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

information transfer network of global market indices abstract we study the topological properties of the information transfer networks itn of the global financial market indices for six different periods itn is a directed weighted network in which the direction and weight are determined by the transfer entropy between market indices by applying the threshold method it is found that itn undergoes a crossover from the complete graph to a small world sw network sw regime of itn for a global crisis is found to be much more enhanced than that for ordinary periods furthermore when itn is in sw regime the average clustering coefficient is found to be synchronized with average volatility of markets we also compare the results with the topological properties of correlation networks

on fitting the pareto levy distribution to stock market index data selecting a suitable cutoff value abstract the so called pareto levy or power law distribution has been successfully used as a model to describe probabilities associated to extreme variations of stock markets indexes worldwide the selection of the threshold parameter from empirical data and consequently the determination of the exponent of the distribution is often done using a simple graphical method based on a log log scale where a power law probability plot shows a straight line with slope equal to the exponent of the power law distribution this procedure can be considered subjective particularly with regard to the choice of the threshold or cutoff parameter in this work a more objective procedure based on a statistical measure of discrepancy between the empirical and the pareto levy distribution is presented the technique is illustrated for data sets from the new york stock exchange djia and the mexican stock market ipc

volatility clustering and scaling for financial time series due to attractor bubbling a microscopic model of financial markets is considered consisting of many interacting agents spins with global coupling and discrete time heat bath dynamics similar to random ising systems the interactions between agents change randomly in time in the thermodynamic limit the obtained time series of price returns show chaotic bursts resulting from the emergence of attractor bubbling or on off intermittency resembling the empirical financial time series with volatility clustering for a proper choice of the model parameters the probability distributions of returns exhibit power law tails with scaling exponents close to the empirical ones

the hele shaw asymptotics for mechanical models of tumor growth models of tumor growth now commonly used present several levels of complexity both in terms of the biomedical ingredients and the mathematical description our first goal here is to formulate a free boundary model of hele shaw type a variant including growth terms starting from the description at the cell level and passing to the stiff limit in the pressure law of state in contrast with the classical hele shaw problem here the geometric motion governed by the pressure is not sufficient to completely describe the dynamics a complete description requires the equation on the cell number density we then go on to consider a more complex model including the supply of nutrients through vasculature and we study the stiff limit for the involved coupled system

the coupling analysis between stock market indices based on permutation measures abstract many information theoretic methods have been proposed for analyzing the coupling dependence between time series and it is significant to quantify the correlation relationship between financial sequences since the financial market is a complex evolved dynamic system recently we developed a new permutation based entropy called cross permutation entropy cpe to detect the coupling structures between two synchronous time series in this paper we extend the cpe method to weighted cross permutation entropy wcpe to address some of cpe s limitations mainly its inability to differentiate between distinct patterns of a certain motif and the sensitivity of patterns close to the noise floor it shows more stable and reliable results than cpe does when applied it to spiky data and ar 1 processes besides we adapt the cpe method to infer the complexity of short length time series by freely changing the time delay and test it with gaussian random series and random walks the modified method shows the advantages in reducing deviations of entropy estimation compared with the conventional one finally the weighted cross permutation entropy of eight important stock indices from the world financial markets is investigated and some useful and interesting empirical results are obtained

characterization of sleep stages by correlations in the magnitude and sign of heartbeat increments we study correlation properties of the magnitude and the sign of the increments in the time intervals between successive heartbeats during light sleep deep sleep and rapid eye movement rem sleep using the detrended fluctuation analysis method we find short range anticorrelations in the sign time series which are strong during deep sleep weaker during light sleep and even weaker during rem sleep in contrast we find long range positive correlations in the magnitude time series which are strong during rem sleep and weaker during light sleep we observe uncorrelated behavior for the magnitude during deep sleep since the magnitude series relates to the nonlinear properties of the original time series while the sign series relates to the linear properties our findings suggest that the nonlinear properties of the heartbeat dynamics are more pronounced during rem sleep thus the sign and the magnitude series provide information which is useful in distinguishing between the sleep stages

volatilities traded volumes and the hypothesis of price increments in derivative securities a detrended fluctuation analysis dfa is applied to the statistics of korean treasury bond ktb futures from which the logarithmic increments volatilities and traded volumes are estimated over a specific time lag in this study the logarithmic increment of futures prices has no long memory property while the volatility and the traded volume exhibit the existence of the long memory property to analyze and calculate whether the volatility clustering is due to a inherent higher order correlation not detected by with the direct application of the dfa to logarithmic increments of ktb futures it is of importance to shuffle the original tick data of future prices and to generate a geometric brownian random walk with the same mean and standard deviation it was found from a comparison of the three tick data that the higher order correlation inherent in logarithmic increments leads to volatility clustering particularly the result of the dfa on volatilities and traded volumes can be supported by the hypothesis of price changes

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

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

on the deformation complex of homotopy affine actions abstract an affine action of an associative algebra a on a vector space v is an algebra morphism a v end v where v is a vector space and v end v is the algebra of affine transformations of v the one dimensional version of the swiss cheese operad denoted sc 1 is the operad whose algebras are affine actions of associative algebras this operad is koszul and admits a minimal model denoted by sc 1 algebras over this minimal model are called homotopy affine actions they consist of an a morphism a v end v where a is an a algebra in this paper we prove a relative version of deligne s conjecture in other words we show that the deformation complex of a homotopy affine action has the structure of an algebra over an sc 2 operad that structure is naturally compatible with the e 2 structure on the deformation complex of the a algebra

log amplitude statistics for beck cohen superstatistics as a possible generalization of beck cohen superstatistical processes we study non gaussian processes with temporal heterogeneity of local variance to characterize the variance heterogeneity we define log amplitude cumulants and log amplitude autocovariance and derive closed form expressions of the log amplitude cumulants for ensuremath chi 2 inverse ensuremath chi 2 and log normal superstatistical distributions furthermore we show that ensuremath chi 2 and inverse ensuremath chi 2 superstatistics with degree 2 are closely related to an extreme value distribution called the gumbel distribution in these cases the corresponding superstatistical distributions result in the q gaussian distribution with q 5 3 and the bilateral exponential distribution respectively thus our finding provides a hypothesis that the asymptotic appearance of these two special distributions may be explained by a link with the asymptotic limit distributions involving extreme values in addition as an application of our approach we demonstrated that non gaussian fluctuations observed in a stock index futures market can be well approximated by the ensuremath chi 2 superstatistical distribution with degree 2

multivariable cochain operations and little cubes this paper has two goals the first see theorem 2 15 and remark 2 16 a is to construct a small em chain operad s which acts naturally on the normalized cochains s x of a topological space x this is of interest in view of a theorem of mandell 15 page 44 which states that if 9 is any e chain operad over f the algebraic closure of the field with p elements which acts naturally on s x 0 f then the homotopy category of connected p complete nilpotent spaces of finite type

on the self linking of knots this note describes a subcomplex f of the de rham complex of parametrized knot space which is combinatorial over a number of universal anomaly integrals the self linking integrals of guadaguini martellini and mintchev perturbative aspects of chern simons field theory phys lett b 227 111 1989 and bar natan perturbative aspects of the chern simons topological quantum field theory ph d thesis princeton university 1991 also on the vassiliev knot invariants to appear in topology are seen to represent the first nontrivial element in h0 f occurring at level 4 and are anomaly free however already at the next level an anomalous term is possible

non extensive behavior of a stock market index at microscopic time scales abstract this paper presents an empirical investigation of the intraday brazilian stock market price fluctuations considering q gaussian distributions that emerge from a non extensive statistical mechanics our results show that when price returns are measured over intervals less than one hour the empirical distributions are well fitted by q gaussians with exponential damped tails scaling behavior is also observed for these microscopic time intervals we find that the time evolution of the return distributions is according to a super diffusive q gaussian stationary process within a nonlinear fokker planck equation this regime breaks down due to the exponential fall off of the tails which in turn governs the transient dynamics to the long term macroscopic gaussian regime this exponentially damped non extensive modeling provides a new framework to investigate the dynamics of other stock markets intraday price fluctuations

scale invariance and universality organizing principles in complex systems this paper is a brief summary of a talk that was designed to address the question of whether two of the pillars of the eld of phase transitions and critical phenomena scale invariance and universality can be useful in guiding research on a broad class of complex phenomena we shall see that while scale invariance has been tested for many years universality is relatively more rarely discussed in particular we shall develop a heuristic argument that serves to make more plausible the universality hypothesis in both thermal critical phenomena and percolation phenomena and suggest that this argument could be developed into a possible coherent approach to understanding the ubiquity of scale invariance and universality in a wide range of complex systems c 2000 elsevier science b v all rights reserved

autocorrelation and cross correlation in time series of homicide and attempted homicide abstract we propose in this paper to establish the relationship between homicides and attempted homicides by a non stationary time series analysis this analysis will be carried out by detrended fluctuation analysis dfa detrended cross correlation analysis dcca and dcca cross correlation coefficient d c c a n through this analysis we can identify a positive cross correlation between homicides and attempted homicides at the same time looked at from the point of view of autocorrelation dfa this analysis can be more informative depending on time scale for short scale days we cannot identify auto correlations on the scale of weeks dfa presents anti persistent behavior and for long time scales n 90 days dfa presents a persistent behavior finally the application of this new type of statistical analysis proved to be efficient and in this sense this paper can contribute to a more accurate descriptive statistics of crime

singular limit of the porous medium equation with a drift abstract we study the stiff pressure limit of a nonlinear drift diffusion equation where the density is constrained to stay below the maximal value one the challenge lies in the presence of a drift and the consequent lack of monotonicity in time in the limit a hele shaw type free boundary problem emerges which describes the evolution of the congested zone where density equals one we discuss pointwise convergence of the densities as well as the bv regularity of the limiting free boundary

a new approach to front propagation problems theory and applications in this paper we present a new definition for the global in time propagation motion of fronts hypersurfaces boundaries with a prescribed normal velocity past the first time they develop singularities we show that if this propagation satisfies a geometric maximum principle inclusion avoidance type property then the normal velocity must depend only on the position of the front and its normal direction and principal curvatures this new approach which is more geometric and as it turns out equivalent to the level set method is then used to develop a very general and simple method to rigorously validate the appearance of moving interfaces at the asymptotic limit of general evolving systems like interacting particles and reaction diffusion equations we finally present a number of new asymptotic results among them are the asymptotics of i reaction diffusion equations with rapidly oscillating coefficients ii fully nonlinear nonlocal integral differential equations and iii stochastic ising models with long range anisotropic interactions and general spin flip dynamics

homogenization of the hele shaw problem in periodic spatiotemporal media we consider the homogenization of the hele shaw problem in periodic media that are inhomogeneous both in space and time after extending the theory of viscosity solutions into this context we show that the solutions of the inhomogeneous problem converge in the homogenization limit to the solution of a homogeneous hele shaw type problem with a general possibly nonlinear dependence of the free boundary velocity on the gradient moreover the free boundaries converge locally uniformly in hausdorff distance

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

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

financial volatility and independent and identically distributed variables abstract given that financial series are poorly described by gaussian distributions how can the volatility behavior of such series be explained here we put forward a possible explanation to add the existing ones we focus on a class of reduced variables that are independent and identically distributed these variables together with an extra exponential law are able to explain the volatility of the intraday brazilian real us dollar exchange rate for the year 2002

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

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

the odd origin of gerstenhaber brackets batalin vilkovisky operators and master equations using five basic principles we treat gerstenhaber lie brackets batalin vilkovisky bv operators and master equations appearing in mathematical and physical contexts in a unified way the different contexts for this are given by the different types of feynman graphs that underlie the particular situation two of the maxims we bring forth are 1 that extending to the non connected graphs gives a commutative multiplication forming a part of the bv structure and 2 that there is a universal odd twist that unifies and explains seemingly ad hoc choices of signs and is responsible for the bv operator being a differential our treatment results in uniform general theorems these allow us to prove new results and recover and connect many constructions that have appeared independently throughout the literature the more general point of view also allows us to disentangle the necessary from the circumstantial

associahedra cyclohedra and a topological solution to the a deligne conjecture abstract we give a topological solution to the a deligne conjecture using associahedra and cyclohedra to this end we construct three cw complexes whose cells are indexed by products of polytopes giving new explicit realizations of the polytopes in terms of different types of trees we are able to show that the cw complexes are cell models for the little discs the cellular chains of one complex in particular which is built out of associahedra and cyclohedra naturally act on the hochschild cochains of an a algebra yielding an explicit topological and minimal solution to the a deligne conjecture along the way we obtain new results about the cyclohedra such as new decompositions into products of cubes and simplices which can be used to realize them via a new iterated blow up construction

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

a quantum anharmonic oscillator model for the stock market abstract a financially interpretable quantum model is proposed to study the probability distributions of the stock price return the dynamics of a quantum particle is considered an analog of the motion of stock price then the probability distributions of price return can be computed from the wave functions that evolve according to schrodinger equation instead of a harmonic oscillator in previous studies a quantum anharmonic oscillator is applied to the stock in liquid market the leptokurtic distributions of price return can be reproduced by our quantum model with the introduction of mixed state and multi potential the trend following dominant market in which the price return follows a bimodal distribution is discussed as a specific case of the illiquid market

congested aggregation via newtonian interaction we consider a congested aggregation model that describes the evolution of a density through the competing effects of nonlocal newtonian attraction and a hard height constraint this provides a counterpoint to existing literature on repulsive attractive nonlocal interaction models where the repulsive effects instead arise from an interaction kernel or the addition of diffusion we formulate our model as the wasserstein gradient flow of an interaction energy with a penalization to enforce the constraint on the height of the density from this perspective the problem can be seen as a singular limit of the keller segel equation with degenerate diffusion two key properties distinguish our problem from previous work on height constrained equations nonconvexity of the interaction kernel which places the model outside the scope of classical gradient flow theory and nonlocal dependence of the velocity field on the density which causes the problem to lack a comparison principle to overcome these obstacles we combine recent results on gradient flows of nonconvex energies with viscosity solution theory we characterize the dynamics of patch solutions in terms of a hele shaw type free boundary problem and using this characterization show that in two dimensions patch solutions converge to a characteristic function of a disk in the long time limit with an explicit rate on the decay of the energy we believe that a key contribution of the present work is our blended approach combining energy methods with viscosity solution theory

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

hochschild homology of structured algebras abstract we give a general method for constructing explicit and natural operations on the hochschild complex of algebras over any prop with a multiplication we think of such algebras as a algebras with extra structure as applications we obtain an integral version of the costello kontsevich soibelman moduli space action on the hochschild complex of open tcfts the tradler zeinalian and kaufmann actions of sullivan diagrams on the hochschild complex of strict frobenius algebras and give applications to string topology in characteristic zero our main tool is a generalization of the hochschild complex

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

a stochastic model of human gait dynamics abstract we present a stochastic model of gait rhythm dynamics based on transitions between different neural centers that reproduces distinctive statistical properties of normal human walking by tuning one model parameter the transition hopping range the model can describe alterations in gait dynamics from childhood to adulthood including a decrease in the correlation and volatility exponents with maturation the model also generates time series with multifractal spectra whose broadness depends only on this parameter moreover we find that the volatility exponent increases monotonically as a function of the width of the multifractal spectrum suggesting the possibility of a change in multifractality with maturation

long memory volatility in derivative hedging abstract the aim of this work is to take into account the effects of long memory in volatility on derivative hedging this idea is an extension of the work by fedotov and tan stochastic long memory process in option pricing int j theor appl finance 8 2005 381 392 where they incorporate long memory stochastic volatility in option pricing and derive pricing bands for option values the starting point is the stochastic black scholes hedging strategy which involves volatility with a long range dependence the stochastic hedging strategy is the sum of its deterministic term that is classical black scholes hedging strategy with a constant volatility and a random deviation term which describes the risk arising from the random volatility using the fact that stock price and volatility fluctuate on different time scales we derive an asymptotic equation for this deviation in terms of the green s function and the fractional brownian motion the solution to this equation allows us to find hedging confidence intervals

the roles of mean residence time on herd behavior in a financial market abstract we investigate the herd behavior of stock prices in a finance system with the heston model based on parameter estimation of the heston model obtained by minimizing the mean square deviation between the theoretical and empirical return distributions we simulate mean residence time of positive return mrtpr plots of mrtpr against the amplitude or mean reversion of volatility demonstrate a phenomenon of herd behavior for a positive cross correlation between noise sources of the heston model also for a negative cross correlation a phenomenon of herd behavior is observed in plots of mrtpr against the long run variance by increasing amplitude or mean reversion of volatility

minority games with score dependent and agent dependent payoffs score dependent and agent dependent payoffs of the strategies are introduced into the standard minority game the intrinsic periodicity is consequently removed and the stylized facts arise such as long range volatility correlations and fat tails in the distribution of the returns the agent dependence of the payoffs is essential in producing the long range volatility correlations the new payoffs lead to a better performance in the dynamic behavior nonlocal in time and can coexist with the inactive strategy we also observe that the standard deviation ensuremath sigma 2 n is significantly reduced thus the efficiency of the system is distinctly improved based on this observation we give a qualitative explanation for the long range volatility correlations

time evolution of stochastic processes with correlations in the variance stability in power law tails of distributions abstract we model the time series of the s p500 index by a combined process the ar garch process where ar denotes the autoregressive process which we use to account for the short range correlations in the index changes and garch denotes the generalized autoregressive conditional heteroskedastic process which takes into account the long range correlations in the variance we study the ar garch process with an initial distribution of truncated levy form we find that this process generates a new probability distribution with a crossover from a levy stable power law to a power law with an exponent outside the levy range beyond the truncation cutoff we analyze the sum of n variables of the ar garch process and find that due to the correlations the ar garch process generates a probability distribution which exhibits stable behavior in the tails for a broad range of values n a feature which is observed in the probability distribution of the s p500 index we find that this power law stability depends on the characteristic scale in the correlations we also find that inclusion of short range correlations through the ar process is needed to obtain convergence to a limiting gaussian distribution for large n as observed in the data

understanding the determinants of volatility clustering in terms of stationary markovian processes abstract volatility is a key variable in the modeling of financial markets the most striking feature of volatility is that it is a long range correlated stochastic variable i e its autocorrelation function decays like a power law for large time lags in the present work we investigate the determinants of such feature starting from the empirical observation that the exponent of a certain stock s volatility is a linear function of the average correlation of such stock s volatility with all other volatilities we propose a simple approach consisting in diagonalizing the cross correlation matrix of volatilities and investigating whether or not the diagonalized volatilities still keep some of the original volatility stylized facts as a result the diagonalized volatilities result to share with the original volatilities either the power law decay of the probability density function and the power law decay of the autocorrelation function this would indicate that volatility clustering is already present in the diagonalized un correlated volatilities we therefore present a parsimonious univariate model based on a non linear langevin equation that well reproduces these two stylized facts of volatility the model helps us in understanding that the main source of volatility clustering once volatilities have been diagonalized is that the economic forces driving volatility can be modeled in terms of a smoluchowski potential with logarithmic tails

information flow between ibovespa and constituent companies abstract we study the direction of information flow between ibovespa index and its constituent companies using the transfer entropy method we find stronger information transfer from individual stocks towards the composite index than in the opposite direction our results differ from those found for developed market where market index was identified as driving force indicating that the role of index increases with the maturity of the market

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

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

correlation and network analysis of global financial indices random matrix theory rmt and network methods are applied to investigate the correlation and network properties of 20 financial indices the results are compared before and during the financial crisis of 2008 in the rmt method the components of eigenvectors corresponding to the second largest eigenvalue form two clusters of indices in the positive and negative directions the components of these two clusters switch in opposite directions during the crisis the network analysis uses the fruchterman reingold layout to find clusters in the network of indices at different thresholds at a threshold of 0 6 before the crisis financial indices corresponding to the americas europe and asia pacific form separate clusters on the other hand during the crisis at the same threshold the american and european indices combine together to form a strongly linked cluster while the asia pacific indices form a separate weakly linked cluster if the value of the threshold is further increased to 0 9 then the european indices france germany and the united kingdom are found to be the most tightly linked indices the structure of the minimum spanning tree of financial indices is more starlike before the crisis and it changes to become more chainlike during the crisis the average linkage hierarchical clustering algorithm is used to find a clearer cluster structure in the network of financial indices the cophenetic correlation coefficients are calculated and found to increase significantly which indicates that the hierarchy increases during the financial crisis these results show that there is substantial change in the structure of the organization of financial indices during a financial crisis

distribution of natural trends in long term correlated records a scaling approach we estimate the exceedance probability w x ensuremath alpha l that in a long term correlated gaussian distributed sub record of length l characterized by a fluctuation exponent ensuremath alpha between 0 5 and 1 5 a relative increase ensuremath delta ensuremath sigma t of size larger than x occurs where ensuremath delta is the total observed increase measured by linear regression and ensuremath sigma t is the standard deviation around the regression line we consider l between 500 and 2000 which is the typical length scale of monthly local and reconstructed annual global temperature records we use scaling theory to obtain an analytical expression for w x ensuremath alpha l from this expression we can determine analytically for a given confidence probability q the boundaries ifmmode pm else textpm fi x q ensuremath alpha l of the confidence interval in the presence of an external linear trend the total observed increase is the sum of the natural and the external increase an observed relative increase ensuremath delta ensuremath sigma t is considered unnatural when it is above x q ensuremath alpha l in this case the size of the external relative increase is bounded by ensuremath delta ensuremath sigma t ifmmode pm else textpm fi x q ensuremath alpha l we apply this approach to various global and local climate data and discuss the different results for the significance of the observed trends

detecting scaling in the period dynamics of multimodal signals application to parkinsonian tremor patients with parkinson s disease exhibit tremor involuntary movement of the limbs the frequency spectrum of tremor typically has broad peaks at harmonic frequencies much like that seen in other physical processes in general this type of harmonic structure in the frequency domain may be due to two possible mechanisms a nonlinear oscillation or a superposition of multiple independent modes of oscillation a broad peak spectrum generally indicates that a signal is semiperiodic with a fluctuating period these fluctuations may posses intrinsic order that can be quantified using scaling analysis we propose a method to extract the correlation scaling properties in the period dynamics of multimodal oscillations in order to distinguish between a nonlinear oscillation and a superposition of individual modes of oscillation the method is based on our finding that the information content of the temporal correlations in a fluctuating period of a single oscillator is contained in a finite frequency band in the power spectrum allowing for decomposition of modes by bandpass filtering our simulations for a nonlinear oscillation show that harmonic modes possess the same scaling properties in contrast when the method is applied to tremor records from patients with parkinson s disease the first two modes of oscillations yield different scaling patterns suggesting that these modes may not be simple harmonics as might be initially assumed

transmission of information and herd behavior an application to financial markets we propose a model for stochastic formation of opinion clusters modeled by an evolving network and herd behavior to account for the observed fat tail distribution in returns of financial price data the only parameter of the model is h the rate of information dispersion per trade which is a measure of herding behavior for h below a critical h the system displays a power law distribution of the returns with exponential cutoff however for hg h an increase in the probability of large returns is found and may be associated with the occurrence of large crashes

on the scaling of the distribution of daily price fluctuations in the mexican financial market index abstract in this paper a statistical analysis of log return fluctuations of the ipc the mexican stock market index is presented a sample of daily data covering the period from 04 09 2000 04 09 2010 was analyzed and fitted to different distributions tests of the goodness of fit were performed in order to quantitatively asses the quality of the estimation special attention was paid to the impact of the size of the sample on the estimated decay of the distributions tail in this study a forceful rejection of normality was obtained on the other hand the null hypothesis that the log fluctuations are fitted to a stable levy distribution cannot be rejected at the 5 significance level

volatility cluster and herding stock markets can be characterized by fat tails in the volatility distribution clustering of volatilities and slow decay of their time correlations for an explanation models with several mechanisms and consequently many parameters as the lux marchesi model have been used we show that a simple herding model with only four parameters leads to a quantitative description of the data as a new type of data we describe the volatility cluster by the waiting time distribution which can be used successfully to distinguish between different models

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

the origin of fat tailed distributions in financial time series abstract a classic problem in physics is the origin of fat tailed distributions generated by complex systems we study the distributions of stock returns measured over different time lags we find that destroying all correlations without changing the 1 d distribution by shuffling the order of the daily returns causes the fat tails to almost vanish for 1 d we argue that the fat tails are caused by the well known long range volatility correlations that have already been systematically studied previously indeed destroying only sign correlations by shuffling the order of only the signs but not the absolute values of the daily returns allows the fat tails to persist for 1 d

uniqueness and existence results on the hele shaw and the stefan problems in this paper we introduce a notion of viscosity solutions for the one phase hele shaw and stefan problems when there is no surface tension we prove the uniqueness and existence of the solutions for both problems and the uniform convergence of solutions of porous medium equation to those of the hele shaw problem

chern simons perturbation theory ii we study the perturbation theory for three dimensional chern simons quantum field theory on a general compact three manifold without boundary we show that after a simple change of variables the action obtained by brs gauge fixing in the lorentz gauge has a superspace formulation the basic properties of the propagator and the feynman rules are written in a precise manner in the language of differential forms using the explicit description of the propagator singularities we prove that the theory is finite finally the anomalous metric dependence of the 2 loop partition function on the riemannian metric which was introduced to define the gauge fixing can be cancelled by a local counterterm as in the 1 loop case in fact the counterterm is equal to the chern simons action of the metric connection normalized precisely as one would expect based on the framing dependence of witten s exact solution invited talk at the xxth conference on differential geometric methods in physics new york june 1991

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

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

radial basis function approach to nonlinear granger causality of time series we consider an extension of granger causality to nonlinear bivariate time series in this frame if the prediction error of the first time series is reduced by including measurements from the second time series then the second time series is said to have a causal influence on the first one not all the nonlinear prediction schemes are suitable to evaluate causality indeed not all of them allow one to quantify how much knowledge of the other time series counts to improve prediction error we present an approach with bivariate time series modeled by a generalization of radial basis functions and show its application to a pair of unidirectionally coupled chaotic maps and to physiological examples

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

regularity for the one phase hele shaw problem from a lipschitz initial surface in this paper we show that if the lipschitz constant of the initial free boundary is small then for small positive time the solution is smooth and satisfies the hele shaw equation in the classical sense a key ingredient in the proof which is of independent interest is an estimate up to order of magnitude of the speed of the free boundary in terms of initial data

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

criticality and phase transition in stock price fluctuations we analyze the behavior of the u s s p 500 index from 1984 to 1995 and characterize the non gaussian probability density functions pdf of the log returns the temporal dependence of fat tails in the pdf of a ten minute log return shows a gradual systematic increase in the probability of the appearance of large increments on approaching black monday in october 1987 reminiscent of parameter tuning towards criticality on the occurrence of the black monday crash this culminates in an abrupt transition of the scale dependence of the non gaussian pdf towards scale invariance characteristic of critical behavior these facts suggest the need for revisiting the turbulent cascade paradigm recently proposed for modeling the underlying dynamics of the financial index to account for time varying phase transitionlike and scale invariant critical like behavior

stochastic theory of log periodic patterns we introduce an analytical model based on birth death clustering processes to help in understanding the empirical log periodic corrections to power law scaling and the finite time singularity as reported in several domains including rupture earthquakes world population and financial systems in our stochastic theory log periodicities are a consequence of transient clusters induced by an entropy like term that may reflect the amount of co operative information carried by the state of a large system of different species the clustering completion rates for the system are assumed to be given by a simple linear death process the singularity at t0 is derived in terms of birth death clustering coefficients

bv estimates in optimal transportation and applications in this paper we study the bv regularity for solutions of certain variational problems in optimal transportation we prove that the wasserstein projection of a measure with bv density on the set of measures with density bounded by a given bv function f is of bounded variation as well and we also provide a precise estimate of its bv norm of particular interest is the case f 1 corresponding to a projection onto a set of densities with an l bound where we prove that the total variation decreases by projection this estimate and in particular its iterations have a natural application to some evolutionary pdes as for example the ones describing a crowd motion in fact as an application of our results we obtain bv estimates for solutions of some non linear parabolic pde by means of optimal transportation techniques we also establish some properties of the wasserstein projection which are interesting in their own right and allow for instance for the proof of the uniqueness of such a projection in a very general framework

minimum entropy density method for the time series analysis abstract the entropy density is an intuitive and powerful concept to study the complicated nonlinear processes derived from physical systems we develop the minimum entropy density method medm to detect the structure scale of a given time series which is defined as the scale in which the uncertainty is minimized hence the pattern is revealed most the medm is applied to the financial time series of standard and poor s 500 index from february 1983 to april 2006 then the temporal behavior of structure scale is obtained and analyzed in relation to the information delivery time and efficient market hypothesis

granger causality and cross recurrence plots in rheochaos our stress relaxation measurements on wormlike micelles using a rheo sals rheology small angle light scattering apparatus allow simultaneous measurements of the stress and the scattered depolarized intensity the latter is sensitive to orientational ordering of the micelles to determine the presence of causal influences between the stress and the depolarized intensity time series we have used the technique of linear and nonlinear granger causality we find there exists a feedback mechanism between the two time series and that the orientational order has a stronger causal effect on the stress than vice versa we have also studied the phase space dynamics of the stress and the depolarized intensity time series using the recently developed technique of cross recurrence plots crps the presence of diagonal line structures in the crps unambiguously proves that the two time series share similar phase space dynamics

a hele shaw problem for tumor growth abstract we consider weak solutions to a problem modeling tumor growth under certain conditions on the initial data solutions can be obtained by passing to the stiff incompressible limit in a porous medium type problem with a lotka volterra source term describing the evolution of the number density of cancerous cells we prove that such limit solutions solve a free boundary problem of hele shaw type we also obtain regularity properties both for the solution and for its free boundary the main new difficulty arises from the competition between the growth due to the source which keeps the initial singularities and the free boundary which invades the domain with a regularizing effect new islands can be generated at singular times

multifractal geometry in stock market time series it has been recently noticed that time series of returns in stock markets are of multifractal multiscaling character in that context multifractality has been always evidenced by its statistical signature i e the scaling exponents associated to a related variable however a direct geometrical framework much more revealing about the underlying dynamics is possible in this paper we present the techniques allowing the multifractal decomposition we will show that there exists a particular fractal component the most singular manifold msm which contains the relevant information about the dynamics of the series it is possible to reconstruct the series at a given precision from the msm we analyze the dynamics of the msm which shows revealing features about the evolution of this type of series