different modes another approach is the widely used dcca cross correlation coefficient by which the level of cross correlation is measured for both original series and imf modes of the stock indices

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

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

saddlepoint expansions in finite population problems summary saddlepoint approximations are derived for the sample mean in the case where samples are obtained randomly without replacement from a finite population asymptotic properties are investigated the great accuracy is demonstrated by numerical examples extensions to more general statistics are discussed

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

random matrix theory and portfolio optimization in moroccan stock exchange abstract in this work we use random matrix theory to analyze eigenvalues and see if there is a presence of pertinent information by using marcenko pastur distribution thus we study cross correlation among stocks of casablanca stock exchange moreover we clean correlation matrix from noisy elements to see if the gap between predicted risk and realized risk would be reduced we also analyze eigenvectors components distributions and their degree of deviations by computing the inverse participation ratio this analysis is a way to understand the correlation structure among stocks of casablanca stock exchange portfolio

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

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

the application of the multifractal cross correlation analysis methods in radar target detection within sea clutter abstract many complex systems generate multifractal time series which are long range cross correlated this paper introduces three multifractal cross correlation analysis methods such as multifractal cross correlation analysis based on the partition function approach mfxpf multifractal detrended cross correlation analysis mfdcca methods based on detrended fluctuation analysis mfxdfa and detrended moving average analysis mfxdma which only consider one moment order we do comparative analysis of the artificial time series binomial multiplicative cascades and cantor sets with different probabilities by these methods then we do a feasibility test of the fixed threshold target detection within sea clutter by applying the multifractal cross correlation analysis methods to the ipix radar sea clutter data the results show that it is feasible to use the method of the fixed threshold based on the multifractal feature parameter f by the mfxpf and mfxdfa 1 methods at last we give the main conclusions and provide a valuable reference on how to choose the multifractal algorithms the detection parameters and the target detection methods within sea clutter in practice

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

quantifying the range of cross correlated fluctuations using a q l dependent ahxa coefficient abstract recently based on analogous height cross correlation analysis ahxa a cross correlation coefficient l has been proposed to quantify the levels of cross correlation on different temporal scales for bivariate series a limitation of this coefficient is that it cannot capture the full information of cross correlations on amplitude of fluctuations in fact it only detects the cross correlation at a specific order fluctuation which might neglect some important information inherited from other order fluctuations to overcome this disadvantage in this work based on the scaling of the q th order covariance and time delay l we define a two parameter dependent cross correlation coefficient q l to detect and quantify the range and level of cross correlations this new version of q l coefficient leads to the formation of a q l surface which not only is able to quantify the level of cross correlations but also allows us to identify the range of fluctuation amplitudes that are correlated in two given signals applications to the classical arfima models and the binomial multifractal series illustrate the feasibility of this new coefficient q l in addition a statistical test is proposed to quantify the existence of cross correlations between two given series applying our method to the real life empirical data from the 1999 2000 california electricity market we find that the california power crisis in 2000 destroys the cross correlation between the price and the load series but does not affect the correlation of the load series during and before the crisis

hardy sobolev spaces on strongly lipschitz domains of rn let be a strongly lipschitz domain of rn the hardy spaces hr1 and hz1 have been introduced by miyachi studia math 95 3 1990 205 jonsson et al studia math 80 2 1984 141 and chang et al j funct anal 114 1993 286 we first investigate spaces of functions in l1 whose gradients belong to hr1 or hz1 which we call hardy sobolev spaces following strichartz coll math 60 61 1 1990 129 secondly if l a is a uniformly elliptic second order divergence operator on with measurable complex coefficients subject to the dirichlet or the neumann boundary condition we compare the norms of l1 2f and f in suitable hardy spaces on depending on the boundary condition under the assumption that the heat kernel of l satisfies suitable estimates

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

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

cross correlations between the csi300 index and commodity markets non stationary principal component analysis nspca abstract 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 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

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

korn inequality on irregular domains abstract in this paper we study the weighted korn inequality on some irregular domains e g s john domains and domains satisfying quasihyperbolic boundary conditions examples regarding sharpness of the korn inequality on these domains are presented moreover we show that korn inequalities imply certain poincare inequality

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