detrended fluctuation analysis made flexible to detect range of cross correlated fluctuations the detrended cross correlation coefficient dcca has recently been proposed to quantify the strength of cross correlations on different temporal scales in bivariate nonstationary time series it is based on the detrended cross correlation and detrended fluctuation analyses dcca and dfa respectively and can be viewed as an analog of the pearson coefficient in the case of the fluctuation analysis the coefficient dcca works well in many practical situations but by construction its applicability is limited to detection of whether two signals are generally cross correlated without the possibility to obtain information on the amplitude of fluctuations that are responsible for those cross correlations in order to introduce some related flexibility here we propose an extension of dcca that exploits the multifractal versions of dfa and dcca multifractal detrended fluctuation analysis and multifractal detrended cross correlation analysis respectively the resulting new coefficient q not only is able to quantify the strength of correlations but also allows one to identify the range of detrended fluctuation amplitudes that are correlated in two signals under study we show how the coefficient q works in practical situations by applying it to stochastic time series representing processes with long memory autoregressive and multiplicative ones such processes are often used to model signals recorded from complex systems and complex physical phenomena like turbulence so we are convinced that this new measure can successfully be applied in time series analysis in particular we present an example of such application to highly complex empirical data from financial markets the present formulation can straightforwardly be extended to multivariate data in terms of the q dependent counterpart of the correlation matrices and then to the network representation

detrended fluctuation analysis based on higher order moments of financial time series in this paper a generalized method of detrended fluctuation analysis dfa is proposed as a new measure to assess the complexity of a complex dynamical system such as stock market we extend dfa and local scaling dfa to higher moments such as skewness and kurtosis labeled smdfa and kmdfa so as to investigate the volatility scaling property of financial time series simulations are conducted over synthetic and financial data for providing the comparative study we further report the results of volatility behaviors in three american countries three chinese and three european stock markets by using dfa and lsdfa method based on higher moments they demonstrate the dynamics behaviors of time series in different aspects which can quantify the changes of complexity for stock market data and provide us with more meaningful information than single exponent and the results reveal some higher moments volatility and higher moments multiscale volatility details that cannot be obtained using the traditional dfa method

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

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

on comparability and permutation graphs this paper presents a technique for orienting a comparability graph transitively in o n 2 time the best previous algorithm for this problem required omega n 3 time when combined with a result in sp we can recognize permutation graphs in o n 2 time and determine in the same time complexity whether two permutation graphs are isomorphic the orientation algorithm can also be used to reduce the problem of recognizing comparability graphs to that of recognizing transitive graphs this gives an upper bound of o n 2 49 for comparability graph recognition while the fastest previous algorithms required omega n 3 time

statistical analysis of digital images of periodic fibrous structures using generalized hurst exponent distributions abstract distinction of diverse two dimensional periodic structures can be based on a large number of methods and parameters while the quantitative description of differences between similar samples is usually difficult this article aims by the use of statistical random walk in a generalized q order dimensional space at introducing a methodology to qualify the networked structures on the basis of exemplary textile samples the presented results were obtained at 1 bit monochromatic maps obtained from optical microscopic pictures significant features of samples were represented by the obtained distributions of hurst exponents and shannon entropy calculations

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

multifractal detrended cross correlation analysis of carbon and crude oil markets abstract the complex dynamics between carbon and crude oil markets have been an increasingly interesting area of research in this paper we try to take a fresh look at the cross correlations between carbon and crude oil markets as well as their dynamic behavior employing multifractal detrended cross correlation analysis first we find that the return series of carbon and crude oil markets are significantly cross correlated second we confirm the existence of multifractality for the return series of carbon and crude oil markets by the multifractal detrended fluctuation analysis third based on the multifractal detrended cross correlation analysis we find the existence of power law cross correlations between carbon and crude oil markets the cross correlated behavior of small fluctuations is found to be more persistent than that of large fluctuations at last some relevant discussions and implications of the empirical results are presented

density level sets asymptotics inference and visualization abstractwe study the plug in estimator for density level sets under hausdorff loss we derive asymptotic theory for this estimator and based on this theory we develop two bootstrap confidence regions for level sets we introduce a new technique for visualizing density level sets even in multidimensions which is easy to interpret and efficient to compute supplementary materials for this article are available online

generalized density clustering we study generalized density based clustering in which sharply defined clusters such as clusters on lower dimensional manifolds are allowed we show that accurate clustering is possible even in high dimensions we propose two data based methods for choosing the bandwidth and we study the stability properties of density clusters we show that a simple graph based algorithm successfully approximates the high density clusters

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

detrended cross correlation analysis consistently extended to multifractality we propose an algorithm multifractal cross correlation analysis mfcca which constitutes a consistent extension of the detrended cross correlation analysis and is able to properly identify and quantify subtle characteristics of multifractal cross correlations between two time series our motivation for introducing this algorithm is that the already existing methods like multifractal extension have at best serious limitations for most of the signals describing complex natural processes and often indicate multifractal cross correlations when there are none the principal component of the present extension is proper incorporation of the sign of fluctuations to their generalized moments furthermore we present a broad analysis of the model fractal stochastic processes as well as of the real world signals and show that mfcca is a robust and selective tool at the same time and therefore allows for a reliable quantification of the cross correlative structure of analyzed processes in particular it allows one to identify the boundaries of the multifractal scaling and to analyze a relation between the generalized hurst exponent and the multifractal scaling parameter ensuremath lambda q this relation provides information about the character of potential multifractality in cross correlations and thus enables a deeper insight into dynamics of the analyzed processes than allowed by any other related method available so far by using examples of time series from the stock market we show that financial fluctuations typically cross correlate multifractally only for relatively large fluctuations whereas small fluctuations remain mutually independent even at maximum of such cross correlations finally we indicate possible utility of mfcca to study effects of the time lagged cross correlations

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

exponentially decayed double power law distribution of bitcoin trade sizes abstract bitcoin is the most important cryptocurrency that leads the cryptocurrency market the 776 629 356 bitcoin trades from 3 january 2009 to 31 december 2017 are retrieved it is found that the medium and large trade sizes comply with the exponentially decayed double power law distribution the tail exponent 1 of the medium trade sizes fluctuates in 2009 increases during the period from 2011 to 2014 and then converges to a stable level at 1 0 266 0 127 the tail exponent 2 of the large trade sizes fluctuates more and we have 2 1 752 1 688

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

planar stage graphs characterizations and applications abstract we consider combinatorial and algorithmic aspects of the well known paradigm killing two birds with one stone we define a stage graph as follows vertices are points from planar point set and u u is an edge if and only if the infinite straight line segment joining u to u intersects a given line segment called a stage we show that a graph is a stage graph if and only if it is a permutation graph the characterization results in a compact linear space representation of stage graphs this has been exploited for designing improved algorithms for maximum matching in permutation graphs two processor task scheduling for dependency graphs known to be permutation graphs and dominance related problems for planar point sets we show that a maximum matching in permutation graphs can be computed in q nlog n time where n is the number of vertices we provide simple optimal sequential and parallel algorithms for several dominance related problems for planar point sets

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

stability of density based clustering high density clusters can be characterized by the connected components of a level set l x p x of the underlying probability density function p generating the data at some appropriate level 0 the complete hierarchical clustering can be characterized by a cluster tree t l in this paper we study the behavior of a density level set estimate l and cluster tree estimate t based on a kernel density estimator with kernel bandwidth h we define two notions of instability to measure the variability of l and t as a function of h and investigate the theoretical properties of these instability measures

multifractal detrended fluctuation analysis of nonstationary time series abstract we develop a method for the multifractal characterization of nonstationary time series which is based on a generalization of the detrended fluctuation analysis dfa we relate our multifractal dfa method to the standard partition function based multifractal formalism and prove that both approaches are equivalent for stationary signals with compact support by analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series by comparing the multifractal dfa results for original series with those for shuffled series we can distinguish multifractality due to long range correlations from multifractality due to a broad probability density function we also compare our results with the wavelet transform modulus maxima method and show that the results are equivalent

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

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

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

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

convergence rates for persistence diagram estimation in topological data analysis computational topology has recently seen an important development toward data analysis giving birth to the field of topological data analysis topological persistence or persistent homology appears as a fundamental tool in this field in this paper we study topological persistence in general metric spaces with a statistical approach we show that the use of persistent homology can be naturally considered in general statistical frameworks and that persistence diagrams can be used as statistics with interesting convergence properties some numerical experiments are performed in various contexts to illustrate our results

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

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

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

dcca cross correlation coefficients reveals the change of both synchronization and oscillation in eeg of alzheimer disease patients abstract alzheimer s disease ad is a degenerative disorder of neural system that affects mainly the older population recently many researches show that the eeg of ad patients can be characterized by eeg slowing enhanced complexity of the eeg signals and eeg synchrony in order to examine the neural synchrony at multi scales and to find a biomarker that help detecting ad in diagnosis detrended cross correlation analysis dcca of eeg signals is applied in this paper several parameters namely dcca coefficients in the whole brain dcca coefficients at a specific scale maximum dcca coefficient over the span of all time scales and the corresponding scale of such coefficients were extracted to examine the synchronization respectively the results show that dcca coefficients have a trend of increase as scale increases and decreases as electrode distance increases comparing dcca coefficients in ad patients with healthy controls a decrease of synchronization in the whole brain and a bigger scale corresponding to maximum correlation is discovered in ad patients the change of max correlation scale may relate to the slowing of oscillatory activities linear combination of max dcca coefficient and max correlation scale reaches a classification accuracy of 90 from the above results it is reasonable to conclude that dcca coefficient reveals the change of both oscillation and synchrony in ad and thus is a powerful tool to differentiate ad patients from healthy elderly individuals

sad and stock returns revisited nonlinear analysis based on mf dcca and granger test abstract using both multifractal detrended fluctuation analysis mf dfa and multifractal detrended cross correlation analysis mf dcca methods this paper examines the effects of seasonal affective disorder sad on stock returns in the chinese stock market we first separate stocks into small and large cap stocks according to market value and find that sad and these two stock return series are multifractal based on mf dfa moreover we employ mf dcca and show that the cross correlation between sad and stock returns is anti persistent and the cross correlation between sad and return of small cap stock is stronger than that between sad and return of large cap stock furthermore we find that long range correlation is the main source of multifractality in the cross correlations between sad and small cap stock while both long range correlation and fat tails contribute to the multifractality between sad and large cap stock finally utilizing nonlinear granger causality test we find that sad is the granger cause of stock returns not vice versa

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

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

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

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

minimax optimal level set estimation this paper describes a new methodology and associated theoretical analysis for rapid and accurate extraction of level sets of a multivariate function from noisy data the identification of the boundaries of such sets is an important theoretical problem with applications for digital elevation maps medical imaging and pattern recognition this problem is significantly different from classical segmentation because level set boundaries may not correspond to singularities or edges in the underlying function as a result segmentation methods which rely upon detecting boundaries would be potentially ineffective in this regime this issue is addressed in this paper through a novel error metric sensitive to both the error in the location of the level set estimate and the deviation of the function from the critical level hoeffding s inequality is used to derive a novel regularization term that is distinctly different from regularization methods used in conventional image denoising settings building upon this foundation it is possible to derive error performance bounds for the proposed estimator and demonstrate that it exhibits near minimax optimal error decay rates for large classes of level set problems the proposed method automatically adapts to the spatially varying regularity of both the boundary of the level set and the underlying function

fuzzy entropy complexity and multifractal behavior of statistical physics financial dynamics abstract the present paper introduces a novel stochastic statistical physics financial system by combining exclusion system with compound poisson process the financial system is a model concerning with price fluctuations derived from dissemination of trading attitudes of financial agents and random drastic jumps caused by exogenous economic factors respectively multifractal detrended cross correlation analysis and fuzzy entropy of simulation dataset are performed fractional fuzzy entropy based on fuzzy entropy method and fractional calculus is also developed to explore nonlinear complexity of the proposed model in the paper empirical results display that there are significant multifractality and fractal asymmetry in the proposed model and the complexity of return series increases when or increases correspondingly and same analyses for actual stock market dataset are comparatively investigated the conclusions reveal that the novel compound dynamics can reproduce various nonlinear behaviors of actual stock markets to a certain extent

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

assessment of 48 stock markets using adaptive multifractal approach abstract in this paper stock market comovements are examined using cointegration granger causality tests and nonlinear approaches in context of mutual information and correlations since underlying data sets are affected by non stationarities and trends we also apply adaptive multifractal detrended fluctuation analysis amf dfa and adaptive multifractal detrended cross correlation analysis amf dxa we find only 170 pair of stock markets cointegrated and according to the granger causality and mutual information we realize that the strongest relations lies between emerging markets and between emerging and frontier markets according to scaling exponent given by amf dfa h q 2 1 we find that all underlying data sets belong to non stationary process according to efficient market hypothesis emh only 8 markets are classified in uncorrelated processes at 2 confidence interval 6 stock markets belong to anti correlated class and dominant part of markets has memory in corresponding daily index prices during january 1995 to february 2014 new zealand with h 0 457 0 004 and jordan with h 0 602 0 006 are far from emh the nature of cross correlation exponents based on amf dxa is almost multifractal for all pair of stock markets the empirical relation h x y h x x h y y 2 is confirmed mentioned relation for q 0 is also satisfied while for q 0 there is a deviation from this relation confirming behavior of markets for small fluctuations is affected by contribution of major pair for larger fluctuations the cross correlation contains information from both local internal and global external conditions width of singularity spectrum for auto correlation and cross correlation are x x 0 304 0 905 and x y 0 246 1 178 respectively the wide range of singularity spectrum for cross correlation confirms that the bilateral relation between stock markets is more complex the value of d c c a indicates that all pairs of stock market studied in this time interval belong to cross correlated processes

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

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

long range correlation analysis among non stationary passive scalar series in the turbulent boundary layer abstract in this paper we investigated the cross correlations among non stationary passive scalars series based on the detrended cross correlation analysis dcca we found that there existed long range cross correlations among these series the dcca exponents for each pair of passive scalars are all greater than 0 5 this implies that the cross correlation is persistent moreover the degree of cross correlation between h 2 o and pm 2 5 is greater compared to co2 and pm 2 5 as well as co2 and h 2 o the same analysis is also performed on randomly shuffled series the calculated dcca exponents fluctuate slightly over 0 5 which verifies that there indeed exist cross correlations among original series

exploring the dynamic relationship between crude oil price and implied volatility indices a mf dcca approach abstract this paper investigates the cross correlation between crude oil prices and implied volatility indices theinvestor s fear gauges using a cross correlation statistical test and multifractal detrended cross correlation analysis mf dcca the results show that the cross correlations between crude oil prices and three different implied volatility indices are multifractal by finding the crossover we separate the three pairs of series into the short and long term respectively and find that the cross correlations are strongly anti persistent in both short and long term moreover cross correlations of small and large fluctuations are anti persistent in the short and long term suggesting that crude oil prices and implied volatility indices are susceptible to each other we also find that the cross correlation exponents are less than the average generalized hurst exponent when q 0 in the short term and that the opposite results are true in the long term

a plug in approach to support estimation we suggest a new approach based on the use of density estimators for the problem of estimating the compact support of a multivariate density this subject motivated in terms of pattern analysis by grenander has interesting connections with detection and clustering a natural class of density based estimators is defined universal consistency results and convergence rates are established for these estimators with respect to the usual measure based metric d between sets further convergence rates with respect to both d and the hausdorff metric d h are also obtained under some fairly intuitive shape restrictions

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

volatility aggregation intensity energy futures series on stochastic finite range exclusion dynamics abstract the stochastic finite range exclusion process one of statistical physics systems is introduced to construct a new agent based financial price model to study the mechanism of market dynamics a novel volatility aggregation intensity vai time series describing the fluctuation aggregation intensity of the volatility series is developed for further investigating the nonlinear volatility behaviors in energy markets for studying the proposed vai series and the proposed price model the new york mercantile exchange energy futures data is selected and analyzed further cross correlation analysis auto correlation analysis with multiscale and multifractal detrended fluctuation analysis are applied to analyze the correlation volatility clustering and multifractal natures of the vai time series the empirical results show that the proposed model has the parallel behaviors with the authentic markets indicating that it is rational and available the new concept of vai series is of great value and can enrich the study of volatility behaviors in energy markets to some extent

algorithm to estimate the hurst exponent of high dimensional fractals we propose an algorithm to estimate the hurst exponent of high dimensional fractals based on a generalized high dimensional variance around a moving average low pass filter as working examples we consider rough surfaces generated by the random midpoint displacement and by the cholesky levinson factorization algorithms the surrogate surfaces have hurst exponents ranging from 0 1 to 0 9 with step 0 1 and different sizes the computational efficiency and the accuracy of the algorithm are also discussed

on nonparametric estimation of density level sets let x 1 x n be independent identically distributed observations from an unknown probability density f consider the problem of estimating the level set g g f x r 2 f x from the sample x 1 x n under the assumption that the boundary of g has a certain smoothness we propose piecewise polynomial estimators of g based on the maximization of local empirical excess masses we show that the estimators have optimal rates of convergence in the asymptotically minimax sense within the studied classes of densities we find also the optimal convergence rates for estimation of convex level sets a generalization to the n dimensional case where n 2 is given

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

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

computational geometry an introduction from the reviews this book offers a coherent treatment at the graduate textbook level of the field that has come to be known in the last decade or so as computational geometry the book is well organized and lucidly written a timely contribution by two founders of the field it clearly demonstrates that computational geometry in the plane is now a fairly well understood branch of computer science and mathematics it also points the way to the solution of the more challenging problems in dimensions higher than two

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

ising game nonequilibrium steady states of resource allocation systems abstract resource allocation systems are ubiquitous in the human society but how external fields affect the state of such systems remains poorly explored due to the lack of a suitable model because the behavior of spins pursuing energy minimization required by physical laws is similar to that of humans chasing payoff maximization studied in game theory here we combine the ising model with the market directed resource allocation game yielding an ising game based on the ising game we show theoretical simulative and experimental evidences for a formula which offers a clear expression of nonequilibrium steady states nesss interestingly the formula also reveals a convertible relationship between the external field exogenous factor and resource ratio endogenous factor and a class of saturation as the external field exceeds certain limits this work suggests that the ising game could be a suitable model for studying external field effects on resource allocation systems and it could provide guidance both for seeking more relations between nesss and equilibrium states and for regulating human systems by choosing nesss appropriately

u processes rates of convergence on introduit un nouveau processus stochastique une collection de statistiques u indicees par une famille de noyaux symetriques on obtient des conditions pour la convergence presque sure uniforme d une suite de tels processus

detrended partial cross correlation analysis of two nonstationary time series influenced by common external forces when common factors strongly influence two power law cross correlated time series recorded in complex natural or social systems using detrended cross correlation analysis dcca without considering these common factors will bias the results we use detrended partial cross correlation analysis dpxa to uncover the intrinsic power law cross correlations between two simultaneously recorded time series in the presence of nonstationarity after removing the effects of other time series acting as common forces the dpxa method is a generalization of the detrended cross correlation analysis that takes into account partial correlation analysis we demonstrate the method by using bivariate fractional brownian motions contaminated with a fractional brownian motion we find that the dpxa is able to recover the analytical cross hurst indices and thus the multiscale dpxa coefficients are a viable alternative to the conventional cross correlation coefficient we demonstrate the advantage of the dpxa coefficients over the dcca coefficients by analyzing contaminated bivariate fractional brownian motions we calculate the dpxa coefficients and use them to extract the intrinsic cross correlation between crude oil and gold futures by taking into consideration the impact of the u s dollar index we develop the multifractal dpxa mf dpxa method in order to generalize the dpxa method and investigate multifractal time series we analyze multifractal binomial measures masked with strong white noises and find that the mf dpxa method quantifies the hidden multifractal nature while the multifractal dcca method fails

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

detrended moving average partial cross correlation analysis on financial time series abstract cross correlations between nonlinear time series widely exist in complex systems it is of great importance to accurately measure the correlations between time series in this work we suggest a combination methodology of detrended moving average processing and partial cross correlation analysis to quantify the correlations between different time series which we call as detrended moving average partial cross correlation analysis d m p c c a this novel approach combines the advantages of detrended moving average processing and partial cross correlation analysis not only exploring power law cross correlations between two signals but removing underlying impacts of other signals on those two signals to demonstrate the advantages of this approach we carry out experiments with synthetic data generated by correlated processes and compare the performance of this measurement to traditional cross correlation techniques it is found that this method can reveal the real cross correlations between systems even when the indirect cross correlations established by other common factors exist then we go further study into the application of d m p c c a to financial time series in order to report its performance in stock markets and investigate cross correlations between different stock indices furthermore the rolling windows method is used in conjunction with d m p c c a to capture the changes of cross correlations between stock indices as time goes on we notice that there is a special period when d m p c c a coefficients between stock indices are obviously different from those of other periods

on the estimation of the gradient lines of a density and the consistency of the mean shift algorithm we consider the problem of estimating the gradient lines of a density which can be used to cluster points sampled from that density for example via the mean shift algorithm of fukunaga and hostetler 1975 we prove general convergence bounds that we then specialize to kernel density estimation

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

measuring mass concentrations and estimating density contour clusters an excess mass approach by using empirical process theory the so called excess mass approach is studied it can be applied to various statistical problems especially in higher dimensions such as testing for multimodality estimating density contour clusters estimating nonlinear functionals of a density density estimation regression problems and spectral analysis we mainly consider the problems of testing for multimodality and estimating density contour clusters but the other problems also are discussed the excess mass over mathbb c is defined as a supremum of a certain functional defined on mathbb c where mathbb c is a class of subsets of the d dimensional euclidean space comparing excess masses over different classes mathbb c yields information about the modality of the underlying probability measure f this can be used to construct tests for multimodality if f has a density f the maximizing sets of the excess mass are level sets or density contour clusters of f provided they lie in mathbb c the excess mass and the density contour clusters can be estimated from the data asymptotic properties of these estimators and of the test statistics are studied for general classes mathbb c including the classes of balls ellipsoids and convex sets

fully adaptive density based clustering the clusters of a distribution are often defined by the connected components of a density level set however this definition depends on the user specified level we address this issue by proposing a simple generic algorithm which uses an almost arbitrary level set estimator to estimate the smallest level at which there are more than one connected components in the case where this algorithm is fed with histogram based level set estimates we provide a finite sample analysis which is then used to show that the algorithm consistently estimates both the smallest level and the corresponding connected components we further establish rates of convergence for the two estimation problems and last but not least we present a simple yet adaptive strategy for determining the width parameter of the involved density estimator in a data depending way

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

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

cascading divide and conquer a technique for designing parallel algorithms techniques for parallel divide and conquer are presented resulting in improved parallel algorithms for a number of problems the problems for which improved algorithms are given include segment intersection detection trapezoidal decomposition and planar point location efficient parallel algorithms are algo given for fractional cascading three dimensional maxima two set dominance counting and visibility from a point all of the algorithms presented run in o log n time with either a linear or a sublinear number of processors in the crew pram model

consistency of single linkage for high density clusters abstract high density clusters are defined on a population with density f in r dimensions to be the maximal connected sets of form x f x c single linkage clustering is evaluated for consistency in detecting such high density clusters other standard hierarchical techniques such as average and complete linkage are hopelessly inconsistent for these clusters the asymptotic consistency of single linkage closely depends on the percolation problem of broadbent and hammersley if small spheres are removed at random from a solid at which density of spheres will water begin to flow through the solid if there is a single critical density such that no flow takes place below a certain density and flow occurs through a single connected set above that density then single linkage is consistent in separating high density clusters by disjoint single linkage clusters that include a positive fraction of sample points in the respective clusters and pass arbitrarily close to all points in the respective clusters

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

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

coupling detrended fluctuation analysis of the relationship between pm2 5 concentration and weather elements abstract pm2 5 pollution in china is getting worse the relationship between pm2 5 concentration and weather elements exhibits complex non linear feature therefore it is very important to study the sophisticated mathematical and nonlinear method about the relationship between pm2 5 concentration and weather elements coupling detrended fluctuation analysis cdfa method can reveal the multifractal properties of more than two series the coupled correlations between pm2 5 concentration and weather elements in hangzhou and guangzhou are explored by cdfa we find that coupled correlations are not only multifractal but also anti persistent compared with guangzhou hangzhou has stronger correlations both long range correlation and fat tailed distribution can cause the coupled multifractality and the long range correlation has a greater influence on the coupled multifractality in addition the coupling sensitivity degree csd y is used to study which weather element plays a key role in the change of pm2 5 concentration

cross correlations between price and volume in chinese gold markets abstract we apply the multifractal detrended cross correlation analysis mf dcca method to investigate the cross correlation behaviors between price and volume in chinese gold spot and futures markets qualitatively we find that the price and volume series are significantly cross correlated using the cross correlation test statistics q c c m and the d c c a coefficients quantitatively by employing the mf dcca analysis we find that there is a power law cross correlation and significant multifractal features between price and volume in gold spot and futures markets furthermore by comparing the multifractality of the original series to the shuffled and surrogated series we find that for the gold spot market the main contribution of multifractality is fat tail distribution for the gold futures market both long range correlations and fat tail distributions play important roles in the contribution of multifractality finally by employing the method of rolling windows we undertake further investigation into the time varying features of the cross correlations between price and volume we find that for both spot and futures markets the cross correlations are anti persistent in general in the short term the cross correlation shows obvious fluctuations due to exogenous shocks while in the long term the relationship tends to be at a metastable level due to the dynamic mechanism

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

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