modified multiscale cross sample entropy for complex time series we introduce the cmcse and further propose the rcmcse method mcse cmcse and rcmcse methods are employed to artificial and financial time series rcmcse reduces standard deviation and the probability of inducing undefined entropy rcmcse can provide better robustness and more accurate entropies rcmcse is more applicable for the study between us and chinese stock markets in this paper we introduce the composite multiscale cross sample entropy cmcse which may induce undefined entropies and then further propose the refined composite multiscale cross sample entropy rcmcse which modifies cmcse first we apply multiscale cross sample entropy mcse cmcse and rcmcse methods to three types of artificial time series in order to test the validity and accuracy of these methods results show that rcmcse reduces not only standard deviation but also the probability of inducing undefined entropy effectively which can provide better robustness and more accurate entropies then these three methods are employed to investigate financial time series including us and chinese stock indices for the study between stock indices in the same region some conclusions which are consistent with previous study are drawn by the rcmcse results meanwhile it can be found that undefined entropies are induced and the numbers of inducing undefined entropy by three methods for investigation between three us stock indices and two chinese mainland stock indices are given compared with mcse and cmcse rcmcse method is capable of reducing the number of undefined entropy and providing more accurate entropies moreover the differences on inducing undefined entropy between results for us stock indices two chinese mainland stock indices and results for us stock indices hsi demonstrate a much closer relation between us stock markets and hsi than between us stock markets and two chinese mainland stock markets hence it can be concluded that rcmcse is more applicable for the study between us and chinese stock markets

on the interplay between short and long term memory in the power law cross correlations setting abstract we focus on emergence of the power law cross correlations from processes with both short and long term memory properties in the case of correlated error terms the power law decay of the cross correlation function comes automatically with the characteristics of separate processes bivariate hurst exponent is then equal to an average of separate hurst exponents of the analyzed processes strength of short term memory has no effect on these asymptotic properties implications of these findings for the power law cross correlations concept are further discussed

cross correlations between baltic dry index and crude oil prices this paper examines the cross correlation properties of baltic dry index bdi and crude oil prices using cross correlation statistics test and multifractal detrended cross correlation analysis mf dcca the empirical results show that the cross correlations between bdi and crude oil prices are significantly multifractal by introducing the concept of a crossover we find that the cross correlations are strongly persistent in the short term and weakly anti persistent in the long term moreover cross correlations of all kinds of fluctuations are persistent in the short time while cross correlations of small fluctuations are persistent and those of large fluctuations are anti persistent in the long term we have also verified that the multifractality of the cross correlations of bdi and crude oil prices is both attributable to the persistence of fluctuations of time series and fat tailed distributions

a study on improvisation in a musical performance using multifractal detrended cross correlation analysis abstract mfdfa the most rigorous technique to assess multifractality was performed on four hindustani music samples played on same raga sung by the same performer each music sample was divided into six parts and multifractal spectral width was determined for each part corresponding to the four samples the results obtained reveal that different parts of all the four sound signals possess spectral width of widely varying values this gives a cue of the so called musical improvisation in all music samples keeping in mind they belong to the bandish part of the same raga formal compositions in hindustani raga are juxtaposed with the improvised portions where an artist manoeuvers his her own creativity to bring out a mood that is specific for that particular performance which is known as improvisation further this observation hints at the association of different emotions even in the same bandish of the same raga performed by the same artist this interesting observation cannot be revealed unless rigorous non linear technique explores the nature of musical structure in the second part we applied mfdxa technique to explore more in depth about improvisation and association with emotion this technique is applied to find the degree of cross correlation x between the different parts of the samples pronounced correlation has been observed in the middle parts of the all the four samples evident from higher values of x whereas the other parts show weak correlation this gets further support from the values of spectral width from different parts of the sample width of those parts is significantly different from other parts this observation is extremely new both in respect of musical structure of so called improvisation and associated emotion the importance of this study in application area of cognitive music therapy is immense

multifractal detrended cross correlation analysis on benchmark cryptocurrencies and crude oil prices abstract in this paper we investigate the cross correlations between three benchmark cryptocurrencies including bitcoin ethereum and ripple and some of the well known crude oils west texas intermediate and brent the data of the study spans from 7 august 2015 to 10 june 2019 we utilized the multifractal detrending moving average cross correlation analysis mf x dma method to examine the multifractal features among data we find that the cross correlations between each pair of time series are significant by using the cross correlation test statistic q c c m analysis and detrended moving average cross correlation analysis dmca coefficient also the cross correlation coefficients d m c a show that the data are positively correlated but the degree of correlation has been elevated by increasing the window intervals v the observed results obtained through the mf x dma method infer the existence of multifractal cross correlations on ten bivariate time series in the study and that the strength of multifractality between ethereum and ripple is the highest followed by the strength of multifractality between wti crude oil and ethereum

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

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

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

on weak convergence implying strong convergence under extremal conditions it is well known that under suitable extreme point conditions for the limit function weak convergence in an l1 space can imply strong convergence t rzezuchowski bull austral math soc 39 1989 201 214 has shown that a similar phenomenon can occur under an extremal subset condition we generalize his result in several respects by means of the associated young measures similar to the analysis given in e j balder bull austral math soc 33 1986 363 368

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

multifractal properties of price change and volume change of stock market indices abstract we study auto correlations and cross correlations of daily price changes and daily volume changes of thirteen global stock market indices using multifractal detrended fluctuation analysis mf dfa and multifractal detrended cross correlation analysis mf dxa we find rather distinct multifractal behavior of price and volume changes our results indicate that the time series of price changes are more complex than those of volume changes and that large fluctuations dominate multifractal behavior of price changes while small fluctuations dominate multifractal behavior of volume changes we also find that there is an absence of correlations in price changes there are anti persistent long term correlations in volume changes and there are anti persistent long term cross correlations between price and volume changes shuffling the series reveals that multifractality of both price changes and volume changes arises from a broad probability density function

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

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

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

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

detrending moving average based bivariate regression estimator in this work a detrending moving average dma based bivariate linear regression analysis method is proposed the method is combination of detrended moving average analysis and standard regression methodology which allows us to estimate the scale dependent regression coefficients for nonstationary and power law correlated time series by using synthetic simulations with error of estimation for different position parameter ensuremath theta of detrending windows we test our dma based bivariate linear regression algorithm and find that the centered detrending technique ensuremath theta 0 5 is of best performance which provides the most accurate estimates in addition the estimated regression coefficients are in good agreement with the theoretical values the center dma based bivariate linear regression estimator is applied to analyze the return series of shanghai stock exchange composite index the hong kong hangseng index and the nikkei 225 index the dependence among the asian stock market across timescales is confirmed furthermore two statistics based on the scale dependent t statistic and the partial detrending moving average cross correlation coefficient are used to demonstrate the significance of the dependence the scale dependent evaluation parameters also show that the dma based bivariate regression model can provide rich information than standard regression analysis

statistical properties of the yuan exchange rate index abstract we choice the yuan exchange rate index based on a basket of currencies as the effective exchange rate of the yuan and investigate the statistical properties of the yuan exchange rate index after china s exchange rate system reform on the 21st july 2005 after dividing the time series into two parts according to the change in the yuan exchange rate regime in july 2008 we compare the statistical properties of the yuan exchange rate index during these two periods we find that the distribution of the two return series has the exponential form we also perform the detrending moving average analysis dma and the multifractal detrending moving average analysis mfdma the two periods possess different degrees of long range correlations and the multifractal nature is also unveiled in these two time series significant difference is found in the scaling exponents q and singularity spectra f of the two periods obtained from the mfdma analysis besides in order to detect the sources of multifractality shuffling and phase randomization procedures are applied to destroy the long range temporal correlation and fat tailed distribution of the yuan exchange rate index respectively we find that the fat tailedness plays a critical role in the sources of multifractality in the first period while the long memory is the major cause in the second period the results suggest that the change in china s exchange rate regime in july 2008 gives rise to the different multifractal properties of the yuan exchange rate index in these two periods and thus has an effect on the effective exchange rate of the yuan after the exchange rate reform on the 21st july 2005

computation of unsteady flowfield over a hydrofoil including boundary layer and wake a time accurate two dimensional semi implicit pressure based navier stokes solver for incompressibleows is used to carry out the numerical simulation of the unsteadyow over a hydrofoil a low reynolds number form of the two equation turbulence model is used to account for the turbulence effects to improve the accuracy of the numerical scheme a central differencing plus arti cial dissipation scheme is implemented to provide a precise control of the numerical dissipation an inner loop iteration scheme is used at each time step to account for the nonlinear effects the information on the upstream time dependentow is speci ed from the experimental data the results show that the characteristics of theunsteady boundary layersalong the foil surfaces are predicted very well by the numerical method including the amplitude of the velocityuctuation and the phase angle changes as well asow features near the surfaces the instantaneousow eld is presented at various locations along the hydrofoil surfaces and downstream of the hydrofoil both the computational and experimental results are interpreted to improve physical understanding of theow phenomena inside unsteady boundary layers

multiscale multifractal detrended fluctuation analysis of multivariate time series abstract this work extends the multivariate multifractal detrended fluctuation analysis mv mfdfa method to multiscale case named multiscale multivariate multifractal detrended fluctuation analysis mmv mfdfa the benefits of the proposed approach are illustrated by numerical simulations on synthetic multivariate processes furthermore the proposed mmv mfdfa method is applied to the fractal auto correlation analysis of six pollutants pm2 5 pm10 so2 no2 co and o3 hourly data in different seasons the results show that the seasonal periodicity has robust impact on the auto correlation of pollutants in spring and summer besides we also find that the pollutants in the four seasons possess strong multifractal auto correlation nature even after the removal of the seasonal pattern finally the source of multifractality among more than two series is also discussed and some interesting results are obtained pm2 5 not only dominates the underlying evolution process in fall and winter but also is more correlated to the other pollutants than the other ones to each other except in spring the proposed mmv mfdfa methodology can provide reliable ways of measuring the fractal auto correlation properties of multivariate series and it can be applied to any system with multiple data channels

the exceedance and cross correlations between the gold spot and futures markets abstract this paper investigates the dynamic features of cross correlations and exceedance correlations between comex gold spot and futures returns using the detrended cross correlation analysis dcca and a test for symmetrical exceedance correlation first we examine the cross correlations both qualitatively and quantitatively by employing the cross correlations test and the dcca method we find that the cross correlations are significant for all lagged orders and are weakly persistent our results from a rolling sample test also show that some exogenous events can apparently affect the cross correlations between gold spot and futures returns second after employing the test statistic our empirical results show that the exceedance correlations between spot and futures returns are both positive and symmetric indicating that the two returns co move in the same direction and that the correlations between them are symmetrical for the upper and lower of the returns however the results from the rolling sample show that occasional events can induce significant asymmetries of exceedance correlations

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

multivariate large deviations spectrum for the multiscale analysis of stock markets abstract we extend the classical roughness exponent detrended fluctuation analysis into multivariate signals aiming at detecting the effectiveness and advantages of the multivariate multifractal detrended fluctuation analysis mmdfa based large deviations spectrum results show that large deviations spectrum is sensitive to non concavities and contains more information than the legendre spectrum further we investigate the large deviations spectrum for stock markets with the closing prices and volumes volumes have a tendency of scale invariance for global markets we construct 9 univariate series and 3 multivariate time series separately for asia europe and america and quantify the scale invariance and generating mechanism of multifractality for multivariate stock markets through comparison it is shown that markets of the same region have a more similar evolution and the q ranges for slope in the fit process are different from each other for both univariate and multivariate situations besides european markets have better scaling properties

multifractal detrended cross correlation analysis of genome sequences using chaos game representation abstract we characterized the multifractal nature and power law cross correlation between any pair of genome sequence through an integrative approach combining 2d multifractal detrended cross correlation analysis and chaos game representation in this paper we have analyzed genomes of some prokaryotes and calculated fractal spectra h q and f from our analysis we observed existence of multifractal nature and power law cross correlation behavior between any pair of genome sequences cluster analysis was performed on the calculated scaling exponents to identify the class affiliation and the same is represented as a dendrogram we suggest this approach may find applications in next generation sequence analysis big data analytics etc

time singularity multifractal spectrum distribution based on detrended fluctuation analysis abstract the time singularity multifractal spectrum distribution ts mfsd generalizes the singularity spectrum in a time varying framework in this paper a new method to compute mfsd based on detrended fluctuation analysis dfa mfsd is introduced we relate dfa mfsd method to the standard partition function based multifractal spectrum distribution formalism and prove that both approaches are equivalent for fractal time series with compact support furthermore we find that dfa mfsd has equivalent results better mathematic foundation less computational cost and is more adapted for fractal time series with arbitrary length compared with mfsd based on wavelet transform modulus maxima wtmm mfsd by analyzing several examples this paper shows that dfam mfsd with different polynomial fitting orders can reliably determine the time varying multifractal scaling behavior of time series including processes embodying chirp type or oscillating singularities to illustrate these results simulations are executed using binomial multiplicative cascades wavelet series and real sea clutter and simulations indicate that dfa m mfsd benefits from excellent theoretical and practical performances

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

modified detrended fluctuation analysis based on empirical mode decomposition for the characterization of anti persistent processes abstract detrended fluctuation analysis dfa is a simple but very efficient method for investigating the power law long term correlations of non stationary time series in which a detrending step is necessary to obtain the local fluctuations at different timescales we propose to determine the local trends through empirical mode decomposition emd and perform the detrending operation by removing the emd based local trends which gives an emd based dfa method similarly we also propose a modified multifractal dfa algorithm called an emd based mfdfa the performance of the emd based dfa and mfdfa methods is assessed with extensive numerical experiments based on fractional brownian motion and multiplicative cascading process we find that the emd based dfa method performs better than the classic dfa method in the determination of the hurst index when the time series is strongly anticorrelated and the emd based mfdfa method outperforms the traditional mfdfa method when the moment order q of the detrended fluctuations is positive we apply the emd based mfdfa to the 1 min data of shanghai stock exchange composite index and the presence of multifractality is confirmed we also analyze the daily austrian electricity prices and confirm its anti persistence

china s soybean crush spread nonlinear analysis based on mf dcca abstract in this paper we investigate cross correlations among the soybean soymeal and soyoil futures return series at china s dalian commodity exchange using both multifractal detrended fluctuation analysis mf dfa and multifractal detrended cross correlation analysis mf dcca methods we find that there exists multifractality in the soybean soymeal and soyoil futures return series using mf dfa method moreover results of mf dcca demonstrate that there exists a power law cross correlation and significant multifractal features among soybean soymeal and soyoil futures returns furthermore by comparing the multifractality of the original series to the shuffled and surrogated series we find that both the long range correlations and fat tailed distribution contribute to the multifractality in cross correlation among soybean soymeal and soyoil futures return series in dalian commodity exchanges furthermore we use nonlinear granger causality test and show that anyone of the three products returns is the granger cause of the other two products returns

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

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

on the scaling ranges of detrended fluctuation analysis for long term memory correlated short series of data abstract we examine the scaling regime for the detrended fluctuation analysis dfa the most popular method used to detect the presence of long term memory in data and the fractal structure of time series first the scaling range for dfa is studied for uncorrelated data as a function of time series length l and the correlation coefficient of the linear regression r 2 at various confidence levels next a similar analysis for artificial short series of data with long term memory is performed in both cases the scaling range is found to change linearly both with l and r 2 we show how this dependence can be generalized to a simple unified model describing the relation l r 2 h where h 1 2 h 1 stands for the hurst exponent of the long range autocorrelated signal our findings should be useful in all applications of dfa technique particularly for instantaneous local dfa where a huge number of short time series has to be analyzed at the same time without possibility of checking the scaling range in each of them separately

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

the informativeness of options trading activities non linear analysis based on mf dcca and granger test abstract using both put call ratio p c and option to stock volume ratio o s as measures of options trading activities this paper investigates the information content of sse 50 etf options we begin by using detrended fluctuation analysis mf dfa method to examine the multifractal properties of p c ratio change series o s ratio change series and etf returns and find that these time series exhibit strong multifractality moreover employing multifractal detrended cross correlation analysis mf dcca we show that there exists strong anti persistent cross correlation between p c ratios and 50 etf returns but no significant cross correlation between o s ratios and 50 etf returns suggesting that p c ratio is more pronounced detecting the information content of options furthermore we use nonlinear granger causality test and show that the granger causality relationships between p c ratio and 50 etf return series is more significant and stronger than that between o s ratio and 50 etf return series our findings imply that p c ratio can better capture the informativeness of options

multifractal detrended cross correlation analysis on gold crude oil and foreign exchange rate time series abstract we apply the recently developed multifractal detrended cross correlation analysis method to investigate the cross correlation behavior and fractal nature between two non stationary time series we analyze the daily return price of gold west texas intermediate and brent crude oil foreign exchange rate data over a period of 18 years the cross correlation has been measured from the hurst scaling exponents and the singularity spectrum quantitatively from the results the existence of multifractal cross correlation between all of these time series is found we also found that the cross correlation between gold and oil prices possess uncorrelated behavior and the remaining bivariate time series possess persistent behavior it was observed for five bivariate series that the cross correlation exponents are less than the calculated average generalized hurst exponents ghe for q 0 and greater than ghe when q 0 and for one bivariate series the cross correlation exponent is greater than ghe for all q values

measuring daily value at risk of ssec index a new approach based on multifractal analysis and extreme value theory abstract recent studies in the econophysics literature reveal that price variability has fractal and multifractal characteristics not only in developed financial markets but also in emerging markets taking high frequency intraday quotes of the shanghai stock exchange component ssec index as example this paper proposes a new method to measure daily value at risk var by combining the newly introduced multifractal volatility mfv model and the extreme value theory evt method two var backtesting techniques are then employed to compare the performance of the model with that of a group of linear and nonlinear generalized autoregressive conditional heteroskedasticity garch models the empirical results show the multifractal nature of price volatility in chinese stock market var measures based on the multifractal volatility model and evt method outperform many garch type models at high risk levels

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

direct determination approach for the multifractal detrending moving average analysis in the canonical framework we propose an alternative approach for the multifractal analysis based on the detrending moving average method mf dma we define a canonical measure such that the multifractal mass exponent q is related to the partition function and the multifractal spectrum f can be directly determined the performances of the direct determination approach and the traditional approach of the mf dma are compared based on three synthetic multifractal and monofractal measures generated from the one dimensional p model the two dimensional p model and the fractional brownian motions we find that both approaches have comparable performances to unveil the fractal and multifractal nature in other words without loss of accuracy the multifractal spectrum f can be directly determined using the new approach with less computation cost we also apply the new mf dma approach to the volatility time series of stock prices and confirm the presence of multifractality

discrete scale invariance in cross correlations between time series abstract the de trended cross correlation analysis dcca is converted to a new form which turns out to be a periodic function modulated power law to evaluate discrete scale long range cross correlation between time series if the modulator is dominated with one frequency the derived form will degenerate to a log periodic power law we investigate a total of five important stock markets distributing in different continents calculations show that the cross correlations between different stock markets may hint at log periodic oscillations this finding may be helpful for us to evaluate financial state in a global way

multifractal detrended cross correlation analysis of coding and non coding dna sequences through chaos game representation abstract we propose a new approach combining the chaos game representation and the two dimensional multifractal detrended cross correlation analysis methods to examine multifractal behavior in power law cross correlation between any pair of nucleotide sequences of unequal lengths in this work we analyzed the characteristic behavior of coding and non coding dna sequences of eight prokaryotes the results show the presence of strong multifractal nature between coding and non coding sequences of all data sets we found that this integrative approach helps us to consider complete dna sequences for characterization and further it may be useful for classification clustering identification of class affiliation of nucleotide sequences etc with high precision

efficiency and multifractality analysis of csi 300 based on multifractal detrending moving average algorithm abstract we apply the multifractal detrending moving average mfdma to investigate and compare the efficiency and multifractality of 5 min high frequency china securities index 300 csi 300 the results show that the csi 300 market becomes closer to weak form efficiency after the introduction of csi 300 future we find that the csi 300 is featured by multifractality and there are less complexity and risk after the csi 300 index future was introduced with the shuffling surrogating and removing extreme values procedures we unveil that extreme events and fat distribution are the main origin of multifractality besides we discuss the knotting phenomena in multifractality and find that the scaling range and the irregular fluctuations for large scales in the f q s vs s plot can cause a knot

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

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

using renyi parameter to improve the predictive power of singular value decomposition entropy on stock market abstract this paper generalizes the method of traditional singular value decomposition entropy by incorporating orders q of renyi entropy we analyze the predictive power of the entropy based on trajectory matrix using shanghai composite index and dow jones index data in both static test and dynamic test in the static test on sci results of global granger causality tests all turn out to be significant regardless of orders selected but this entropy fails to show much predictability in american stock market in the dynamic test we find that the predictive power can be significantly improved in sci by our generalized method but not in dji this suggests that noises and errors affect sci more frequently than dji in the end results obtained using different length of sliding window also corroborate this finding

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

multifractal analysis of the wti crude oil market us stock market and epu abstract this paper adopts multifractal methods to analyze the nonlinear correlations among economic policy uncertainty epu the crude oil market and the stock market first using multifractal detrended fluctuation analysis mf dfa we find that each of the three series shows multifractality and the sources of multifractality are all from long range correlations and fat tailed distributions however for the stock and oil price series the long range correlation has a greater impact while the fat tailed distribution contributes more to epu multifractality furthermore we apply multifractal detrended cross correlation analysis mf dcca to analyze the cross correlation multifractal features among the three series the generalized hurst exponents of any two series are significantly greater than 0 5 and the stock and oil price series have the strongest cross correlation values coupling detrended fluctuation cdfa analysis of the three series shows that the coupling correlation among the three sequences is also multifractal the chi squared statistic reveals that the contribution of the stock market to the multifractality of the coupling correlation is greater than that of other series and epu has the smallest influence on the coupling correlation finally we employ multiscale multifractal analysis mma to visualize the dynamic behaviors of the correlations among the series the results show that the cross correlation of stock with the oil price has some symmetry at small and large scale fluctuations additionally the influence of epu on the overall coupling features is mainly reflected under small scale fluctuations and at large scales the coupling correlation of the three series remains similar to the hurst surface of stock with the oil price these results are useful for building predictive models

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

binomial markov switching multifractal model with skewed t innovations and applications to chinese ssec index abstract this paper presents the binomial markov switching multifractal bmsm model of asset returns with skewed t innovations bmsm skewed t for short which considers the fat tails skewness and multifractality in asset returns simultaneously the parameters of bmsm skewed t model can be estimated by maximum likelihood ml methods and volatility forecasting can be accomplished via bayesian updating in order to evaluate the performance of bmsm skewed t model bmsm model with normal innovations bmsm n bmsm model with student t innovations bmsm t and garch 1 1 models garch n garch t and garch skewed t are chosen for comparison through empirical studies on shanghai stock exchange composite index ssec we find that for sample estimation bmsm models outperform the garch 1 1 models through bic and aic rules and bmsm skewed t performs the best among all the models due to its fat tails skewness and multifractality in addition bmsm skewed t model dominates other models at most forecasting horizons for out of sample volatility forecasts in terms of mse mae and spa test

a comparative study of two dimensional multifractal detrended fluctuation analysis and two dimensional multifractal detrended moving average algorithm to estimate the multifractal spectrum multifractal detrended fluctuation analysis mfdfa and multifractal detrended moving average mfdma algorithm have been established as two important methods to estimate the multifractal spectrum of the one dimensional random fractal signal they have been generalized to deal with two dimensional and higher dimensional fractal signals this paper gives a brief introduction of the two dimensional multifractal detrended fluctuation analysis 2d mfdfa and two dimensional multifractal detrended moving average 2d mfdma algorithm and a detailed description of the application of the two dimensional fractal signal processing by using the two methods by applying the 2d mfdfa and 2d mfdma to the series generated from the two dimensional multiplicative cascading process we systematically do the comparative analysis to get the advantages disadvantages and the applicabilities of the two algorithms for the first time from six aspects such as the similarities and differences of the algorithm models the statistical accuracy the sensitivities of the sample size the selection of scaling range the choice of the q orders and the calculation amount the results provide a valuable reference on how to choose the algorithm from 2d mfdfa and 2d mfdma and how to make the schemes of the parameter settings of the two algorithms when dealing with specific signals in practical applications

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