can one make any crash prediction in finance using the local hurst exponent idea abstract we apply the hurst exponent idea for investigation of djia index time series data the behavior of the local hurst exponent prior to drastic changes in financial series signal is analyzed the optimal length of the time window over which this exponent can be calculated in order to make some meaningful predictions is discussed our prediction hypothesis is verified with examples of 1929 and 1987 crashes as well as with more recent phenomena in stock market from the period 1995 to 2003 some interesting agreements are found

poisson harmonic forms kostant harmonic forms and the s1 equivariant cohomology ofk t abstract we characterize the harmonic forms on a flag manifold k t defined by kostant in 1963 in terms of a poisson structure namely they are poisson harmonic with respect to the so called bruhat poisson structure on k t this enables us to give poisson geometrical proofs of many of the special properties of these harmonic forms in particular we construct explicit representatives for the schubert basis of the s 1 equivariant cohomology of k t where the s 1 action is defined by using a simple argument in equivariant cohomology we recover the connection between the kostant harmonic forms and the schubert calculus on k t that was found by kostant and kumar in 1986 by using a family of symplectic structures on k t we also show that the kostant harmonic forms are limits of the more familiar hodge harmonic forms with respect to a family of hermitian metrics on k t

multifractal hurst analysis of crude oil prices abstract daily records of international crude oil prices are studied using multifractal analysis methods rescaled range hurst analysis provides evidence that the crude oil market is a persistent process with long run memory effects on the other hand height height correlation analysis reveals evidence of multifractal structures in the sense that the crude oil dynamics displays mixing of rough hurst exponents the existence of two characteristic time scales in the order of weeks and quarters is discovered and the corresponding prices dynamics are extracted using moving average based filtering these results seem to demonstrate that the crude oil market is consistent with the random walk assumption only at time scales of the order of days to weeks a plausible oil price formation mechanism is discussed in terms of the market dynamics at three different time scales

poisson structures on complex flag manifolds associated with real forms for a complex semisimple lie group g and a real form go we define a poisson structure on the variety of borel subgroups of g with the property that all go orbits in x as well as all bruhat cells for a suitable choice of a borel subgroup of g are poisson submanifolds in particular we show that every non empty intersection of a go orbit and a bruhat cell is a regular poisson manifold and we compute the dimension of its symplectic leaves

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

the nil hecke ring and cohomology of g p for a kac moody group g abstract let g be the group with borel subgroup b associated to a kac moody lie algebra unk with weyl group w and cartan subalgebra unk then h g b has among others four distinguished structures i an algebra structure ii a distinguished basis given by the schubert cells iii a module for w and iv a module for hecke type operators aw for w unk w we construct a ring r which we refer to as the nil hecke ring which is very simply and explicitly defined as a functor of w together with the w module unk alone and such that all these four structures on h g b arise naturally from the ring r

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

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

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

a multifractal detrended fluctuation description of iranian rial us dollar exchange rate the miltifractal properties and scaling behaviour of the exchange rate variations of the iranian rial against the us dollar from a daily perspective is numerically investigated for this purpose the multifractal detrended fluctuation analysis mf dfa is used through multifractal analysis the scaling exponents generalized hurst exponents generalized fractal dimensions and singularity spectrum are derived moreover contribution of two major sources of multifractality that is fat tailed probability distributions and nonlinear temporal correlations are studied

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

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

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

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

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 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

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

analysis of the efficiency and multifractality of gold markets based on multifractal detrended fluctuation analysis abstract in this paper we investigate the efficiency and multifractality of a gold market based on multifractal detrended fluctuation analysis our evidence shows that the gold return series are multifractal both for time scales smaller than a month and for time scales larger than a month for time scales smaller than a month the main contribution of multifractality is fat tail distribution for time scales larger than a month both long range correlations and fat tail distribution play important roles in the contribution of multifractality using the method of rolling windows we find that the gold market became more and more efficient over time especially after 2001 the abnormal points of scaling exponents can also be related to some occasional events by defining a new inefficiency measure related to the multifractality we find that the gold market is more efficient during the upward periods than during the downward periods

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

on the derivation of guaranteed and p robust a posteriori error estimates for the helmholtz equation we propose a novel a posteriori error estimator for conforming finite element discretizations of two and three dimensional helmholtz problems the estimator is based on an equilibrated flux that is computed through the solve of patchwise mixed finite element problems we show that the estimator is reliable up to a prefactor that tends to one with mesh refinement or with polynomial degree increase we also derive a fully computable upper bound on this prefactor for several common settings of domains and boundary conditions leading to a guaranteed estimate in all wavenumber regimes without any assumption on the mesh size or the polynomial degree we finally demonstrate that the estimator is locally efficient as soon as the mesh exhibits sufficiently many degrees of freedom per wavelength in such a regime the estimator is also robust with respect to the polynomial degree we present numerical experiments that illustrate our analysis and indicate that our theoretical results are sharp

the poisson geometry of su 1 1 we study the natural poisson structure on the group su 1 1 and related questions in particular we give an explicit description of the ginzburg weinstein isomorphism for the sets of admissible elements we also establish an analog of thompson s conjecture for this group

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

long term memory in stock market prices a test for long term memory that is robust to short range dependence is developed it is a modification of the r s statistic and the relevant asymptotic sampling theory is derived via functional central limit theory contrary to previous findings when applied to daily and monthly stock returns indexes over several time periods this test yields no evidence of long range dependence once short range dependence is accounted for monte carlo experiments show that the modified r s test has power against at least two specific models of long term memory suggesting that models with short range dependence may adequately capture the behavior of historical stock returns copyright 1991 by the econometric society

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

fractionally integrated process for transition economics we analyze the european transition economics and show that many time series of major indices exhibit i power law correlations in their values ii power law correlations in their magnitudes and iii an asymmetric probability distribution applying the phase randomization procedure to these time series we show that magnitude correlations completely vanish we propose a stochastic model that can generate time series with features i ii and iii and we show by means of numerical simulations that this model is capable of reproducing these three features found in the empirical data

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

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

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

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

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

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

asymptotic exactness of the least squares finite element residual the discrete minimal least squares functional ls f u is equivalent to the squared error u u 2 in least squares finite element methods and so leads to an embedded reliable and efficient a

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

dynamic relationship between chinese rmb exchange rate index and market anxiety a new perspective based on mf dcca abstract this paper employs multifractal detrended cross correlation analysis mf dcca to study the cross correlations between the chinese rmb exchange rate index and market anxiety using data from june 21 2010 to december 28 2018 cross correlation statistics and coefficients verify the existence of cross correlations and the mf dcca method quantitatively confirms the presence of multifractality between the chinese rmb index and market anxiety for both the long and short term the results of the rolling window analysis reveal that cross correlation scaling exponents of the chinese rmb index and market anxiety are sensitive to external shocks

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

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

a short note on plain convergence of adaptive least squares finite element methods abstract we show that adaptive least squares finite element methods driven by the canonical least squares functional converge under weak conditions on pde operator mesh refinement and marking strategy contrary to prior works our plain convergence does neither rely on sufficiently fine initial meshes nor on severe restrictions on marking parameters finally we prove that convergence is still valid if a contractive iterative solver is used to obtain the approximate solutions e g the preconditioned conjugate gradient method with optimal preconditioner the results apply within a fairly abstract framework which covers a variety of model problems