multifractal diffusion entropy analysis on stock volatility in financial markets abstract this paper introduces a generalized diffusion entropy analysis method to analyze long range correlation then applies this method to stock volatility series the method uses the techniques of the diffusion process and renyi entropy to focus on the scaling behaviors of regular volatility and extreme volatility respectively in developed and emerging markets it successfully distinguishes their differences where regular volatility exhibits long range persistence while extreme volatility reveals anti persistence

stable grothendieck polynomials and k theoretic factor sequences we formulate a nonrecursive combinatorial rule for the expansion of the stable grothendieck polynomials of fomin and kirillov proc formal power series alg comb 1994 in the basis of stable grothendieck polynomials for partitions this gives a common generalization as well as new proofs of the rule of fomin and greene discret math 193 565 596 1998 for the expansion of the stable schubert polynomials into schur polynomials and the k theoretic grassmannian littlewood richardson rule of buch acta math 189 1 37 78 2002 the proof is based on a generalization of the robinson schensted and edelman greene insertion algorithms our results are applied to prove a number of new formulas and properties for k theoretic quiver polynomials and the grothendieck polynomials of lascoux and schutzenberger c r acad sci paris ser i math 294 13 447 450 1982 in particular we provide the first k theoretic analogue of the factor sequence formula of buch and fulton invent math 135 3 665 687 1999 for the cohomological quiver polynomials

multifractal fluctuations in the survival probability of an open quantum system we predict a multifractal behavior of transport in the deep quantum regime for the opened kicked rotor model our analysis focuses on intermediate and large scale correlations in the transport signal and generalizes previously found parametric mono fractal fluctuations in the quantum survival probability on small scales

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

scale invariance analysis of the premature ecg signals abstract the multifractal detrended fluctuation analysis and detrending moving average algorithm were introduced in detail and applied to the study of the multifractal characteristics of the normal signals the atrial premature beat apb signals and the premature ventricular contraction pvc signals by analyzing the generalized hurst exponents renyi exponents and multifractal spectrum and comparing the relation of h h q for original signals and their shuffled time series the result indicated that the three signals have multifractality and present long range correlation in a certain range according to the mean value of we found that the strength of the multifractality is varying the pvc signals is the strongest and the normal signals is the weakest it is useful for clinical practice of medicine to distinguish apb signals with pvc signals

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

application of the detrended fluctuation analysis dfa method for describing cloud breaking abstract a method to sort out correlations and decorrelations in stratus cloud formation persistence and breakup is introduced the detrended fluctuation analysis dfa statistical method is applied to microwave radiometer data the existence of long range power law correlations in stratus cloud liquid water content fluctuations is demonstrated over a 2 h period moreover using a finite size time interval window a change from brownian to non brownian fluctuation regimes is clearly shown to define the cloud structure changes such findings are similar to those found in dna and financial data sequences when mosaics of persistent and antipersistent patches are present the occurrence of these statistics in stratus cloud liquid water content suggests the usefulness of similar studies on cloud resolving model output and for better meteorological predictability

blocks adjustment reduction of bias and variance of detrended fluctuation analysis using monte carlo simulation abstract the length of minimal and maximal blocks equally distant on log log scale versus fluctuation function considerably influences bias and variance of dfa through a number of extensive monte carlo simulations and different fractional brownian motion fractional gaussian noise generators we found the pair of minimal and maximal blocks that minimizes the sum of mean squared error of estimated hurst exponents for the series of length n 2 p p 7 15 sensitivity of dfa to sort range correlations was examined using arfima p d q generator due to the bias of the estimator for anti persistent processes we narrowed down the range of hurst exponent to 1 2 h 1

multifractal detrended fluctuation analysis for clustering structures of electricity price periods abstract a new model is proposed to investigate the structure of electricity price in different time periods a popular method the multifractal detrended fluctuation analysis mf dfa method is employed to analyze the features achieved from three types of electricity price data after filtering some trends by fourier detrended fluctuation function twelve multifractal parameters are calculated and selected as the characteristic indicators for comparison moreover the minimum number of indicators is determined so that the discriminant accuracy reaches maximum based on fisher s linear discriminant algorithm fisher s lda for each time period these indicators form a multi dimensional space in which each point represents a price time series this allows us to cluster the three price time periods namely the low price time periods the average price time periods and the peak price time periods fisher s lda is employed to evaluate the discriminant accuracy on these three kinds of time periods our analysis is then applied to the data in california1999 2000 and pjm2001 2002 electricity markets to demonstrate the applicability of our methods

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

refined composite multiscale weighted permutation entropy of financial time series abstract for quantifying the complexity of nonlinear systems multiscale weighted permutation entropy mwpe has recently been proposed mwpe has incorporated amplitude information and been applied to account for the multiple inherent dynamics of time series however mwpe may be unreliable because its estimated values show large fluctuation for slight variation of the data locations and a significant distinction only for the different length of time series therefore we propose the refined composite multiscale weighted permutation entropy rcmwpe by comparing the rcmwpe results with other methods results on both synthetic data and financial time series rcmwpe method shows not only the advantages inherited from mwpe but also lower sensitivity to the data locations more stable and much less dependent on the length of time series moreover we present and discuss the results of rcmwpe method on the daily price return series from asian and european stock markets there are significant differences between asian markets and european markets and the entropy values of hang seng index hsi are close to but higher than those of european markets the reliability of the proposed rcmwpe method has been supported by simulations on generated and real data it could be applied to a variety of fields to quantify the complexity of the systems over multiple scales more accurately

research on the relationship between the multifractality and long memory of realized volatility in the sseci abstract we examine the multifractal properties of the realized volatility rv and realized bipower variation rbv series in the shanghai stock exchange composite index sseci by using the multifractal detrended fluctuation analysis mf dfa method we find that there exist distinct multifractal characteristics in the volatility series the contributions of two different types of source of multifractality namely fat tailed probability distributions and nonlinear temporal correlations are studied by using the unit root test we also find the strength of the multifractality of the volatility time series is insensitive to the sampling frequency but that the long memory of these series is sensitive

integrated approach to the assessment of long range correlation in time series data to assess whether a given time series can be modeled by a stochastic process possessing long range correlation one usually applies one of two types of analysis methods the spectral method and the random walk analysis the first objective of this work is to show that each one of these methods used alone can be susceptible to producing false results we thus advocate an integrated approach which requires the use of both methods in a consistent fashion we provide the theoretical foundation of this approach and illustrate the main ideas using examples the second objective relates to the observation of long range anticorrelation hurst exponent hl1 2 in real world time series data the very peculiar nature of such processes is emphasized in light of the stringent condition under which such processes can occur using examples we discuss the possible factors that could contribute to the false claim of long range anticorrelations and demonstrate the particular importance of the integrated approach in this case

the scaling properties of stock markets based on modified multiscale multifractal detrended fluctuation analysis abstract here we propose the new method dh mma based on multiscale multifractal detrended fluctuation analysis mma to investigate the scaling properties in stock markets it is demonstrated that our approach can provide a more stable and faithful description of the scaling properties in comprehensive range rather than fixing the window length and slide length it allows the assessment of more universal and subtle scaling characteristics we illustrate dh mma by selecting power law artificial data sets and six stock markets from us and china the us stocks exhibit very strong multifractality for positive values of q however the chinese stocks show stronger multifractality for negative q than positive q in general the us stock markets show similar behaviors but chinese stock markets display distinguishing characteristics

method for generating long range correlations for large systems we propose a new method to generate a sequence of random numbers with long range power law correlations that overcomes known difficulties associated with large systems the new method presents an improvement on the commonly used methods we apply the algorithm to generate enhanced diffusion isotropic and anisotropic self affine surfaces and isotropic and anisotropic correlated percolation

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

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

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

multifractal detrended cross correlation analysis of sunspot numbers and river flow fluctuations abstract we use the detrended cross correlation analysis dcca to investigate the influence of sun activity represented by sunspot numbers on one of the climate indicators specifically rivers represented by river flow fluctuation for daugava holston nolichucky and french broad rivers the multifractal detrended cross correlation analysis mf dxa shows that there exist some crossovers in the cross correlation fluctuation function versus time scale of the river flow and sunspot series one of these crossovers corresponds to the well known cycle of solar activity demonstrating a universal property of the mentioned rivers the scaling exponent given by dcca for original series at intermediate time scale 12 24 s 130 months is 1 17 0 04 which is almost similar for all underlying rivers at 1 confidence interval showing the second universal behavior of river runoffs to remove the sinusoidal trends embedded in data sets we apply the singular value decomposition svd method our results show that there exists a long range cross correlation between the sunspot numbers and the underlying streamflow records the magnitude of the scaling exponent and the corresponding cross correlation exponent are 0 76 0 85 and 0 30 0 48 respectively different values for scaling and cross correlation exponents may be related to local and external factors such as topography drainage network morphology human activity and so on multifractal cross correlation analysis demonstrates that all underlying fluctuations have almost weak multifractal nature which is also a universal property for data series in addition the empirical relation between scaling exponent derived by dcca and detrended fluctuation analysis dfa h sun h river 2 is confirmed

universal scaling behaviors of meteorological variables volatility and relations with original records abstract volatility series defined as the magnitude of the increments between successive elements of five different meteorological variables over china are analyzed by means of detrended fluctuation analysis dfa for short universal scaling behaviors are found in all volatility records whose scaling exponents take similar distributions with similar mean values and standard deviations to reconfirm the relation between long range correlations in volatility and nonlinearity in original series dfa is also applied to the magnitude records defined as the absolute values of the original records the results clearly indicate that the nonlinearity of the original series is more pronounced in the magnitude series

is non gaussianity sufficient to produce long range volatile correlations abstract scaling analysis of the magnitude series volatile series has been proposed recently to identify possible non linear multifractal signatures in the given data y ashkenazy et al phys rev lett 86 2001 1900 y ashkenazy et al physica a 323 2003 19 t kalisky y ashkenazy s havlin phys rev e 72 2005 011913 in this article correlations of volatile series generated from stationary first order linear feedback process with gaussian and non gaussian innovations are investigated while volatile correlations corresponding to gaussian innovations exhibited uncorrelated behavior across all time scales those of non gaussian innovations showed significant deviation from uncorrelated behavior even at large time scales the results presented raise the intriguing question whether non gaussian innovations can be sufficient to realize long range volatile correlations

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

volatility of linear and nonlinear time series previous studies indicated that nonlinear properties of gaussian distributed time series with long range correlations u i can be detected and quantified by studying the correlations in the magnitude series ensuremath mid u i ensuremath mid the volatility however the origin for this empirical observation still remains unclear and the exact relation between the correlations in u i and the correlations in ensuremath mid u i ensuremath mid is still unknown here we develop analytical relations between the scaling exponent of linear series u i and its magnitude series ensuremath mid u i ensuremath mid moreover we find that nonlinear time series exhibit stronger or the same correlations in the magnitude time series compared with linear time series with the same two point correlations based on these results we propose a simple model that generates multifractal time series by explicitly inserting long range correlations in the magnitude series the nonlinear multifractal time series is generated by multiplying a long range correlated time series that represents the magnitude series with uncorrelated time series that represents the sign series mathrm sgn u i we apply our techniques on daily deep ocean temperature records from the equatorial pacific the region of the el nin o phenomenon and find i long range correlations from several days to several years with 1 f power spectrum ii significant nonlinear behavior as expressed by long range correlations of the volatility series and iii broad multifractal spectrum

multifractal characterization of stochastic resonance we use a multifractal formalism to study the effect of stochastic resonance in a noisy bistable system driven by various input signals to characterize the response of a stochastic bistable system we introduce a new measure based on the calculation of a singularity spectrum for a return time sequence we use wavelet transform modulus maxima method for the singularity spectrum computations it is shown that the degree of multifractality defined as a width of singularity spectrum can be successfully used as a measure of complexity both in the case of periodic and aperiodic stochastic or chaotic input signals we show that in the case of periodic driving force singularity spectrum can change its structure qualitatively becoming monofractal in the regime of stochastic synchronization this fact allows us to consider the degree of multifractality as a new measure of stochastic synchronization also moreover our calculations have shown that the effect of stochastic resonance can be catched by this measure even from a very short return time sequence we use also the proposed approach to characterize the noise enhanced dynamics of a coupled stochastic neurons model

statistical properties of the volatility of price fluctuations we study the statistical properties of volatility measured by locally averaging over a time window t the absolute value of price changes over a short time interval ensuremath delta t we analyze the s 500 stock index for the 13 year period jan 1984 to dec 1996 we find that the cumulative distribution of the volatility is consistent with a power law asymptotic behavior characterized by an exponent ensuremath mu ensuremath approx 3 similar to what is found for the distribution of price changes the volatility distribution retains the same functional form for a range of values of t further we study the volatility correlations by using the power spectrum analysis both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents also both methods show the presence of a crossover at approximately 1 5 days in addition we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 u s companies over the two year period jan 1994 to dec 1995

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

vacillating hecke tableaux and linked partitions we introduce the structure of vacillating hecke tableaux by using the hecke insertion algorithm developed by buch kresch shimozono tamvakis and yong we establish a one to one correspondence between vacillating hecke tableaux and linked partitions which arise in free probability theory we define a hecke diagram as a young diagram possibly with a marked corner a vacillating hecke tableau is defined as a sequence of hecke diagrams subject to a certain condition on addition and deletion of rook strips the notion of a rook strip was introduced by buch in the study of the littlewood richardson rule for stable grothendieck polynomials we show that the crossing number and the nesting number of a linked partition can be determined by the maximal number of rows and the maximal number of columns of diagrams in the corresponding vacillating hecke tableau the proof relies on a theorem due to thomas and yong as consequences we confirm two conjectures on the distribution of the crossing number and the nesting number over linked partitions and ordinary partitions respectively proposed by de mier and kim

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

power spectrum and detrended fluctuation analysis application to daily temperatures the variability measures of fluctuation analysis fa and detrended fluctuation analysis dfa are expressed in terms of the power spectral density and of the autocovariance of a given process the diagnostic potential of these methods is tested on several model power spectral densities in particular we find that both fa and dfa reveal an algebraic singularity of the power spectral density at small frequencies corresponding to an algebraic decay of the autocovariance a scaling behavior of the power spectral density in an intermediate frequency regime is better reflected by dfa than by fa we apply fa and dfa to ambient temperature data from the 20th century with the primary goal to resolve the controversy in literature whether the low frequency behavior of the corresponding power spectral densities are better described by a power law or a stretched exponential as a third possible model we suggest a weibull distribution however it turns out that neither fa nor dfa can reliably distinguish between the proposed models

multilinear function series and transforms in free probability theory abstract the algebra mul b of formal multilinear function series over an algebra b and its quotient symmul b are introduced as well as corresponding operations of formal composition in the setting of mul b the unsymmetrized r and t transforms of random variables in b valued noncommutative probability spaces are introduced these satisfy properties analogous to the usual r and t transforms the latter being just the reciprocal of the s transform but describe all moments of a random variable not only the symmetric moments the partially ordered set of noncrossing linked partitions is introduced and is used to prove properties of the unsymmetrized t transform

complexity and multifractal behaviors of multiscale continuum percolation financial system for chinese stock markets abstract a new financial agent based time series model is developed and investigated by multiscale continuum percolation system which can be viewed as an extended version of continuum percolation system in this financial model for different parameters of proportion and density two poisson point processes where the radii of points represent the ability of receiving or transmitting information among investors are applied to model a random stock price process in an attempt to investigate the fluctuation dynamics of the financial market to validate its effectiveness and rationality we compare the statistical behaviors and the multifractal behaviors of the simulated data derived from the proposed model with those of the real stock markets further the multiscale sample entropy analysis is employed to study the complexity of the returns and the cross sample entropy analysis is applied to measure the degree of asynchrony of return autocorrelation time series the empirical results indicate that the proposed financial model can simulate and reproduce some significant characteristics of the real stock markets to a certain extent

finite size effect and the components of multifractality in transport economics volatility based on multifractal detrending moving average method abstract analysis of freight rate volatility characteristics attracts more attention after year 2008 due to the effect of credit crunch and slowdown in marine transportation the multifractal detrended fluctuation analysis technique is employed to analyze the time series of baltic dry bulk freight rate index and the market trend of two bulk ship sizes namely capesize and panamax for the period march 1st 1999 february 26th 2015 in this paper the degree of the multifractality with different fluctuation sizes is calculated besides multifractal detrending moving average mf dma counting technique has been developed to quantify the components of multifractal spectrum with the finite size effect taken into consideration numerical results show that both capesize and panamax freight rate index time series are of multifractal nature the origin of multifractality for the bulk freight rate market series is found mostly due to nonlinear correlation

comparative analysis of grey detrended fluctuation analysis methods based on empirical research on china s interest rate market abstract this study empirically compares the development of china s interest rate market in the past decade the yield of shibor market from 2006 to 2016 showed anti persistence and the later five year trend was stronger than that in the previous half period indicating a significantly growing trend of china s interest rate market we perform a comparative analysis of detrended fluctuation analysis dfa detrending moving average dma algorithm and the maximum overlap wavelet transform dfa modwt using grey and original sequences the autoregressive integrated moving average model is adopted to generate set point h sequences results illustrated that 1 for original sequences both the dfa modwt and dma 0 5 shows outstanding performances when the set hurst exponents are 0 6 and 0 7 and 0 8 and 0 9 respectively 2 for grey sequences g dfa performs best among the three methods followed by g dma and g dfa modwt 3 the long range correlation of the original sequences is slightly lower than the set values on the contrary the long range correlation of grey sequences is much higher than the set values thus the grey sequence exerts a strong aggregation effect as it can accumulate the trend of the sequence our results show that the grey sequence can determine the regular pattern from the messy sequence however grey sequences tend to be overly analyzed and misleading when large volumes of data are involved empirical studies confirm that china s interest rate market remains an inefficient market

numerical analysis of periodic solutions and bifurcations in the planetary annulus problem this paper discusses the dynamics of particles orbiting planetary rings under a general central potential starting with the mathematical description of the dynamical system we analyze the motion of a particle with infinitesimal mass as attracted by a central body surrounded by a homogeneous circular annular disk throughout the paper we carry out an analytic search of the most relevant equilibria solutions and based on that we investigate numerically the stability matrix of the system to find stability inequalities in this way we describe the in plane and out of plane motion by means of the numerical continuation of a wide number of uni parametric families of planar and spatial periodic orbits we present a description of the main families of periodic orbits encountered their bifurcations and linear stability with the aim of reproducing a more realistic scenario we analyse different mass proportions between the annulus and the central body we consider an oblate planet and we also include a composition of rings in the dynamical model

long range correlation properties of coding and noncoding dna sequences genbank analysis an open question in computational molecular biology is whether long range correlations are present in both coding and noncoding dna or only in the latter to answer this question we consider all 33301 coding and all 29453 noncoding eukaryotic sequences each of length larger than 512 base pairs bp in the present release of the genbank to dtermine whether there is any statistically significant distinction in their long range correlation properties standard fast fourier transform fft analysis indicates that coding sequences have practically no correlations in the range from 10 bp to 100 bp spectral exponent beta 0 00 0 04 where the uncertainty is two standard deviations in contrast for noncoding sequences the average value of the spectral exponent beta is positive 0 16 0 05 which unambiguously shows the presence of long range correlations we also separately analyze the 874 coding and the 1157 noncoding sequences that have more than 4096 bp and find a larger region of power law behavior we calculate the probability that these two data sets coding and noncoding were drawn from the same distribution and we find that it is less than 10 10 we obtain independent confirmation of these findings using the method of detrended fluctuation analysis dfa which is designed to treat sequences with statistical heterogeneity such as dna s known mosaic structure patchiness arising from the nonstationarity of nucleotide concentration the near perfect agreement between the two independent analysis methods fft and dfa increases the confidence in the reliability of our conclusion

forecasting volatility in shanghai and shenzhen markets based on multifractal analysis abstract this paper analyzes the multifractality in shanghai and shenzhen stock markets using multifractal spectrum analysis and multifractal detrended fluctuation analysis we find that the main source of multifractality is long range correlations of large and small fluctuations then we introduce a multifractal volatility measure mv and find that by taking mv as daily conditional volatility the simulated series displayed similar stylized facts to the original daily return series by capturing the dynamics of mv using the arfima model we find that the out of sample forecasting performance of the arfima mv model is better than some garch class models and the arfima rv model under some criteria of loss function

detrended fluctuation analysis of time series of a firing fusimotor neuron abstract we study the interspike intervals isi time series of the spontaneous fusimotor neuron activity by applying the detrended fluctuation analysis that is a modification of the random walk model analysis thus we have found evidence for the white noise characteristics of the isi time series which means that the fusimotor activity does not possess temporal correlations we conclude that such an activity represents the requisite noisy component for occurrence of the stochastic resonance mechanism in the neural coordination of muscle spindles

nonlinear strength quantifier based on phase correlation abstract distinguishing linear series from nonlinear ones is of great importance for not only understanding the processes generating these series but also their modeling and prediction there are many methods and their nonlinear quantifiers to reach this goal but no one is powerful enough to deal with any given series in this study the artificially generating series with given tailored phase correlation strength is applied to test the performance of some widely used methods and their nonlinear quantifiers given in the previous studies both advantages and shortcomings are shown for these methods and their nonlinear metrics especially spurious results from these methods and their nonlinear metrics can be found for some cases much weak or strong phase correlations in order to avoid these spurious results modified phase correlation quantifiers are proposed at the same time multiple stripes found in the phase map can be explained from the view point of enhanced nonlinear strength

multifractal detrended fluctuation analysis of the chinese stock index futures market abstract based on the multifractal detrended fluctuation analysis mf dfa and multifractal spectrum analysis this paper empirically studies the multifractal properties of the chinese stock index futures market using a total of 2942 ten minute closing prices we find that the chinese stock index futures returns exhibit long range correlations and multifractality making the single scale index insufficient to describe the futures price fluctuations further by comparing the original time series with the transformed time series through shuffling procedure and phase randomization procedure we show the existence of two different sources of the multifractality for the chinese stock index futures market our results suggest that the multifractality is mainly due to long range correlations although the fat tailed probability distributions also contribute to such multifractal behaviour

effect of the signal filtering on detrended fluctuation analysis abstract detrended fluctuation analysis dfa is an effective method to accurately quantify long term correlations embedded in a nonstationary time series in this paper we study the effect of signal filtering of a signal on the dfa method the theoretical and simulated results show that the signal filtering will affect the range of scale in dfa moreover this effect is different for fractal gaussian noise series and fractal brown movement series our study is meaningful for improving accuracy and efficiency of dfa method in theory and practice

multifractal formalism by enforcing the universal behavior of scaling functions a b s t r a c t despite its solid foundations multifractal analysis is still a challenging task the inversed singularity spectrum is a major pitfall in standard multifractal analyses especially for empirical signals to resolve this issue we identified the fan like convergent geometry of scaling functions yielding a limit value termed focus for all moments at the largest scale building on this behavior of scaling we introduce the novel concept of focus based multifractal formalism it relies on enforcing this universal behavior when the moment wise scaling exponents are assessed for the scaling functions besides developing focus based variants of the established multifractal detrended fluctuation analysis and the wavelet leader method we present a novel analytical tool of multifractal signal summation conversion all methods are extensively tested on exact multifractal signals synthesized by the generalized binomial multifractal model in terms of precision and incidence of inversed singularity spectra our focus based variants never yielded inversed spectra and their precision was found similar to that of standard methods our approach allowed computing a moment wise and a global error parameter describing the impact of finite size effect and degree of multifractality as compared to that of the fitted exact multifractal model we demonstrate that the standard approach to multifractal analyses contains a central element that is essentially monofractal due to its regression scheme assessing the scaling exponents for each and every moment separately hence these methods can yield reliable estimates only for ideally behaving multifractal signals in contrast our focus based variants due to their genuine multifractal model fitting always yield reliable estimates accompanied by goodness of fit statistics the presented novel multifractal tools offer means of dealing with the consequences of endogenous impurities of potentially multifractal empirical signals

exact series solution to the epstein hubbell generalized elliptic type integral using complex variable residue theory in this paper complex variable residue theory is used to arrive at an exact infinite series solution to the epstein hubbell integral this method of solution is different from those used to derive previous solutions to the epstein hubbell integral but produces exactly equivalent results several sets of numerical data are included that verify the results additional information on the improvement of convergence will be forthcoming at a later date

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

random cascades on wavelet dyadic trees we introduce a new class of random fractal functions using the orthogonal wavelet transform these functions are built recursively in the space scale half plane of the orthogonal wavelet transform cascading from an arbitrary given large scale towards small scales to each random fractal function corresponds a random cascading process referred to as a w cascade on the dyadic tree of its orthogonal wavelet coefficients we discuss the convergence of these cascades and the regularity of the so obtained random functions by studying the support of their singularity spectra then we show that very different statistical quantities such as correlation functions on the wavelet coefficients or the wavelet based multifractal formalism partition functions can be used to characterize very precisely the underlying cascading process we illustrate all our results on various numerical examples

autocorrelation type timescale and statistical property in financial time series abstract earlier studies have documented that three types of autocorrelations exist in financial time series sign volatility and return autocorrelation in this paper we examine how each type of the above autocorrelations affects the statistical properties of financial time series and its role in maintaining such statistical properties using three different shuffling series that correspondingly destroy each type of autocorrelation upon different timescales we find that 1 the statistical properties of the shuffling series significantly vary from the original ones 2 volatility and return autocorrelations show greater impacts than sign autocorrelation 3 the effects on the statistical properties are intensified as time scale expands 4 the nonlinear component of autocorrelation is the major drive of the effect

visibility graph analysis of heart rate time series and bio marker of congestive heart failure abstract study of rr interval time series for congestive heart failure had been an area of study with different methods including non linear methods in this article the cardiac dynamics of heart beat are explored in the light of complex network analysis viz visibility graph method heart beat rr interval time series data taken from physionet database 46 47 belonging to two groups of subjects diseased congestive heart failure 29 in number and normal 54 in number are analyzed with the technique the overall results show that a quantitative parameter can significantly differentiate between the diseased subjects and the normal subjects as well as different stages of the disease further the data when split into periods of around 1 hour each and analyzed separately also shows the same consistent differences this quantitative parameter obtained using the visibility graph analysis thereby can be used as a potential bio marker as well as a subsequent alarm generation mechanism for predicting the onset of congestive heart failure

arbitrary order hilbert spectral analysis for time series possessing scaling statistics comparison study with detrended fluctuation analysis and wavelet leaders in this paper we present an extended version of hilbert huang transform namely arbitrary order hilbert spectral analysis to characterize the scale invariant properties of a time series directly in an amplitude frequency space we first show numerically that due to a nonlinear distortion traditional methods require high order harmonic components to represent nonlinear processes except for the hilbert based method this will lead to an artificial energy flux from the low frequency large scale to the high frequency small scale part thus the power law if it exists is contaminated we then compare the hilbert method with structure functions sf detrended fluctuation analysis dfa and wavelet leader wl by analyzing fractional brownian motion and synthesized multifractal time series for the former simulation we find that all methods provide comparable results for the latter simulation we perform simulations with an intermittent parameter 0 15 we find that the sf underestimates scaling exponent when q 3 the hilbert method provides a slight underestimation when q 5 however both dfa and wl overestimate the scaling exponents when q 5 it seems that hilbert and dfa methods provide better singularity spectra than sf and wl we finally apply all methods to a passive scalar temperature data obtained from a jet experiment with a taylor s microscale reynolds number re 250 due to the presence of strong ramp cliff structures the sf fails to detect the power law behavior for the traditional method the ramp cliff structure causes a serious artificial energy flux from the low frequency large scale to the high frequency small scale part thus dfa and wl underestimate the scaling exponents however the hilbert method provides scaling exponents q quite close to the one for longitudinal velocity indicating a less intermittent passive scalar field than what was believed before 2011 american physical society

generalized elliptic type integrals and their representations epstein hubbell l f epstein j h hubbell evaluation of a generalized elliptic type integral j res nbs 67b 1963 1 17 elliptic type integrals occur in radiation field problems in this paper we consider a generalization 10 of the elliptic type integrals introduced by kalla and tuan s l kalla vu kim tuan asymptotic formulas for generalized elliptic type integrals comput math appl 32 1996 49 55 many generalizations of elliptic type integrals studied earlier by several authors can be derived as particular cases of our unified form we study the uniform convergence of the integral representation 10 we derive the power series representations which are valid in different domains also we obtain some relationships between this generalized form and laurecella s hypergeometric function of three variables f d 3 appell s hypergeometric functions f 1 and f 3 and gauss hypergeometric function 2f 1 some important particular cases of these representations are derived

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

multifractal analysis of spot rates in tanker markets and their comparisons with crude oil markets abstract this paper investigates the dynamic features of the spot rates for vlcc ulcc suezmax aframax panamax and handysize tanker markets by means of multifractal detrended fluctuation analysis mf dfa the hurst exponents especially the time dependent hurst exponents of the daily rate returns are calculated to capture the fractal properties of these different tanker markets the origins of multifractility in these markets are identified by comparing their multifractal scaling exponents based on the original data the shuffled data and the surrogate data furthermore the non periodic cycles for these markets are detected by the v statistic finally the comparisons of the fractal properties between the tanker markets and the crude oil commodity markets suggest that the tanker markets are more fractal than their upstream counterparts

statistical volatility duration and complexity of financial dynamics on sierpinski gasket lattice percolation abstract a novel agent based financial dynamics is established based on the percolation system on sierpinski gasket lattice to reproduce the statistical characteristics of financial markets sierpinski gasket lattice is a fractal like graph which corresponds to the fractal well known sierpinski gasket modeling a financial dynamics on sierpinski gasket lattice is a new approach in financial micro mechanism construction in an attempt to investigate the statistical properties of returns and prove the feasibility of the proposed model two new nonlinear statistics maximum and average monotonous volatility duration are introduced in this work for the first time which describe the trend of volatility of return time series in financial markets furthermore a new method cmcid is proposed to measure the synchronization and similarity behaviors of return volatility duration in multiscale the results show that the pairs of real data and simulated data have synchronization and the synchronization becomes stronger when the scale increases and the power law distribution is employed to investigate the corresponding statistical properties which shows that the proposed model shares a common power law distribution with regard to monotonous volatility duration the empirical results show that the simulated series from the financial model and the historical data share common statistical properties which indicate that the proposed model is reasonable in terms of volatility behavior

asymptotic formulas for generalized elliptic type integrals abstract epstein hubbell 1 elliptic type integrals occur in radiation field problems the object of the present paper is to consider a unified form of different elliptic type integrals defined and developed recently by several authors we obtain asymptotic formulas for the generalized elliptic type integrals

detecting long range correlations with detrended fluctuation analysis abstract we examine the detrended fluctuation analysis dfa which is a well established method for the detection of long range correlations in time series we show that deviations from scaling which appear at small time scales become stronger in higher orders of dfa and suggest a modified dfa method to remove them the improvement is necessary especially for short records that are affected by non stationarities furthermore we describe how crossovers in the correlation behavior can be detected reliably and determined quantitatively and show how several types of trends in the data affect the different orders of dfa

multiple sources and multiple measures based traffic flow prediction using the chaos theory and support vector regression method abstract this study proposes a multiple sources and multiple measures based traffic flow prediction algorithm using the chaos theory and support vector regression method in particular first the chaotic characteristics of traffic flow associated with the speed occupancy and flow are identified using the maximum lyapunov exponent then the phase space of multiple measures chaotic time series are reconstructed based on the phase space reconstruction theory and fused into a same multi dimensional phase space using the bayesian estimation theory in addition the support vector regression svr model is designed to predict the traffic flow numerical experiments are performed using the data from multiple sources the results show that compared with the single measure the proposed method has better performance for the short term traffic flow prediction in terms of the accuracy and timeliness

asymmetric multifractal detrending moving average analysis in time series of pm2 5 concentration abstract in this paper we propose the asymmetric multifractal detrending moving average analysis a mfdma method to explore the asymmetric correlation in non stationary time series the proposed method is applied to explore the asymmetric correlation of pm2 5 daily average concentration with uptrends or downtrends in china in addition shuffling and phase randomization procedures are applied to detect the sources of multifractality the results show that existences of asymmetric correlations and the asymmetric correlations are multifractal further the multifractal scaling behavior in the chinese pm2 5 is caused not only by long range correlation but also by fat tailed distribution but the major source of multifractality is fat tailed distribution

time dependent limited penetrable visibility graph analysis of nonstationary time series abstract recent years have witnessed the development of visibility graph theory which allows us to analyze a time series from the perspective of complex network we in this paper develop a novel time dependent limited penetrable visibility graph tdlpvg two examples using nonstationary time series from rr intervals and gas liquid flows are provided to demonstrate the effectiveness of our approach the results of the first example suggest that our tdlpvg method allows characterizing the time varying behaviors and classifying heart states of healthy congestive heart failure and atrial fibrillation from rr interval time series for the second example we infer tdlpvgs from gas liquid flow signals and interestingly find that the deviation of node degree of tdlpvgs enables to effectively uncover the time varying dynamical flow behaviors of gas liquid slug and bubble flow patterns all these results render our tdlpvg method particularly powerful for characterizing the time varying features underlying realistic complex systems from time series

long range correlation and predictability of chinese stock prices abstract it is well known that the price time series of an efficient market display a brownian motion in such a case the best prediction of a future price is the last known price thus no arbitrage is possible a real market is however possibly not perfectly efficient in this paper we apply an error back propagation neural network to tick by tick high frequency time series of chinese a share stock prices and try to predict their future values the performance of the predictions varies largely for different stocks in order to seek for the dependence of the performance we study the long range correlation lrc of the data by the conventional detrended fluctuation analysis dfa and its generalization the multifractal detrended fluctuation analysis mfdfa clear relevance between the performance and the lrc is observed the prediction is particularly good when the time series are strongly anti persistent

levy flights and random searches in this work we discuss some recent contributions to the random search problem our analysis includes superdiffusive levy processes and correlated random walks in several regimes of target site density mobility and revisitability we present results in the context of mean field like and closed form average calculations as well as numerical simulations we then consider random searches performed in regular lattices and lattices with defects and we discuss a necessary criterion for distinguishing true superdiffusion from correlated random walk processes we invoke energy considerations in relation to critical survival states on the edge of extinction and we analyze the emergence of levy behavior in deterministic search walks finally we comment on the random search problem in the context of biological foraging

scaling and memory of intraday volatility return intervals in stock markets we study the return interval tau between price volatilities that are above a certain threshold q for 31 intraday data sets including the standard and poor s 500 index and the 30 stocks that form the dow jones industrial index for different threshold q the probability density function pq tau scales with the mean interval tau as formula see text similar to that found in daily volatilities since the intraday records have significantly more data points compared to the daily records we could probe for much higher thresholds and still obtain good statistics we find that the scaling function f x is consistent for all 31 intraday data sets in various time resolutions and the function is well approximated by the stretched exponential f x similar to e ax gamma with gamma 0 38 0 05 and a 3 9 0 5 which indicates the existence of correlations we analyze the conditional probability distribution pq tau tau0 for tau following a certain interval tau0 and find pq tau tau0 depends on tau0 which demonstrates memory in intraday return intervals also we find that the mean conditional interval tau tau0 increases with tau0 consistent with the memory found for pq tau tau0 moreover we find that return interval records in addition to having short term correlations as demonstrated by pq tau tau0 have long term correlations with correlation exponents similar to that of volatility records

a better understanding of long range temporal dependence of traffic flow time series abstract long range temporal dependence is an important research perspective for modelling of traffic flow time series various methods have been proposed to depict the long range temporal dependence including autocorrelation function analysis spectral analysis and fractal analysis however few researches have studied the daily temporal dependence i e the similarity between different daily traffic flow time series which can help us better understand the long range temporal dependence such as the origin of crossover phenomenon moreover considering both types of dependence contributes to establishing more accurate model and depicting the properties of traffic flow time series in this paper we study the properties of daily temporal dependence by simple average method and principal component analysis pca based method meanwhile we also study the long range temporal dependence by detrended fluctuation analysis dfa and multifractal detrended fluctuation analysis mfdfa the results show that both the daily and long range temporal dependence exert considerable influence on the traffic flow series the dfa results reveal that the daily temporal dependence creates crossover phenomenon when estimating the hurst exponent which depicts the long range temporal dependence furthermore through the comparison of the dfa test pca based method turns out to be a better method to extract the daily temporal dependence especially when the difference between days is significant

detrended fluctuation analysis and the difference between external drifts and intrinsic diffusionlike nonstationarity detrended fluctuation analysis dfa has been shown to be an effective method to study long range correlation of nonstationary series in principle dfa considers f text dfa 2 s the mean of variance around the local polynomial fit in segments with length s and then estimates the scaling exponent ensuremath alpha text dfa in f text dfa s ensuremath sim s ensuremath alpha text dfa with varying s usually the methodological studies of dfa focus on its effect on removing the drift due to the external trends only few paid attention to nonstationary series without drift such as fractional brownian motion fbm with nonstationarity due to its intrinsic dynamics both of these types of nonstationarity can shift the local mean by drift or diffusion and can be treated as the additive nonstationarity eliminable by the additive decomposition in this study we limit our discussion to such additive nonstationarity and furthermore specifically distinguish these two types of nonstationarity namely the drift and the intrinsic diffusionlike nonstationarity to understand how dfa works for the intrinsic diffusionlike nonstationarity we take fbm as the example and seek for the answers to two fundamental questions 1 what dfa removes from fbm and 2 why dfa can handle such intrinsic diffusionlike nonstationarity in contrast to methods only applicable to stationary series such as the fluctuation analysis a crucial condition i e statistical equivalence among all segments is proposed and checked in the fluctuation analysis and dfa as shown the crucial condition is a natural requirement for the connection between dfa and autocorrelation function with the help of the crucial condition our study analytically and numerically demonstrates for the intrinsic diffusionlike nonstationary series that 1 rather than the nonstationarity as thought dfa actually removes the difference among all segments 2 the detrended segments fulfill the crucial condition so that the average over segments becomes equivalent to the ensemble average over realizations these answers are also true for series with a drift thus we provide a unified perspective to refresh the understanding of how dfa works on nonstationarity and underpin the mathematical ground of dfa

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

are the phases in the anderson model long range correlated we investigate the local cumulative phases at single sites of the lattice for time dependent wave functions in the anderson model in d 2 and 3 in addition to a local linear trend the phases exhibit some fluctuations we study the time correlations of these fluctuations using detrended fluctuation analysis our results suggest that the phase fluctuations are long range correlated decaying as a power law with time it seems that the exponent depends on the degree of disorder in d 3 close to the critical disorder wc 16 5 the correlation exponent exhibits a maximum value of 0 6 which is significantly above random fluctuations 0 5

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

crossings and nestings of matchings and partitions we present results on the enumeration of crossings and nestings for matchings and set partitions using a bijection between partitions and vacillating tableaux we show that if we fix the sets of minimal block elements and maximal block elements the crossing number and the nesting number of partitions have a symmetric joint distribution it follows that the crossing numbers and the nesting numbers are distributed symmetrically over all partitions of n as well as over all matchings on 2n as a corollary the number of k noncrossing partitions is equal to the number of k nonnesting partitions the same is also true for matchings an application is given to the enumeration of matchings with no k crossing or with no k nesting mathematics subject classification primary 05a18 secondary 05e10 05a15

multifractal moving average analysis and test of multifractal model with tuned correlations we address two common major problems in the study of time series characterizing fluctuations in complex systems multifractal analysis and multifractal modeling specifically we introduce a multi fractal centered moving average mf cma analysis which is computationally easier but equivalently performing compared with the well established multi fractal detrended fluctuation analysis mf dfa with linear detrending in addition we study in detail a generalized binomial multi fractal model gb mfm to conveniently and reliably generate multifractal surrogate data with arbitrary singularity strengths and arbitrary long term persistence we use the data generated by this model as well as realistic by construction monofractal data series with crossovers and trends to test and compare the multifractal analysis methods and discuss finite size effects as well as limitations due to spurious multifractality

multifractal random walk we introduce a class of multifractal processes referred to as multifractal random walks mrws to our knowledge it is the first multifractal process with continuous dilation invariance properties and stationary increments mrws are very attractive alternative processes to classical cascadelike multifractal models since they do not involve any particular scale ratio the mrws are indexed by four parameters that are shown to control in a very direct way the multifractal spectrum and the correlation structure of the increments we briefly explain how in the same way one can build stationary multifractal processes or positive random measures

multifractal properties of chinese stock market in shanghai abstract in this article we apply three methods of multifractal analysis partition function method singular spectrum method and multifractal detrended fluctuation analysis method to analyze the closing index fluctuations of shanghai stock market during the past seven years we have found that shanghai stock market has weak multifractal features and there are long range power law correlations between index series the shapes of singular spectrums do not change with time scales and their strengths weaken when the scales shorten but when the orders of partition function increase the strengths of multifractal increase the singular spectrums become rougher and the general hurst exponents decrease these results provide solid and important values for further study on the dynamic mechanism of stock market price fluctuation

multifractal estimates of monofractality in rr heart series in power spectrum ranges abstract two popular estimators of multifractal properties the wavelet transform modulus maxima method and multifractal detrended fluctuation analysis are applied to investigate signals consisting of normal rr series in 39 healthy subjects and 90 patients suffering from systolic dysfunction of the left ventricle however differently from standards for multifractal analysis the scaling is performed separately in intervals corresponding to standard power spectral bands low lf very low vlf and ultra low frequencies ulf tests on fractional brownian motions fbm are done to quantify properties of the estimators as detectors of monofractality in lf vlf and ulf bands arguments are given that multifractal analysis of rr series performed in these bands has a physiological meaning the increased activation of the sympathetic nervous system caused by heart disease is detected evidently only by analysis in lf the transition in multifractal characteristics between diurnal and nocturnal activity takes place when the analysis moves from lf and vlf to ulf only in ulf the diurnal heart rate variability can be approximated by fbm with a self similarity index of h 0 20

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

the moving averages demystified a common method in technical analysis is the construction of moving averages along time series of stock prices we show that they present a practical interest for physicists and raise new questions on fundamental ground indeed self ane signals characterized by a dened roughness exponent h can be investigated through moving averages the density of crossing points between two moving averages is shown to be a measure of long range power law correlations in a signal finally we present a specic transform with which various structures in a signal e g trends cycles noise etc can be investigated in a systematic way c 1999 elsevier science

generalized hurst exponent and multifractal function of original and translated texts mapped into frequency and length time series a nonlinear dynamics approach can be used in order to quantify complexity in written texts as a first step a one dimensional system is examined two written texts by one author lewis carroll are considered together with one translation into an artificial language i e esperanto are mapped into time series their corresponding shuffled versions are used for obtaining a baseline two different one dimensional time series are used here one based on word lengths lts the other on word frequencies fts it is shown that the generalized hurst exponent h q and the derived f curves of the original and translated texts show marked differences the original texts are far from giving a parabolic f function in contrast to the shuffled texts moreover the esperanto text has more extreme values this suggests cascade model like with multiscale time asymmetric features as finally written texts a discussion of the difference and complementarity of mapping into a lts or fts is presented the fts f curves are more opened than the lts ones

dynamical generalized hurst exponent as a tool to monitor unstable periods in financial time series we investigate the use of the hurst exponent dynamically computed over a weighted moving time window to evaluate the level of stability instability of financial firms financial firms bailed out as a consequence of the 2007 2008 credit crisis show a neat increase with time of the generalized hurst exponent in the period preceding the unfolding of the crisis conversely firms belonging to other market sectors which suffered the least throughout the crisis show opposite behaviors we find that the multifractality of the bailed out firms increase at the crisis suggesting that the multi fractal properties of the time series are changing these findings suggest the possibility of using the scaling behavior as a tool to track the level of stability of a firm in this paper we introduce a method to compute the generalized hurst exponent which assigns larger weights to more recent events with respect to older ones in this way large fluctuations in the remote past are less likely to influence the recent past we also investigate the scaling associated with the tails of the log returns distributions and compare this scaling with the scaling associated with the hurst exponent observing that the processes underlying the price dynamics of these firms are truly multi scaling