explicit solutions of grassmannian σ models classical solutions of the two dimensional grassmannian models of respectively euclidean and minkowskian type are compared with each other some explicit solutions of both types are constructed and some of their graphs are presented

statistical properties of german dax and chinese indices abstract we investigate statistical properties of the german dax and chinese indices including the volatility distribution autocorrelation function dfa function and return volatility correlation function with both the daily data and minutely data at the minutely time scale the chinese indices may show irregular dynamic behavior at the daily time scale the volatility distribution autocorrelation function and dfa function of the chinese indices are qualitatively similar to those of the german dax while the return volatility correlation function exhibits an anti leverage effect different from the leverage effect of the german dax

modeling financial markets by the multiplicative sequence of trades we introduce the stochastic multiplicative point process modeling trading activity of financial markets such a model system exhibits power law spectral density s f 1 f b scaled as power of frequency for various values of b between 0 5 and 2 furthermore we analyze the relation between the power law autocorrelations and the origin of the power law probability distribution of the trading activity the model reproduces the spectral properties of trading activity and explains the mechanism of power law distribution in real markets r 2004 elsevier b v all rights reserved

statistical properties of the indonesian stock exchange index abstract using the tools developed for statistical physics we have analyzed statistical properties of the indonesian stock exchange index ihsg in spite of the small number of available data used in the analysis the result still shows the universal behavior of complex systems previously found in the leading stock indices we also found that the fluctuation of the index return becomes more random after the crisis

invariants of the heat equation for non minimal operators a special class of non minimal operators which are relevant for quantum field theory is introduced the general form of the heat kernel coefficients of these operators on manifolds without boundary is described new results are presented for the traces of the first two heat kernel coefficients for vector yang mills and perturbative gravity it is argued that non minimal operators can be used to define gauge fixing independent actions and solve the conformal mode problem in quantum gravity

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

multi fractal structure of traded volume in financial markets abstract in this article we explore the multi fractal properties of 1 minute traded volume of the equities which compose the dow jones 30 we also evaluate the weights of linear and non linear dependencies in the multi fractal structure of the observable our results show that the multi fractal nature of traded volume comes essentially from the non gaussian form of the probability density functions and from non linear dependencies

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

assessment of the relative ratio of correlated and uncorrelated waiting times in the southern california earthquakes catalogue abstract in the present study we investigated the interevent time interval distribution of earthquakes in southern california we analyzed and compared datasets of waiting times between consecutive earthquakes and time structure distorted datasets the aim of this study was to determine the proportion of waiting time values in the original catalogue that can be regarded as statistically distinguishable or indistinguishable from the baseline time intervals datasets where the original structure of the temporal distribution of earthquakes was disrupted we compiled two types of time structure distorted baseline sequences which comprised mean values of a shuffled original interevent data and b interevent times data from time randomized catalogues to compare the dynamical characteristics of the original and time structure distorted baseline sequences we used several data analysis methods such as power spectrum regression detrended fluctuation and multifractal detrended fluctuation analysis we also tested the nonlinear structure of the original and baseline sequences using the magnitude and sign scaling analysis method we calculated the z s c o r e in order to assess whether the interevent time values in the original dataset shared statistical similarity or dissimilarity with the time structure distorted baseline interevent data sequence we compared the interevent time values in the original dataset with the mean baseline interevent times computed for two types of time structure distorted sequences the results showed that about 30 of the original interevent times were statistically indistinguishable from the mean of the shuffled dataset and 10 from the mean of the time structure distorted baseline interevent dataset we performed similar analyses for other catalogues obtained from different parts of the world according to the results of this analysis the proportion of events in the original catalogues that were indistinguishable from sequences with disturbed time structure did not contradict the results obtained for the southern california catalogue

measuring statistical heterogeneity the pietra index abstract there are various ways of quantifying the statistical heterogeneity of a given probability law statistics uses variance which measures the law s dispersion around its mean physics and information theory use entropy which measures the law s randomness economics uses the gini index which measures the law s egalitarianism in this research we explore an alternative to the gini index the pietra index which is a counterpart of the kolmogorov smirnov statistic the pietra index is shown to be a natural and elemental measure of statistical heterogeneity which is especially useful in the case of asymmetric and skewed probability laws and in the case of asymptotically paretian laws with finite mean and infinite variance moreover the pietra index is shown to have immediate and fundamental interpretations within the following applications renewal processes and continuous time random walks infinite server queueing systems and shot noise processes financial derivatives the interpretation of the pietra index within the context of financial derivatives implies that derivative markets in effect use the pietra index as their benchmark measure of statistical heterogeneity

arithmetic brownian motion subordinated by tempered stable and inverse tempered stable processes abstract in the last decade the subordinated processes have become popular and have found many practical applications therefore in this paper we examine two processes related to time changed subordinated classical brownian motion with drift called arithmetic brownian motion the first one so called normal tempered stable is related to the tempered stable subordinator while the second one to the inverse tempered stable process we compare the main properties such as probability density functions laplace transforms ensemble averaged mean squared displacements of such two subordinated processes and propose the parameters estimation procedures moreover we calibrate the analyzed systems to real data related to indoor air quality

characteristics of the volatility in the korea composite stock price index abstract we empirically analyze the time series of the korea composite stock price index kospi from march of 1992 to february of 2007 using methods from the hydrodynamic turbulence to this end we focus on characteristics of the return and volatility which are respectively the price change and a measure of the financial market fluctuation over a time interval with these we show that the non gaussian probability distribution of the return can be modeled by the convolution of the conditional probability distribution of the return given the volatility and the distribution of the volatility per se from this model we suggest that the non gaussian characteristic of the return results from the fluctuation of the volatility that is a large return is partly if not entirely due to the market fluctuation in a long time scale influencing the fluctuation in a short time scale via net information flow we further show that the volatility has a multi fractal property which resembles the multifractality of the energy dissipation in the turbulence

fractional brownian motion time changed by gamma and inverse gamma process abstract many real time series exhibit behavior adequate to long range dependent data additionally very often these time series have constant time periods and also have characteristics similar to gaussian processes although they are not gaussian therefore there is need to consider new classes of systems to model these kinds of empirical behavior motivated by this fact in this paper we analyze two processes which exhibit long range dependence property and have additional interesting characteristics which may be observed in real phenomena both of them are constructed as the superposition of fractional brownian motion fbm and other process in the first case the internal process which plays role of the time is the gamma process while in the second case the internal process is its inverse we present in detail their main properties paying main attention to the long range dependence property moreover we show how to simulate these processes and estimate their parameters we propose to use a novel method based on rescaled modified cumulative distribution function for estimation of parameters of the second considered process this method is very useful in description of rounded data like waiting times of subordinated processes delayed by inverse subordinators by using the monte carlo method we show the effectiveness of proposed estimation procedures finally we present the applications of proposed models to real time series

effects of coarse graining on the scaling behavior of long range correlated and anti correlated signals abstract we investigate how various coarse graining signal quantization methods affect the scaling properties of long range power law correlated and anti correlated signals quantified by the detrended fluctuation analysis specifically for coarse graining in the magnitude of a signal we consider i the floor ii the symmetry and iii the centro symmetry coarse graining methods we find that for anti correlated signals coarse graining in the magnitude leads to a crossover to random behavior at large scales and that with increasing the width of the coarse graining partition interval this crossover moves to intermediate and small scales in contrast the scaling of positively correlated signals is less affected by the coarse graining with no observable changes when 1 while for 1 a crossover appears at small scales and moves to intermediate and large scales with increasing for very rough coarse graining 3 based on the floor and symmetry methods the position of the crossover stabilizes in contrast to the centro symmetry method where the crossover continuously moves across scales and leads to a random behavior at all scales thus indicating a much stronger effect of the centro symmetry compared to the floor and the symmetry method for coarse graining in time where data points are averaged in non overlapping time windows we find that the scaling for both anti correlated and positively correlated signals is practically preserved the results of our simulations are useful for the correct interpretation of the correlation and scaling properties of symbolic sequences

cross correlations between volume change and price change in finance one usually deals not with prices but with growth rates r defined as the difference in logarithm between two consecutive prices here we consider not the trading volume but rather the volume growth rate r the difference in logarithm between two consecutive values of trading volume to this end we use several methods to analyze the properties of volume changes r and their relationship to price changes r we analyze 14 981 daily recordings of the standard and poor s s p 500 index over the 59 year period 1950 2009 and find power law cross correlations between r and r by using detrended cross correlation analysis dcca we introduce a joint stochastic process that models these cross correlations motivated by the relationship between r and r we estimate the tail exponent of the probability density function p r r 1 for both the s p 500 index as well as the collection of 1819 constituents of the new york stock exchange composite index on 17 july 2009 as a new method to estimate we calculate the time intervals q between events where r q we demonstrate that q the average of q obeys q q we find 3 furthermore by aggregating all q values of 28 global financial indices we also observe an approximate inverse cubic law

modeling long range memory trading activity by stochastic differential equations we propose a model of fractal point process driven by the nonlinear stochastic differential equation the model is adjusted to the empirical data of trading activity in financial markets this reproduces the probability distribution function and power spectral density of trading activity observed in the stock markets we present a simple stochastic relation between the trading activity and return which enables us to reproduce long range memory statistical properties of volatility by numerical calculations based on the proposed fractal point process r 2007 elsevier b v all rights reserved

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

investigation on gait time series by means of factorial moments abstract by means of factorial moments fm the fractal structures embedded in gait time series are investigated intermittency is found in records for healthy objects and this kind of intermittency is much sensitive to disease or outside influences it is found that fm is an effective tool to deal with this kind of time series

the dynamics of traded value revisited we conclude from an analysis of high resolution nyse data that the distribution of the traded value f i or volume has a finite variance si for the very large majority of stocks i and the distribution itself is non universal across stocks the hurst exponent of the same time series displays a crossover from weakly to strongly correlated behavior around the time scale of 1 day the persistence in the strongly correlated regime increases with the average trading activity hf ii as hi h0 g loghf ii which is another sign of non universal behavior the existence of such liquidity dependent correlations is consistent with the empirical observation that si h f ii a where a is a non trivial time scale dependent exponent

scaling and memory in the non poisson process of limit order cancelation abstract the order submission and cancelation processes are two crucial aspects in the price formation of stocks traded in order driven markets we investigate the dynamics of order cancelation by studying the statistical properties of inter cancelation durations defined as the waiting times between consecutive order cancelations of 22 liquid stocks traded on the shenzhen stock exchange of china in year 2003 three types of cancelations are considered including cancelation of any limit orders of buy limit orders and of sell limit orders we find that the distributions of the inter cancelation durations of individual stocks can be well modeled by weibulls for each type of cancelation and the distributions of rescaled durations of each type of cancelations exhibit a scaling behavior for different stocks complex intra day patterns are also unveiled in the inter cancelation durations the detrended fluctuation analysis dfa and the multifractal dfa show that the inter cancelation durations possess long term memory and multifractal nature which are not influenced by the intra day patterns no clear crossover phenomenon is observed in the detrended fluctuation functions with respect to the time scale these findings indicate that the cancelation of limit orders is a non poisson process which has potential worth in the construction of order driven market models

surfaces immersed in lie algebras obtained from the sigma models we study some geometrical aspects of two dimensional orientable surfaces arising from the study of sigma models to this aim we employ an identification of with the lie algebra by means of which we construct a generalized weierstrass formula for immersion of such surfaces the structural elements of the surface like its moving frame the gauss weingarten and the gauss codazzi ricci equations are expressed in terms of the solution of the model defining it further the first and second fundamental forms the gaussian curvature the mean curvature vector the willmore functional and the topological charge of surfaces are expressed in terms of this solution we present detailed implementation of these results for surfaces immersed in and lie algebras

backlund transformations for nonlinear sigma models with values in riemannian symmetric spaces this work deals with backlund transformations for the principal sl n sigma model together with all reduced models with values in riemannian symmetric spaces first the dressing method of zakharov mikhailov and shabat is shown for the case of a meromorphic dressing matrix to be equivalent to a backlund transformation for an associated linearly extended system comparison of this multi backlund transformation with the composition of ordinary ones leads to a new proof of the permutability theorem a new method of solution for such multi backlund transformations mbt is developed by the introduction of a soliton correlation matrix which satisfies a riccati system equivalent to the mbt using the geometric structure of this system a linearization is achieved leading to a nonlinear superposition formula expressing the solution explicitly in terms of solutions of a single backlund transformation through purely linear algebraic relations a systematic study of all reductions of the system by involutive automorphisms is made thereby defining the multi backlund transformations and their solution for all riemannian symmetric spaces

modeling interactions of trading volumes in financial dynamics abstract a dynamic herding model with interactions of trading volumes is introduced at time t an agent trades with a probability which depends on the ratio of the total trading volume at time t 1 to its own trading volume at its last trade the price return is determined by the volume imbalance and number of trades the model can reproduce the power law distributions of the trading volume number of trades and price return and the probable relation between them the exponents are tunable by adjusting the values of the parameters but show slight deviation from those revealed in empirical studies moreover the time series generated are long range correlated we demonstrate that the results are rather robust and do not depend on the particular form of the trading probability

cross correlations in volume space differences between buy and sell volumes abstract we study the cross correlations of buy and sell volumes on the korean stock market in high frequency we observe that the pulling effects of volumes are as small as that of returns the properties of the correlations of buy and sell volumes differ they are explained by the degree of synchronization of stock volumes further the pulling effects on the minimal spanning tree are studied in minimal spanning trees with directed links the large pulling effects are clustered at the center not uniformly distributed the epps effect of buy and sell volumes are observed the reversal of the cross correlations of buy and sell volumes is also detected

on higher spin partition functions we observe that the partition function of the set of all free massless higher spins s 0 1 2 3 in flat space is equal to one the ghost determinants cancel against the physical ones or equivalently the regularized total number of degrees of freedom vanishes this reflects large underlying gauge symmetry and suggests analogy with supersymmetric or topological theory the z 1 property extends also to the ads background i e the 1 loop vacuum partition function of vasiliev theory is equal to 1 assuming a particular regularization of the sum over spins this was noticed earlier as a consistency requirement for the vectorial ads cft duality we find that z 1 is true also in the conformal higher spin theory with higher derivative kinetic terms expanded near flat or conformally flat s4 background we also consider the partition function of free conformal theory of symmetric traceless rank s tensor field which has 2 derivative kinetic term but only scalar gauge invariance in flat 4d space this non unitary theory has weyl invariant action in curved background and it corresponds to partially massless field in ads5 we discuss in detail the special case of s 2 or conformal graviton compute the corresponding conformal anomaly coefficients and compare them with previously found expressions for generic representations of conformal group in 4 dimensions

statistical properties of trading volume depending on size abstract by analyzing high frequency data of transactions on the italian stock index futures we show that the statistical properties of average volume depend on the size of transactions defined as the number of contracts transacted in a single operation in particular we find that large transactions are less correlated with market volatility and display a longer memory

multifractal analysis of indian public sector enterprises abstract in this paper we apply the methods multifractal detrended fluctuation analysis mf dfa and multifractal detrended cross correlation analysis mf dxa to study the auto correlation cross correlation behaviour and multifractal characteristics on twenty three stock market indices of department of public enterprises dpe india the auto correlation and cross correlation have been measured from the hurst scaling exponents and the singularity spectrum quantitatively from the calculated power law scaling exponents we observe the volume and price volume change time series possess strong anti persistent behaviour the price change of different time series shows persistent stochastic and anti persistent behaviour we also observe the existence of multifractal characteristics in all price volume and price volume change time series the price changes in the time series shows high complexity compared to volume and cross correlated price volume

noncommutative residue and sub dirac operators for foliations in this paper we define lower dimensional volumes associated with sub dirac operators for foliations in some cases we compute these lower dimensional volumes we also prove the kastler kalau walze type theorems for foliations with or without boundary as a corollary we give an explanation of the gravitational action for the robertson walker space a b f m3

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

analytical representation of stock and stock indexes returns non gaussian random walks with various jump laws abstract empirical data for stock and stock indexes returns that is available for international markets as well as for the russian stock market is introduced and discussed random walk process with a specific law of an elementary independent increment jump in some random walk space is proposed for a proper basic description an analytical representation of a random walk distribution law is derived from a general conception of stochastic elementary jumps this representation covers classic s chandrasekhar s results for gauss random walks with limited jumps and jumps having distributions with all moments as well as p levy flights with jump distributions without moments starting from the second one finally it describes truncated levy random walks for jumps having distributions with at least the second moment the natural generalization of truncated levy walks is done the random walk process is compared with known empirical data for the above discussed return fluctuations of international assets and stock indexes there is a very good agreement of the elaborated theory with empirical data

effects of non stationarity on the magnitude and sign scaling in the multi scale vertical velocity increment abstract we study the scaling properties of multi scale increment series from the stationary and non stationary vertical velocity records by the detrended fluctuation analysis dfa and series decomposition methods and show the impact of non stationarity on the magnitude and sign scaling properties firstly we show it is difficult to define a significant scaling range for stationary records themselves secondly for increment series with lag one the nonlinear correlation found in magnitude fluctuation i e volatility fluctuation is obvious for both cases and over the smaller scale range the linear correlation found usually in the sign series is the same for both cases however over the larger scale range the difference is sharp and marked nonlinear correlation is also incorporated for the non stationary sign series thirdly with the lags in increment increasing there exist two scaling ranges in both the magnitude and sign fluctuations the nonlinear correlation in the magnitude series over both small and large scale ranges decreases with the lags increasing for the sign series the linear correlation is dominant over both small and large scale ranges for stationary case however the nonlinear correlation can be found over the large scale ranges for non stationary case and will decrease with lags increasing the nonlinear correlation found in the sign series over large scale range is resulted from the modulation of the large scale structures found in the non stationary data which will incorporate parts of the magnitude information into the sign series

economic fluctuations and statistical physics quantifying extremely rare and less rare events in finance one challenge of economics is that the systems treated by these sciences have no perfect metronome in time and no perfect spatial architecture crystalline or otherwise nonetheless as if by magic out of nothing but randomness one finds remarkably fine tuned processes in time we present an overview of recent research joining practitioners of economic theory and statistical physics to try to better understand puzzles regarding economic fluctuations one of these puzzles is how to describe outliers phenomena that lie outside of patterns of statistical regularity we review evidence consistent with the possibility that such outliers may not exist this possibility is supported by recent analysis of databases containing information about each trade of every stock r 2007 elsevier b v all rights reserved

scaling analysis of multi variate intermittent time series abstract the scaling properties of the time series of asset prices and trading volumes of stock markets are analysed it is shown that similar to the asset prices the trading volume data obey multi scaling length distribution of low variability periods in the case of asset prices such scaling behaviour can be used for risk forecasts the probability of observing next day a large price movement is super universally inversely proportional to the length of the ongoing low variability period finally a method is devised for a multi factor scaling analysis we apply the simplest two factor model to equity index and trading volume time series

quantifying economic fluctuations abstract this manuscript is a brief summary of a talk designed to address the question of whether two of the pillars of the field of phase transitions and critical phenomena scale invariance and universality can be useful in guiding research on interpreting empirical data on economic fluctuations using this conceptual framework as a guide we empirically quantify the relation between trading activity measured by the number of transactions n and the price change g t for a given stock over a time interval t t t we relate the time dependent standard deviation of price changes volatility to two microscopic quantities the number of transactions n t in t and the variance w2 t of the price changes for all transactions in t we find that the long ranged volatility correlations are largely due to those of n we then argue that the tail exponent of the distribution of n is insufficient to account for the tail exponent of p g x since n and w display only weak inter dependency our results show that the fat tails of the distribution p g x arises from w finally we review recent work on quantifying collective behavior among stocks by applying the conceptual framework of random matrix theory rmt rmt makes predictions for universal properties that do not depend on the interactions between the elements comprising the system and deviations from rmt provide clues regarding system specific properties we compare the statistics of the cross correlation matrix c whose elements cij are the correlation coefficients of price fluctuations of stock i and j against a random matrix having the same symmetry properties it is found that rmt methods can distinguish random and non random parts of c the non random part of c which deviates from rmt results provides information regarding genuine collective behavior among stocks we also discuss results that are reminiscent of phase transitions in spin systems where the divergent behavior of the response function at the critical point zero magnetic field leads to large fluctuations and we discuss a curious symmetry breaking a feature qualitatively identical to the behavior of the probability density of the magnetization for fixed values of the inverse temperature

the noncommutative residue for manifolds with boundary abstract we construct a trace on the algebra of classical elements in boutet de monvel s calculus on a compact manifold with boundary of dimensionn 2 this trace coincides with wodzicki s noncommutative residue if the boundary is reduced to the empty set moreover we show that it is the unique continuous trace on this algebra up to multiplication by a constant

modeling non stationarities in high frequency financial time series abstract we study tick by tick financial returns for the ftse mib index of the italian stock exchange borsa italiana we confirm previously detected non stationarities scaling properties reported before for other high frequency financial data are only approximately valid as a consequence of our empirical analyses we propose a simple model for non stationary returns based on a non homogeneous normal compound poisson process it turns out that our model can approximately reproduce several stylized facts of high frequency financial time series moreover using monte carlo simulations we analyze order selection for this class of models using three information criteria akaike s information criterion aic the bayesian information criterion bic and the hannan quinn information criterion hq for comparison we perform a similar monte carlo experiment for the acd autoregressive conditional duration model our results show that the information criteria work best for small parameter numbers for the compound poisson type models whereas for the acd model the model selection procedure does not work well in certain cases

statistical properties of share volume traded in financial markets we quantitatively investigate the ideas behind the often expressed adage it takes volume to move stock prices and study the statistical properties of the number of shares traded q deltat for a given stock in a fixed time interval deltat we analyze transaction data for the largest 1000 stocks for the two year period 1994 95 using a database that records every transaction for all securities in three major us stock markets we find that the distribution p q deltat displays a power law decay and that the time correlations in q deltat display long range persistence further we investigate the relation between q deltat and the number of transactions n deltat in a time interval deltat and find that the long range correlations in q deltat are largely due to those of n deltat our results are consistent with the interpretation that the large equal time correlation previously found between q deltat and the absolute value of price change g deltat related to volatility are largely due to n deltat

heat equation asymptotics of nonminimal operators on differential forms let d d d e be a natural operator on differential forms for example dv j k kvj c1 j kvk c2rjkvk has this form it will be shown that when the lower order term e is absent the integrated heat kernel coefficients an d can be simply expressed in terms of the familiar coefficients an j for the laplacian operators on forms the first two coefficients when a zeroth order term is present are evaluated

trace expansions and the noncommutative residue for manifolds with boundary for a pseudodifferential boundary operator a of order 2 z and class 0 in the boutet de monvel calculus on a compact n dimensional manifold with boundary we consider the function tr ab s where b is an auxiliary system formed of the dirichlet realization of a second order strongly elliptic differential operator and an elliptic operator on the boundary we prove that tr ab s has a meromorphic extension to c with poles at the half integers s n j 2 j 2 n possibly double for s 0 and we prove that its residue at 0 equals the noncommutative residue of a as defined by fedosov golse leichtnam and schrohe by a different method to achieve this we establish a full asymptotic expansion of tr a b k in powersl 2 and log powersl 2 log where the noncommutative residue equals the coefficient of the highest order log power there is a related expansion of tr ae tb the paper will appear in journal reine angew math crelle s journal then is a holomorphic function of s for large re s we show that it extends to a mero morphic function on the whole complex plane with at most double poles moreover we prove that the noncommutative residue res a of a can be recovered as a residue in this

constant curvature surfaces of the supersymmetric ℂpn 1 sigma model constant curvature surfaces are constructed from the finite action solutions of the supersymmetric pn 1 sigma model it is shown that there is a unique holomorphic solution which leads to constant curvature surfaces the generalized veronese curve we give a general criterion to construct non holomorphic solutions of the model we extend our analysis to general supersymmetric grassmannian models

a new proof of weyl s formula on the asymptotic distribution of eigenvalues one of the more perplexing problems of finite particle quantum mechanics is to find the appropriate quantum mechanical description of a given classical mechanical system unfortunately from the mathematical point of view this problem is not terribly well posed suppose the classical system in question is represented by a symplectic manifold x and a classical observable p x r suppose also for simplicity that this system is a confined system in the sense that the sets p 1 are all compact let h be a hilbert space and let p be a self adjoint operator on h representing a quantum observable without specifying anything further about p for instance its relation to other observables there is practically no way of ascertaining whether p is an appropriate quantum counterpart of p at first glance the only requirements this appears to impose on p are that the spectrum of p be discrete and that the number of eigenvalues n a less than 1 be finite for all 1 this is the analogue of the condtion that p 1 be compact by examining the statistical properties of a large aggregate of classical systems each a copy of x p one can in fact say a little bit more about the relation p to p by comparing classical and quantum partition functions one can show that for iz large

model for interevent times with long tails and multifractality in human communications an application to financial trading social technological and economic time series are divided by events which are usually assumed to be random albeit with some hierarchical structure it is well known that the interevent statistics observed in these contexts differs from the poissonian profile by being long tailed distributed with resting and active periods interwoven understanding mechanisms generating consistent statistics has therefore become a central issue the approach we present is taken from the continuous time random walk formalism and represents an analytical alternative to models of nontrivial priority that have been recently proposed our analysis also goes one step further by looking at the multifractal structure of the interevent times of human decisions we here analyze the intertransaction time intervals of several financial markets we observe that empirical data describe a subtle multifractal behavior our model explains this structure by taking the pausing time density in the form of a superstatistics where the integral kernel quantifies the heterogeneous nature of the executed tasks a stretched exponential kernel provides a multifractal profile valid for a certain limited range a suggested heuristic analytical profile is capable of covering a broader region

price fluctuations and market activity we empirically quantify the relation between trading activity measured by the number of transactions n and the price change g t for a given stock over a time interval t t t we relate the time dependent standard deviation of price changes volatility to two microscopic quantities the number of transactions n t in t and the variance w 2 t of the price changes for all transactions in t we find that the long ranged volatility correlations are largely due to those of n we then argue that the tail exponent of the distribution of n is insufficient to account for the tail exponent of p g x our results suggest that the fat tails of the distribution p g x arises from w which has a power law distribution with an exponent consistent with that of g

fokker planck equation of distributions of financial returns and power laws abstract our purpose is to relate the fokker planck formalism proposed by friedrich et al phys rev lett 84 2000 5224 for the distribution of stock market returns to the empirically well established power law distribution with an exponent in the range 3 5 we show how to use friedrich et al s formalism to predict that the distribution of returns is indeed asymptotically a power law with an exponent that can be determined from the kramers moyal coefficients determined by friedrich et al however with their values determined for the u s dollar german mark exchange rates the exponent predicted from their theory is found to be around 12 in disagreement with the often quoted value between 3 and 5 this could be explained by the fact that the large asymptotic value of 12 does not apply to real data that lie still far from the stationary state of the fokker planck description another possibility is that power laws are inadequate the mechanism for the power law is based on the presence of multiplicative noise across time scales which is different from the multiplicative noise at fixed time scales implicit in the arch models developed in the finance literature

description of surfaces associated with grassmannian sigma models on minkowski space we construct and investigate smooth orientable surfaces in su n algebras the structural equations of surfaces associated with grassmannian sigma models on minkowski space are studied using moving frames adapted to the surfaces the first and second fundamental forms of these surfaces as well as the relations between them as expressed in the gauss weingarten and gauss codazzi ricci equations are found the scalar curvature and the mean curvature vector expressed in terms of a solution of grassmanian sigma model are obtained

probability distribution function and multiscaling properties in the korean stock market abstract we consider the probability distribution function pdf and the multiscaling properties of the index and the traded volume in the korean stock market we observed the power law of the pdf at the fat tail region for the return volatility the traded volume and changes of the traded volume we also investigate the multifractality in the korean stock market we consider the multifractality by the detrended fluctuation analysis mfdfa we observed the multiscaling behaviors for index return traded volume and the changes of the traded volume we apply mfdfa method for the randomly shuffled time series to observe the effects of the autocorrelations the multifractality is strongly originated from the long time correlations of the time series

price fluctuations from the order book perspective empirical facts and a simple model abstract statistical properties of an order book and the effect they have on price dynamics were studied using the high frequency nasdaq level ii data it was observed that the size distribution of marketable orders transaction sizes has power law tails with an exponent 1 market 2 4 0 1 the distribution of limit order or quote sizes was found to be consistent with a power law with an exponent close to 2 a somewhat better fit to this distribution was obtained by using a log normal distribution which has an effective power law exponent equal to 2 in the middle of the observed range the depth of the order book measured as a price impact of a hypothetical large market order was observed to be a non linear function of its size a large imbalance in the number of limit orders placed at bid and ask sides of the book was shown to lead to a predictable short term price change which is in accord with the law of supply and demand

covariant algebraic method for calculation of the low energy heat kernel using our recently proposed covariant algebraic approach the heat kernel for a laplace like differential operator in a low energy approximation is studied neglecting all the covariant derivatives of the gauge field strength yang mills curvature and the covariant derivatives of the potential term of third order and higher a closed formula for the heat kernel as well as its diagonal is obtained explicit formulas for the coefficients of the asymptotic expansion of the heat kernel diagonal in terms of the yang mills curvature the potential term and its first two covariant derivatives are obtained

coupling detrended fluctuation analysis of asian stock markets abstract this paper uses the coupling detrended fluctuation analysis cdfa method to investigate the multifractal characteristics of four asian stock markets using three stock indices stock price returns trading volumes and the composite index the results show that coupled correlations exist among the four stock markets and the coupled correlations have multifractal characteristics we then use the chi square 2 test to identify the sources of multifractality for the different stock indices the contributions of a single series to multifractality are different in other words the contributions of each country to coupled correlations are different the comparative analysis shows that the research on the combine effect of stock price returns and trading volumes may be more comprehensive than on an individual index by comparing the strength of multifractality for original data with the residual errors of the vector autoregression var model we find that the var model could not be used to describe the dynamics of the coupled correlations among four financial time series

price volume cross correlation analysis of csi300 index futures abstract we investigate the cross correlation between price returns and trading volumes for the china securities index 300 csi300 index futures which are the only stock index futures traded on the china financial futures exchange cffex the basic statistics suggest that distributions of these two time series are not normal but exhibit fat tails based on the detrended cross correlation analysis dcca we obtain that returns and trading volumes are long range cross correlated the existence of multifractality in the cross correlation between returns and trading volumes has been proven with the multifractal detrended cross correlation analysis mfdcca algorithm the multifractal analysis also confirms that returns and trading volumes have different degrees of multifractality we further perform a cross correlation statistic to verify whether the cross correlation significantly exists between returns and trading volumes for csi300 index futures in addition results of the test for lead lag effect demonstrate that contemporaneous cross correlation of return and trading volume series is stronger than cross correlations of leaded or lagged series

minimizing the effect of trends on detrended fluctuation analysis of long range correlated noise abstract detrended fluctuation analysis dfa has been proposed as a robust technique to determine possible long range correlations in power law processes phys rev e 49 1994 1685 1989 however recent studies have reported the susceptibility of dfa to trends phys rev e 64 2001 011114 011133 which give rise to spurious crossovers and prevent reliable estimation of the scaling exponents inspired by these reports we propose a technique based on singular value decomposition svd of the trajectory matrix to minimize the effect of linear power law periodic and also quasi periodic trends superimposed on long range correlated power law noise the effectiveness of the technique is demonstrated on publicly available data sets phys rev e 64 2001 011114 011133

nonextensive statistical mechanics and economics abstract ergodicity this is to say dynamics whose time averages coincide with ensemble averages naturally leads to boltzmann gibbs bg statistical mechanics hence to standard thermodynamics this formalism has been at the basis of an enormous success in describing among others the particular stationary state corresponding to thermal equilibrium there are however vast classes of complex systems which accommodate quite badly or even not at all within the bg formalism such dynamical systems exhibit in one way or another nonergodic aspects in order to be able to theoretically study at least some of these systems a formalism was proposed 14 years ago which is sometimes referred to as nonextensive statistical mechanics we briefly introduce this formalism its foundations and applications furthermore we provide some bridging to important economical phenomena such as option pricing return and volume distributions observed in the financial markets and the fascinating and ubiquitous concept of risk aversion one may summarize the whole approach by saying that bg statistical mechanics is based on the entropy s bg k i p i ln p i and typically provides exponential laws for describing stationary states and basic time dependent phenomena while nonextensive statistical mechanics is instead based on the entropic form s q k 1 i p i q q 1 with s 1 s bg and typically provides for the same type of description asymptotic power laws

a long range memory stochastic model of the return in financial markets abstract we present a nonlinear stochastic differential equation sde which mimics the probability density function pdf of the return and the power spectrum of the absolute return in financial markets absolute return as a measure of market volatility is considered in the proposed model as a long range memory stochastic variable the sde is obtained from the analogy with an earlier proposed model of trading activity in the financial markets and generalized within the nonextensive statistical mechanics framework the proposed stochastic model generates time series of the return with two power law statistics i e the pdf and the power spectral density reproducing the empirical data for the one minute trading return in the nyse

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

a multifractal detrended fluctuation analysis of trading behavior of individual and institutional traders in tehran stock market abstract employing the multifractal detrended fluctuation analysis mf dfa the multifractal properties of trading behavior of individual and institutional traders in the tehran stock exchange tse are numerically investigated using daily trading volume time series of these two categories of traders the scaling exponents generalized hurst exponents generalized fractal dimensions and singularity spectrum are derived furthermore two main sources of multifractality i e temporal correlations and fat tailed probability distributions are also examined we also compare our results with data of s p 500 results of this paper suggest that for both classes of investors in tse multifractality is mainly due to long range correlation while for s p 500 the fat tailed probability distribution is the main source of multifractality

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

connected graph representations of the quantum propagator and semiclassical expansions the time evolution operator u t s of a spinless nonrelativistic n body quantum system in euclidean space with real analytic time dependent scalar interaction v x t is studied a complete formal asymptotic expansion involving simple connected graphs is derived for the full coordinate and mixed coordinate momentum representation propagators the derivation is based on dyson s series for u t s and the combinatorics involved in the cluster expansion of the classical grand partition function these results provide an efficient means of generating nonperturbative propagator expansions in the physical variables mass m planck s constant h time displacement t s the structural bridge between the wkb and wigner kirkwood expansions is sketched for mixed representations of u t s in the heat equation context the graphical expansions are found for mixed representations of the density operator e beta h finally an explicit differential formula is obtained for wigner s distribution function f x p beta

quantifying signals with power law correlations a comparative study of detrended fluctuation analysis and detrended moving average techniques detrended fluctuation analysis dfa and detrended moving average dma are two scaling analysis methods designed to quantify correlations in noisy nonstationary signals we systematically study the performance of different variants of the dma method when applied to artificially generated long range power law correlated signals with an a priori known scaling exponent alpha 0 and compare them with the dfa method we find that the scaling results obtained from different variants of the dma method strongly depend on the type of the moving average filter further we investigate the optimal scaling regime where the dfa and dma methods accurately quantify the scaling exponent alpha 0 and how this regime depends on the correlations in the signal finally we develop a three dimensional representation to determine how the stability of the scaling curves obtained from the dfa and dma methods depends on the scale of analysis the order of detrending and the order of the moving average we use as well as on the type of correlations in the signal

dynamics of the number of trades of financial securities abstract we perform a parallel analysis of the spectral density of i the logarithm of price and ii the daily number of trades of a set of stocks traded in the new york stock exchange the stocks are selected to be representative of a wide range of stock capitalization the observed spectral densities show a different power law behavior we confirm the 1 f2 behavior for the spectral density of the logarithm of stock price whereas we detect a 1 f like behavior for the spectral density of the daily number of trades

integrable systems and reductions of the self dual yang mills equations many integrable equations are known to be reductions of the self dual yang mills equations this article discusses some of the well known reductions including the standard soliton equations the classical painleve equations and integrable generalizations of the darboux halphen system and chazy equations the chazy equation first derived in 1909 is shown to correspond to the equations studied independently by ramanujan in 1916

analysis of aggregated tick returns evidence for anomalous diffusion in order to investigate the origin of large price fluctuations we analyze stock price changes of ten frequently traded nasdaq stocks in the year 2002 though the influence of the trading frequency on the aggregate return in a certain time interval is important it cannot alone explain the heavy tailed distribution of stock price changes for this reason we analyze intervals with a fixed number of trades in order to eliminate the influence of the trading frequency and investigate the relevance of other factors for the aggregate return we show that in tick time the price follows a discrete diffusion process with a variable step width while the difference between the number of steps in positive and negative direction in an interval is gaussian distributed the step width is given by the return due to a single trade and is long term correlated in tick time hence its mean value can well characterize an interval of many trades and turns out to be an important determinant for large aggregate returns we also present a statistical model reproducing the cumulative distribution of aggregate returns for an accurate agreement with the empirical distribution we also take into account asymmetries of the step widths in different directions together with cross correlations between these asymmetries and the mean step width as well as the signs of the steps

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

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

understanding the cubic and half cubic laws of financial fluctuations recent empirical research has uncovered regularities in nancial u ii the half cubic law of volumes volumes follow a power law distribution with exponent 3 iii approximate cubic law of number of trades the number of trades in a given time intervals follows a power law distribution with exponent around 3 we discuss a new theory that explains them as well as some related facts c 2003 published by elsevier science b v

the action functional in non commutative geometry we establish the equality between the restriction of the adler manin wodzicki residue or non commutative residue to pseudodifferential operators of order n on ann dimensional compact manifoldm with the trace which j dixmier constructed on the macaev ideal we then use the latter trace to recover the yang mills interaction in the context of non commutative differential geometry

modeling long range cross correlations in two component arfima and fiarch processes we investigate how simultaneously recorded long range power law correlated multivariate signals cross correlate to this end we introduce a two component arfima stochastic process and a two component fiarch process to generate coupled fractal signals with long range power law correlations which are at the same time long range cross correlated we study how the degree of cross correlations between these signals depends on the scaling exponents characterizing the fractal correlations in each signal and on the coupling between the signals our findings have relevance when studying parallel outputs of multiple component of physical physiological and social systems

the level crossing and inverse statistic analysis of german stock market index dax and daily oil price time series a b s t r a c t the level crossing and inverse statistics analysis of dax and oil price time series are given we determine the average frequency of positive slope crossings where t 1 is the average waiting time for observing the level again we estimate the probability p k which provides us the probability of observing k times of the level with positive slope in time scale t for analyzed time series we found that maximum k is about 6 we show that by using the level crossing analysis one can estimate how the dax and oil time series will develop we carry out the same analysis for the increments of dax and oil price log returns which is known as inverse statistics and provide the distribution of waiting times to observe some level for the increments 2011 elsevier b v all rights reserved stochastic processes occur in many natural and man made phenomena ranging from various indicators of economic activities in the stock market velocity fluctuations in turbulent flows and heartbeat dynamics etc 1 the level crossing analysis of stochastic processes has been introduced by rice 1944 1945 2 26 and used to describe the turbulence 16 rough surfaces 27 stock markets 28 burgers turbulence and kardar parisi zhang equation 29 30 the level crossing analysis of the data set has the advantage that it gives important global properties of the time series and do not need the scaling feature the almost of the methods in time series analysis are using the scaling features of time series and their applications are restricted to the time series with scaling properties our goal with the level crossing analysis is to characterize the statistical properties of the data set with the hope to better understand the underlying stochastic dynamics and provide a possible tool to estimate its dynamics the level crossing and inverse statistics analysis can be viewed as the complementary method to the other well known methods such as detrended fluctuation analysis dfa 31 detrended moving average dma 32 wavelet transform modulus maxima wtmm 33 rescaled range analysis r s 34 scaled windowed variance swv 35 langevin dynamics 36 detrended cross correlation analysis 37 multifactor analysis of

asymptotic behaviors of the heat kernel in covariant perturbation theory the trace of the heat kernel is expanded in a basis of nonlocal curvature invariants of nth order the coefficients of this expansion the nonlocal form factors are calculated to third order in the curvature inclusive the early time and late time asymptotic behaviors of the trace of the heat kernel are presented with this accuracy the late time behavior gives the criterion of analyticity of the effective action in quantum field theory the latter point is exemplified by deriving the effective action in two dimensions

gauge theories on manifolds with boundary the boundary value problem for laplace type operators acting on smooth sections of a vector bundle over a compact riemannian manifold with generalized local boundary conditions including both normal and tangential derivatives is studied the condition of strong ellipticity of this boundary value problem is formulated the resolvent kernel and the heat kernel in the leading approximation are explicitly constructed as a result the previous work in the literature on heat kernel asymptotics is shown to be a particular case of a more general structure for a bosonic gauge theory on a compact riemannian manifold with smooth boundary the problem of obtaining a gauge field operator of laplace type is studied jointly with local and gauge invariant boundary conditions which should lead to a strongly elliptic boundary value problem the scheme is extended to fermionic gauge theories by means of local and gauge invariant projectors after deriving a general condition for the validity of strong ellipticity for gauge theories it is proved that for euclidean yang mills theory and rarita schwinger fields all the above conditions can be satisfied for euclidean quantum gravity however this property no longer holds i e the corresponding boundary value problem is not strongly elliptic some non standard local formulae for the leading asymptotics of the heat kernel diagonal are also obtained it is shown that due to the lack of strong ellipticity the heat kernel diagonal is non integrable near the boundary

causalities of the taiwan stock market abstract volatility fitting with first order landau expansion stationarity and causality of the taiwan stock market taiex are investigated based on daily records instead of consensuses that consider stock market index change as a random time series we propose the market change as a dual time series consists of the index and the corresponding volume therefore causalities between these two time series are investigated our results suggest the volume time series is of second order importance than the index time series the index time series receives slightly stronger influence from the previous 67th trading day while the volume time series is slightly stronger influenced by the previous 62nd trading day

nonminimal operators and non commutative residue in this paper we get the kastler kalau walze type theorem associated to nonminimal operators by heat equation asymptotics on compact manifolds without boundary we compute the lower dimensional volume associated to nonminimal operators for five dimensional compact manifolds with boundary and we also compute lower dimensional volume associated to the de rham hodge operators for six dimensional compact manifolds with boundary

common scaling patterns in intertrade times of u s stocks we analyze the sequence of time intervals between consecutive stock trades of thirty companies representing eight sectors of the u s economy over a period of 4 yrs for all companies we find that i the probability density function of intertrade times may be fit by a weibull distribution ii when appropriately rescaled the probability densities of all companies collapse onto a single curve implying a universal functional form iii the intertrade times exhibit power law correlated behavior within a trading day and a consistently greater degree of correlation over larger time scales in agreement with the correlation behavior of the absolute price returns for the corresponding company and iv the magnitude series of intertrade time increments is characterized by long range power law correlations suggesting the presence of nonlinear features in the trading dynamics while the sign series is anticorrelated at small scales our results suggest that independent of industry sector market capitalization and average level of trading activity the series of intertrade times exhibit possibly universal scaling patterns which may relate to a common mechanism underlying the trading dynamics of diverse companies further our observation of long range power law correlations and a parallel with the crossover in the scaling of absolute price returns for each individual stock support the hypothesis that the dynamics of transaction times may play a role in the process of price formation

similarities and differences between physics and economics in this opening talk we discuss some of the similarities between work being done by economists and by physicists seeking to contribute to economics we also mention some of the dierences in the approaches taken and justify these dierent approaches by developing the argument that by approaching the same problem from dierent points of view new results might emerge in particular we review some recent results for example the 1nding that there are two new universal scaling models in economics i the 3uctuation of price changes of any stock market is characterized by a pdf which is a simple power law with exponent 4 that extends over 10 2 standard deviations a factor of 10 8 on the y axis ii for a wide range of economic organizations the histogram that shows how size of organization is inversely correlated to 3uc tuations in size with an exponent 1 6 neither of these two new laws has a 1rm theoretical foundation we also discuss results that are reminiscent of phase transitions in spin systems where the divergent behavior of the response function at the critical point zero magnetic 1eld leads to large 3uctuations c 2001 published by elsevier science b v

infinite dimensional lie algebras acting on the solution space of various sigma models infinite dimensional lie algebras of infinitesimal transformations acting on the solution space of various two dimensional models are investigated the main tools are i takasaki s interpretation commun math phys 94 35 1984 of the solutions of the associated linear system in terms of points in an infinite dimensional grassmann manifold and ii mikhailov s reduction procedure physica d 3 73 1981 for linear systems takasaki s approach leads for the models with values in a lie group g to a set of transformations that has the structure of the loop algebra g r t t 1 where g is the lie algebra of g this algebra has already been encountered by dolan phys rev lett 47 1371 1981 and by wu nucl phys b 211 160 1983 among others the models with a wess zumino term are also considered the algebraic structure is found to be the same finally mikhailov s procedure is used to study the models with values in a riemannian symmetric space rss g h which is not a lie group th

yet on statistical properties of traded volume correlation and mutual information at different value magnitudes abstract in this article we analyse linear correlation and non linear dependence of traded volume v of the 30 constituents of dow jones industrial average at different value scales specifically we have raised v to some real value or which introduces a bias for small 0 or large 1 values our results show that small values of v are regularly anti correlated with values at other scales of traded volume this is consistent with the high liquidity of the 30 equities analysed and the asymmetric form of the multi fractal spectrum for traded volume which has supported the dynamical scenario presented by us

empirical shape function of limit order books in the chinese stock market abstract we have analyzed the statistical probabilities of limit order book lob shape through building the book using the ultra high frequency data from 23 liquid stocks traded on the shenzhen stock exchange in 2003 we find that the averaged lob shape has a maximum away from the same best price for both buy and sell sides of the lob the lob shape function has nice exponential form in the right tail the buy side of the lob is found to be abnormally thicker for the price levels close to the same best although there are much more sell orders on the book we also find that the lob shape functions for both buy and sell sides have periodic peaks with a period of five the 1 min averaged volumes at fixed tick level follow log normal distributions except for the left tails which display power law behaviors exhibit abnormal intraday patterns with increasing trend and possess long memory that cannot be explained by the intraday patterns academic implications of our empirical results are also briefly discussed

multiplicative point process as a model of trading activity signals consisting of a sequence of pulses show that inherent origin of the 1 f noise is a brownian 1uctuation of the average interevent time between subsequent pulses of the pulse sequence in this paper we generalize the model of interevent time to reproduce a variety of self a5ne time series exhibiting power spectral density s f scaling as a power of the frequency f furthermore we analyze the relation between the power law correlations andthe origin of the power law probability distribution of the signal intensity we introduce a stochastic multiplicative model for the time intervals between point events and analyze the statistical properties of the signal analytically and numerically such model system exhibits power law spectral den

variety and volatility in financial markets we study the price dynamics of stocks traded in a financial market by considering the statistical properties of both a single time series and an ensemble of stocks traded simultaneously we use the n stocks traded on the new york stock exchange to form a statistical ensemble of daily stock returns for each trading day of our database we study the ensemble return distribution we find that a typical ensemble return distribution exists in most of the trading days with the exception of crash and rally days and of the days following these extreme events we analyze each ensemble return distribution by extracting its first two central moments we observe that these moments fluctuate in time and are stochastic processes themselves we characterize the statistical properties of ensemble return distribution central moments by investigating their probability density functions and temporal correlation properties in general time averaged and portfolio averaged price returns have different statistical properties we infer from these differences information about the relative strength of correlation between stocks and between different trading days last we compare our empirical results with those predicted by the single index model and we conclude that this simple model cannot explain the statistical properties of the second moment of the ensemble return distribution

statistical properties of trading volume of chinese stocks abstract the cumulative distribution of trading volume is investigated for chinese stocks different from the power law scaling of mature markets the distribution is well fitted by a stretched exponential function f x e x with the autocorrelation function and the detrended fluctuation analysis the long range autocorrelation of trading volume is revealed the conditional dependence of volume on volatility and the volume volatility cross correlation are studied and a positive long range correlation between volume and volatility is observed