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

multifractal property of chinese stock market in the csi 800 index based on mf dfa approach abstract csi 800 index consists of csi 500 index and csi 300 index aiming to reflect the performance of stocks with large mid and small size of china a share market in this paper we analyze the multifractal structure of chinese stock market in the csi 800 index based on the multifractal detrended fluctuation analysis mf dfa method we find that the fluctuation of the closing logarithmic returns have multifractal properties the shape and width of multifractal spectrum are depended on the weighing order q more interestingly we observe a bigger market crash in june august 2015 than the one in 2008 based on the local hurst exponents the result provides important information for further study on dynamic mechanism of return fluctuation and whether it would trigger a new financial crisis

long range power law correlations in stock returns abstract this study investigates long range power law correlations in us uk japanese german french and spanish stock markets using daily data and applying a recently developed residual analysis termed detrended fluctuation analysis dfa we quantify correlations for the returns absolute value of returns and square of returns the results show that there is little evidence of long range correlations in returns but there is strong evidence of long range correlation in absolute and squared returns for the absolute returns a cross over of approximately 41 days is found

multiscale statistical behaviors for ising financial dynamics with continuum percolation jump abstract a financial dynamics of interaction and jump is developed and investigated by two statistical physics systems ising model and continuum percolation this proposed model aiming at understanding price fluctuations needs to define a mechanism for the formation of the price in an attempt to describe interacting micromechanism and sudden jump for stock price changes further the corresponding fluctuation behaviors and various complexity properties of logarithmic returns for the financial model are investigated by some statistical and complex analyses then p order multiscale autocorrelation function and q order multiscale entropy are also introduced to study the financial model with scaled analysis methods moreover the real stock market indexes are used to compare with the simulation returns from the financial model the empirical research shows that the simulation time series exhibits the similar fluctuation patterns with real time series

self similarity and network perspective of the chinese fund market abstract by testing 88 different funds of the chinese fund market cfm we find fractal behavior and long range correlations in the return series which are insensitive to the kind of funds meanwhile a power law relationship between the deviation d of prices and the hurst exponent h has been obtained which may be useful for predicting the price time series in addition with funds being viewed as nodes and the connections among the funds being determined by the cross correlation coefficients using a winner takes all approach we investigate the topological properties of the fund network our analysis reveals that during different time periods the cumulative degree distributions of the fund network all obey the double power law format moreover the small world property is also found for the fund network

the derivatives of homotopy theory we construct a functor of spaces mn and show that its multilinearization is equivalent to the nth layer of the taylor tower of the identity functor of spaces this allows us to identify the derivatives of the identity functor and determine their homotopy type the calculus of homotopy functors developed by goodwillie gi g2 g3 establishes that a homotopy functor f satisfying certain connectivity conditions has associated to it a tower of functors pf pn f these functors act like a taylor series approximation to f in the sense that for a space x there is a map pnf x f x k pnf x for each n and the connectivity of this map increases with n this theory has been applied to the study of the functor a waldhausen s algebraic k theory of spaces in this paper we turn our attention to the taylor tower of the identity functor of spaces i the ultimate goal is to identify the taylor tower of i and use it to study homotopy theory in this paper we construct a collection of symmetric functors mn and show that the multilinearization of mn is equivalent to the nth layer fiber pni pn i of the taylor tower of i this construction also allows us to identify the nth derivative of i this is a spectrum with l action which is equivalent to the functor fiber pni k pni the paper is organized as follows in section 1 we summarize the basic results and terminology of calculus that will be used throughout the paper in section 2 we describe the problem of finding the taylor tower of i in more detail and state the main results in section 3 we outline the method by which the nth derivative of a functor is determined in section 4 we construct the functor mn and a natural transformation tn used to establish the equivalence between the multilinearization of mn and fiber pnf pnf in section 5 we determine the homotopy type of the derivatives and in section 6 we show that t is sufficiertly connected to induce an equivalence between the multilinearization of mn and fiber p f pif l the results in this paper come from the author s thesis written uncler the direction of tom goodwillie at brown university the author wishes to thank him for his guidance and for many insightful discussions the author alsq wishes to thank randy mccarthy for his helpful suggestions during the writing of this paper received by the editors february 10 1994 1991 mathematics subject clqssification primary 55p65 1995 american mathematical society 0002 9947 95 1 00 25 per page

generalized aic method based on higher order moments and entropy of financial time series abstract in this paper a generalized method of traditional akaike information criterion is proposed as a new measurement to compare and evaluate the volatility behaviors of time series in stock market this new method is modified by extending variance to high order statistics such as skewness kurtosis and permutation entropy so as to demonstrate the different aspects of volatility behaviors of time series compared to low order method furthermore a new model of creating an aic plane is proposed in order to derive more accurate results numerical simulations are conducted over synthetic data to provide comparative study in addition further reports about the results of distinguishing behaviors in stock market composite index of america china and hong kong by using generalized aic method and aic plane are utilized to reflect the feasibility our results can effectively differentiate multiscale volatility details of time series from three areas

modified dfa and dcca approach for quantifying the multiscale correlation structure of financial markets abstract we use multiscale detrended fluctuation analysis msdfa and multiscale detrended cross correlation analysis msdcca to investigate auto correlation ac and cross correlation cc in the us and chinese stock markets during 1997 2012 the results show that us and chinese stock indices differ in terms of their multiscale ac structures stock indices in the same region also differ with regard to their multiscale ac structures we analyze ac and cc behaviors among indices for the same region to determine similarity among six stock indices and divide them into four groups accordingly we choose s p500 nqci hsi and the shanghai composite index as representative samples for simplicity msdfa and msdcca results and average msdfa spectra for local scaling exponents lses for individual series are presented we find that the msdcca spectrum for lse cc between two time series generally tends to be greater than the average msdfa lse spectrum for individual series we obtain detailed multiscale structures and relations for cc between the four representatives msdfa and msdcca with secant rolling windows of different sizes are then applied to reanalyze the ac and cc vertical and horizontal comparisons of different window sizes are made the msdfa and msdcca results for the original window size are confirmed and some new interesting characteristics and conclusions regarding multiscale correlation structures are obtained

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

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

on the homotopy of simplicial algebras over an operad according to a result of h cartan cf 5 the homotopy of a simplicial commutative algebra is equipped with divided power operations in this paper we provide a general approach to the construction of such operations in the context of simplicial algebras over an operad to be precise we work over a fixed field f and we consider operads in the category of f modules an operad is an algebraic device that specifies a type of algebras there are operads com as lie and pois whose algebras are respectively commutative algebras associative algebras lie algebras and poisson algebras in general if p denotes an operad then we call p algebras the associated algebras first we generalize the notion of a divided power in the context of algebras over an operad this is done as follows recall that the free commutative algebra is given by the formula t com v n v sn for v modf

long term memory in extreme returns of financial time series abstract it is well known that while daily price returns of financial markets are uncorrelated their absolute values volatility are long term correlated here we provide evidence that certain subsequences of the returns themselves also exhibit long term memory these subsequences consist of maxima or minima of returns in consecutive time windows of r days our analysis shows that for both stocks and currency exchange rates long term correlations are significant for r 4 we argue that this long term memory which is similar to that observed in volatility clustering sheds further insight on price dynamics that might be used for risk estimation

curves of every genus with many points ii asymptotically good families we resolve a 1983 question of serre by constructing curves with many points of every genus over every finite field more precisely we show that for every prime power q there is a positive constant cq with the following property for every integer g 0 there is a genus g curve over fq with at least cqg rational points over fq moreover we show that there exists a positive constant d such that for every q we can choose cq d log q we show also that there is a constant c 0 such that for every q and every n 0 and for every sufficiently large g there is a genus g curve over fq that has at least cg n rational points and whose jacobian contains a subgroup of rational points isomorphic to z nz for some r cg n

the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis a new method for analysing nonlinear and non stationary data has been developed the key part of the method is the empirical mode decomposition method with which any complicated data set can be dec

the mis specification of the expected rescaled adjusted range abstract rescaled range analysis has regained popularity in the recent econophysics literature as a means of identifying long term dependence in time series data conclusions derived from the rescaled adjusted range statistic are conditional however upon the choice of an appropriate benchmark against which calculated results can be compared one recent paper in physica a by couillard and davison physica a 348 2005 404 concludes that the anis and lloyd biometrika 63 1976 111 model of the expected rescaled adjusted range is more accurate than that proposed by peters fractal market analysis wiley new york 1994 this finding is contrary to the evidence presented by peters this paper reveals significant inconsistencies in the empirical results reported by peters which when considered support the conclusions of couillard and davison and explain the apparent contradiction in their results versus those of peters

hurst exponents for interacting random walkers obeying nonlinear fokker planck equations abstract anomalous diffusion of random walks has been extensively studied for the case of non interacting particles here we study the evolution of nonlinear partial differential equations by interpreting them as fokker planck equations arising from interactions among random walkers we extend the formalism of generalized hurst exponents to the study of nonlinear evolution equations and apply it to several illustrative examples they include an analytically solvable case of a nonlinear diffusion constant and three nonlinear equations which are not analytically solvable the usual fisher equation which contains a quadratic nonlinearity a generalization of the fisher equation with density dependent diffusion constant and the nagumo equation which incorporates a cubic rather than a quadratic nonlinearity we estimate the generalized hurst exponents

the goodwillie tower of the identity functor and the unstable periodic homotopy of spheres we investigate goodwillie s taylor tower of the identity functor from spaces to spaces more specifically we reformulate johnson s description of the goodwillie derivatives of the identity and prove that in the case of an odd dimensional sphere the only layers in the tower that are not contractible are those indexed by powers of a prime moreover in the case of a sphere the tower is finite in v k periodic homotopy

long range anticorrelations and non gaussian behavior of the heartbeat we find that the successive increments in the cardiac beat to beat interals of healthy subjects display scale invariant long range anticorrelations up to 10 4 heart beats furthermore we find that the histogram for the heartbeat intervals increments is well described by a l evy stable distribution for a group of subjects with severe heart disease we find that the distribution is unchanged but the long range correlations vanish therefore the different scaling behavior in health and disease must relate to the underlying dynamics of the heartbeat

a comment on measuring the hurst exponent of financial time series abstract a fundamental hypothesis of quantitative finance is that stock price variations are independent and can be modeled using brownian motion in recent years it was proposed to use rescaled range analysis and its characteristic value the hurst exponent to test for independence in financial time series theoretically independent time series should be characterized by a hurst exponent of 1 2 however finite brownian motion data sets will always give a value of the hurst exponent larger than 1 2 and without an appropriate statistical test such a value can mistakenly be interpreted as evidence of long term memory we obtain a more precise statistical significance test for the hurst exponent and apply it to real financial data sets our empirical analysis shows no long term memory in some financial returns suggesting that brownian motion cannot be rejected as a model for price dynamics

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

application of multifractal measures to tehran price index we report an empirical study of tehran price index tepix to analyze our data we use various methods like as rescaled range analysis r s modified rescaled range analysis lo s method detrended fluctuation analysis dfa and generalized hurst exponents analysis based on numerical results the scaling range of tepix returns is specified long memory effect or long range correlation property in this market is investigated characteristic exponent for probability distribution function of tepix returns is derived and finally the stage of development in tehran stock exchange is determined

tables of curves with many points these tables record results on curves with many points over finite fields for relatively small genus 0 g 50 and q a small power of 2 or 3 we give in two tables the best presently known bounds for n q g the maximum number of rational points on a smooth absolutely irreducible projective curve of genus g over a field f q of cardinality q in additional tables we list for a given pair g q the type of construction of the best curve so far and we give a reference to the literature where such a curve can be found

inhomogeneous scaling behaviors in malaysian foreign currency exchange rates in this paper we investigate the fractal scaling behaviors of foreign currency exchange rates with respect to malaysian currency ringgit malaysia these time series are examined piecewise before and after the currency control imposed in 1st september 1998 using the monofractal model based on fractional brownian motion the global hurst exponents are determined using the r s analysis the detrended fluctuation analysis and the method of second moment using the correlation coefficients the limitation of these monofractal analyses is discussed the usual multifractal analysis reveals that there exists a wide range of hurst exponents in each of the time series a new method of modelling the multifractal time series based on multifractional brownian motion with time varying hurst exponents is studied

volatility distribution in the s p500 stock index abstract we study the volatility of the s p500 stock index from 1984 to 1996 and find that the volatility distribution can be very well described by a log normal function further using detrended fluctuation analysis we show that the volatility is power law correlated with hurst exponent 0 9

volatility behavior of visibility graph emd financial time series from ising interacting system abstract a financial market dynamics model is developed and investigated by stochastic ising system where the ising model is the most popular ferromagnetic model in statistical physics systems applying two graph based analysis and multiscale entropy method we investigate and compare the statistical volatility behavior of return time series and the corresponding imf series derived from the empirical mode decomposition emd method and the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model further we find that the degree distribution of visibility graph for the simulation series has the power law tails and the assortative network exhibits the mixing pattern property all these features are in agreement with the real market data the research confirms that the financial model established by the ising system is reasonable

investigation of non gaussian effects in the brazilian option market abstract an empirical study of the brazilian option market is presented in light of three option pricing models namely the black scholes model the exponential model and a model based on a power law distribution the so called q gaussian distribution or tsallis distribution it is found that the q gaussian model performs better than the black scholes model in about one third of the option chains analyzed but among these cases the exponential model performs better than the q gaussian model in 75 of the time the superiority of the exponential model over the q gaussian model is particularly impressive for options close to the expiration date where its success rate rises above ninety percent

on the fractal dimension of self affine profiles one dimensional profiles f x can be characterized by a minkowski bouligand dimension d and by a scale dependent generalized roughness w f epsilon this roughness can be defined as the dispersion around a chosen fit to f x in an epsilon scale it is shown that d limepsilon to 0 2 in w f epsilon in epsilon holds for profiles nowhere differentiable this establishes a close connection between the roughness and the fractal dimension and proves that d 2 h for self affine profiles h is the roughness or hurst exponent two numerical algorithms based on the roughness one around the local average f x epsilon usual roughness and the other around the local rms straight line a generalized roughness are discussed the estimates of d for standard self affine profiles are reliable and robust especially for the last method

time varying hurst exponent for us stock markets abstract in this work the dynamical behavior of the us stock markets is characterized on the basis of the temporal variations of the hurst exponent estimated with detrended fluctuation analysis dfa over moving windows for the historical dow jones 1928 2007 and the s p 500 1950 2007 daily indices according to the results drawn i the hurst exponent displays an erratic dynamics with some episodes alternating low and high persistent behavior ii the major breakthrough of the long term trend of the scaling behavior occurred in 1972 at the end of the bretton woods system when the hurst exponent shifted form a positive to a negative long term trend other effects such as the 1987 crisis and the emergence of anti correlated behavior in the recent two years are also discussed

bootstrap testing for detrended fluctuation analysis abstract detrended fluctuation analysis dfa is a scaling method that allows the detection of long memory in a time series until now no asymptotic distribution has been found for this statistic the bootstrap technique allows the simulation of the probability distribution of any statistic in this paper the results of the monte carlo study using bootstrap method show that the dfa test has reasonably good power for short time series another advantage of the bootstrap technique is that allows the calculation of finite sample critical values as an example we calculate bootstrap p values for financial returns time series using dfa

the mod 2 homology of free spectral lie algebras the goodwillie derivatives of the identity functor on pointed spaces form an operad id in spectra we compute the mod 2 homology of free algebras for this operad on suspension spectra of simply connected spaces

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

does the singular value decomposition entropy have predictive power for stock market evidence from the shenzhen stock market abstract this paper analyzes the predictive ability of the singular value decomposition entropy for the shenzhen component index based on different scales it is found that the predictive ability of the entropy for the index is affected by the width of moving time windows and the structural break in stock market by moving time windows with one year the predictive power of singular value decomposition entropy of shenzhen stock market for its component index is found after the reform of non tradable shares

a tower of artin schreier extensions of function fields attaining the drinfeld vladut bound for an algebraic function fieldf having a finite constant field letg f resp n f denote the genus off resp the number of places off of degree one we construct a tower of function fields f 1 subseteq f 2 subseteq f 3 subseteq ldots over mathbb f q 2 such that the ration fi g fi tends to the drinfeld vladut boundq 1

scaling behaviors in differently developed markets scaling properties of four di erent stock market indices are studied in terms of a generalized hurst exponent approach we nd that the deviations from pure brownian motion behavior are associated with the degrees of development of the markets and we observe strong di erentiations in the scaling properties of markets at di erent development stage c

identification of short term and long term time scales in stock markets and effect of structural break abstract the paper presents the comparative study of the nature of stock markets in short term and long term time scales with and without structural break in the stock data structural break point has been identified by applying zivot and andrews structural trend break model to break the original time series t s o into two time series time series before structural break t s b and time series after structural break t s a in order to identify the of short term and long term market the hurst exponent h technique has been applied on the intrinsic mode functions i m f obtained from the t s o t s b and t s a by using empirical mode decomposition method h 0 5 for all the imfs of t s o t s b and t s a having in the range of few days d to 3 months m and h 0 75 for all the imfs of t s o t s b and t s a having 5 m based on the value of h the market has been divided into two time horizons short term market having 3 d 3 m and h 0 5 and long term market having 5 m and h 0 75 as h 0 5 in short term and h 0 75 in long term the market is random in short term and has long range correlation in long term robustness of the results has also been verified by using detrended fluctuation exponent analysis and normalised variance n v techniques we obtained 0 5 for reconstructed short term time series and 1 68 for long term reconstructed time series separation of short term and long term market are also identified using n v technique the time scales for short term and long term markets are independent of structural break happened due to extreme event the obtained using the proposed method for short term and long term market may be useful for investors to identify the investment time horizon and hence to design the investment and trading strategies

multifractality of stock markets based on cumulative distribution function and multiscale multifractal analysis abstract considering the diverse application of multifractal techniques in natural scientific disciplines this work underscores the versatility of multiscale multifractal detrended fluctuation analysis mma method to investigate artificial and real world data sets the modified mma method based on cumulative distribution function is proposed with the objective of quantifying the scaling exponent and multifractality of nonstationary time series it is demonstrated that our approach can provide a more stable and faithful description of multifractal properties in comprehensive range rather than fixing the window length and slide length our analyzes based on cdf mma method reveal significant differences in the multifractal characteristics in the temporal dynamics between us and chinese stock markets suggesting that these two stock markets might be regulated by very different mechanism the cdf mma method is important for evidencing the stable and fine structure of multiscale and multifractal scaling behaviors and can be useful to deepen and broaden our understanding of scaling exponents and multifractal characteristics

coherent and random sequences in financial fluctuations abstract the detrended fluctuation analysis dfa is used to sort out temporal correlations in financial data its usefulness for the investigations of long range power law correlations in economic sequences is shown our findings of persistent and antipersistent sequences are suprisingly similar to those for dna sequences which appeared as a mosaic of coding and non coding patches

correlations in economic time series a financial index of the new york stock exchange the sp here f is called the crossover frequency iii we confirm these results using the dfa detrended fluctuation analysis method see fig 2b which allows accurate estimates of exponents independent of local trends

the use of the hurst exponent to investigate the global maximum of the warsaw stock exchange wig20 index abstract the wig20 index the index of the 20 biggest companies traded on the warsaw stock exchange reached the global maximum on 29th october 2007 i have used the local dfa detrended functional analysis to obtain the hurst exponent diffusion exponent and investigate the signature of anti correlation of share price evolution around the maximum the analysis was applied to the share price evolution for variable dfa parameters for many values of parameters the evidence of anti correlation near the wig20 maximum was pointed out

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

curves of every genus with many points i abelian and toric families abstract let nq g denote the maximal number of f q rational points on any curve of genus g over f q ihara for square q and serre for general q proved that lim supg nq g g 0 for any fixed q here we prove limg nq g more precisely we use abelian covers of p 1 to prove lim infg nq g g log g 0 and we use curves on toric surfaces to prove lim infg nq g g1 3 0 we also show that these results are the best possible that can be proved using these families of curves

long range correlations and nonstationarity in the brazilian stock market abstract we report an empirical study of the ibovespa index of the sao paulo stock exchange in which we detect the existence of long range correlations to analyze our data we introduce a rescaled variant of the usual detrended fluctuation analysis that allows us to obtain the hurst exponent through a one parameter fitting we also compute a time dependent hurst exponent h t using 3 year moving time windows in particular we find that before the launch of the collor plan in 1990 the curve h t remains in general well above 1 2 while afterwards it stays close to 1 2 we thus argue that the structural reforms set off by the collor plan has lead to a more efficient stock market in brazil we also suggest that the time dependence of the ibovespa hurst exponent could be described in terms of a multifractional brownian motion

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

truncated levy walks and an emerging market economic index abstract in this paper we perform a statistical analysis of the major stock index in latin america the sao paulo stock exchange index in brazil ibovespa database contains daily records for the 15 year period 1986 2000 we find that the time evolution of the index of share prices is well described by an exponentially truncated levy flight etlf characterized by a levy exponent 1 6 1 7 and a cutoff exponent 1 7 the etlf statistics accounts for the observed short term large fluctuations of the financial data time series and describes the long term convergence to the gaussian regime we derive the characteristic crossover time scale n c dependence on and according to this model as well as the volatility dependence on and n c we find an uncorrelated behaviour of the historical data and n c 20 trading days which are in numerical agreement with the analytical results this dynamic model provides a framework within which it is possible to develop an efficient risk management and option pricing practice for emerging economies

deviations from uniform power law scaling in nonstationary time series a classic problem in physics is the analysis of highly nonstationary time series that typically exhibit long range correlations here we test the hypothesis that the scaling properties of the dynamics of healthy physiological systems are more stable than those of pathological systems by studying beat to beat fluctuations in the human heart rate we develop techniques based on the fano factor and allan factor functions as well as on detrended fluctuation analysis for quantifying deviations from uniform power law scaling in nonstationary time series by analyzing extremely long data sets of up to n 10 5 beats for 11 healthy subjects we find that the fluctuations in the heart rate scale approximately uniformly over several temporal orders of magnitude by contrast we find that in data sets of comparable length for 14 subjects with heart disease the fluctuations grow erratically indicating a loss of scaling stability