a markov model of financial returns abstract we address the general problem of how to quantify the kinematics of time series with stationary first moments but having non stationary multifractal long range correlated second moments we show that a markov process is sufficient to model important aspects of the multifractality observed in financial time series and propose a kinematic model of price fluctuations we test the proposed model by analyzing index closing prices of the new york stock exchange and the dem usd tick by tick exchange rates obtained from reuters efx we show that the model captures the characteristic features observed in actual financial time series including volatility clustering time scaling and fat tails in the probability density functions power law behavior of volatility correlations and most importantly the observed nonuniversal multifractal singularity spectrum motivated by our finding of strong agreement between the model and the data we argue that at least two independent stochastic gaussian variables are required to adequately model price fluctuations

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

a model for stock returns and volatility we prove that student s t distribution provides one of the better fits to returns of s p component stocks and the generalized inverse gamma distribution best fits vix and vxo volatility data we further prove that stock returns are best fit by the product distribution of the generalized inverse gamma and normal distributions we find brown noise in vix and vxo time series and explain the mean and the variance of the relaxation times on approach to the steady state distribution

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

inflation and deflation in financial markets abstract the aim of this paper is to show new empirical results on the statistical properties of absolute log returns defined as the absolute value of the log return in a stock market we used the daily data of the nikkei 225 index of the 28 year period from january of 1975 to december of 2002 and compared the statistical properties of the return and absolute log returns in the inflationary bubble period with those in the deflationary anti bubble period our results show that the distribution of absolute log returns is approximated by the q exponential distribution where q 1 14 that is a power law distribution in the inflationary period from january of 1975 to december of 1989 and it is accurately described by the q exponential distribution where q 1 that is an exponential distribution in the deflationary period from january of 1990 to december of 2002

bifurcations of small limit cycles in lienard systems with cubic restoring terms abstract in this paper we study bifurcations of small amplitude limit cycles of lienard systems of the form x y f x y g x where g x is a cubic polynomial and f x is a smooth or piecewise smooth polynomial of degree n by using involutions we obtain sharp upper bounds of the number of small amplitude limit cycles produced around a singular point for some systems of this type

passive motion in dynamical disorder as a model for stock market prices abstract a new model for stock price fluctuations is proposed based upon an analogy with the motion of tracers in gaussian random fields as used in turbulent dispersion models and in studies of transport in dynamically disordered media analytical and numerical results for this model in a special limiting case of a single scale field show characteristics similar to those found in empirical studies of stock market data specifically short term returns have a non gaussian distribution with super diffusive volatility assuming a power law decay of the time correlation of the disorder the returns correlation decays rapidly but the correlation function of the absolute returns exhibits a slow power law decay the returns distribution converges towards gaussian over long times some important characteristics of empirical data are not however reproduced by the model notably the scaling of tails of the cumulative distribution function of returns implied volatilities for options pricing are found by numerical simulation

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

statistics of superior records we study statistics of records in a sequence of random variables these identical and independently distributed variables are drawn from the parent distribution the running record equals the maximum of all elements in the sequence up to a given point we define a superior sequence as one where all running records are above the average record expected for the parent distribution we find that the fraction of superior sequences s n decays algebraically with sequence length n s n n in the limit n interestingly the decay exponent is nontrivial being the root of an integral equation for example when is a uniform distribution with compact support we find 0 450265 in general the tail of the parent distribution governs the exponent we also consider the dual problem of inferior sequences where all records are below average and find that the fraction of inferior sequences i n decays algebraically albeit with a different decay exponent i n n we use the above statistical measures to analyze earthquake data language en

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

gaussian multiplicative chaos revisited in this article we extend the theory of multiplicative chaos for positive definite functions in rd of the form f x 2 ln t x g x where g is a continuous and bounded function the construction is simpler and more general than the one defined by kahane in 1985 as main application we give a rigorous mathematical meaning to the kolmogorov obukhov model of energy dissipation in a turbulent flow

evidence of increment of efficiency of the mexican stock market through the analysis of its variations abstract it is well known that there exist statistical and structural differences between the stock markets of developed and emerging countries in this work and in order to find out if the efficiency of the mexican stock market has been changing over time we have performed and compared several analyses of the variations of the mexican stock market index ipc and dow jones industrial average index djia for different periods of their historical daily data we have analyzed the returns autocorrelation function acf and used detrended fluctuation analysis dfa to study returns variations we also analyze the volatility mean value and standard deviation of both markets and compare their evolution we conclude from the overall result of these studies that they show compelling evidence of the increment of efficiency of the mexican stock market over time the data samples analyzed here correspond to daily values of the ipc and djia for the period 10 30 1978 02 28 2006

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

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

microcanonical multifractal formalism a geometrical approach to multifractal systems part i singularity analysis multifractal formalism in the microcanonical framework has proved to be a valuable approach to understand and analyze complex signals typically associated with natural phenomena in scale invariant systems in this paper we discuss the multifractal microcanonical formalism in a comprehensive unified way including new theoretical proofs and validation tests on real signals so completing some known gaps in the foundations of this theory we also review the latest advances and describe the present perspectives in this field some technical details on the implementation of involved algorithms and relevant open issues are also discussed

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

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

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

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

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

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

on linear combinations of two commuting hypergeneralized projectors the concept of a hypergeneralized projector as a matrix h satisfying h 2 h where h denotes the moore penrose inverse of h was introduced by grosz and trenkler in j grosz g trenkler generalized and hypergeneralized projectors linear algebra appl 264 1997 463 474 generalizing substantially preliminary observations given therein baksalary et al in j k baksalary o m baksalary j grosz on some linear combinations of hypergeneralized projectors linear algebra appl 413 2006 264 273 characterized some situations in which a linear combination c 1h 1 c 2h 2 where c 1 c email protected c and h 1 h 2 are hypergeneralized projectors such that h 1h email protected 1h 1 email protected 2h 2 2 h 2h 1 for some h 1 h email protected c inherits the hypergenerality property in the present paper the problem considered in the latter paper is revisited and solved completely under the essentially weaker assumption that h 1h 2 h 2h 1

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

multiscale multifractal dcca and complexity behaviors of return intervals for potts price model abstract to investigate the characteristics of extreme events in financial markets and the corresponding return intervals among these events we use a potts dynamic system to construct a random financial time series model of the attitudes of market traders we use multiscale multifractal detrended cross correlation analysis mm dcca and lempel ziv complexity lzc perform numerical research of the return intervals for two significant china s stock market indices and for the proposed model the new mm dcca method is based on the hurst surface and provides more interpretable cross correlations of the dynamic mechanism between different return interval series we scale the lzc method with different exponents to illustrate the complexity of return intervals in different scales empirical studies indicate that the proposed return intervals from the potts system and the real stock market indices hold similar statistical properties

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

power law of quiet time distribution in the korean stock market abstract we report the quiet time probability distribution of the absolute return in the korean stock market index we define the quiet time as a time interval during the absolute return of the stock index that are above a threshold r c through an exponential bin plot we observe that the quiet time distribution qtd shows power law behavior p f t t for a range of threshold values the quiet time distribution has two scaling regimes separated by the crossover time t c 200 min the power law exponents of the quiet time distribution decrease when the return time t increases in the late time regime t t c the power law exponents are independent of the threshold within the error bars for the fixed return time the scaled qtd is characterized by a scaling function such as p f t 1 t f t t where the scaling function f x x 2 and t is the average quiet time the scaling exponents 2 depend on the return time t and are independent of the threshold r c the average quiet time follows the power law such as t r c where the exponents depend on the return time t

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

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

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

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

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

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 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

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

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

binary indices of time series complexity measures and entropy plane abstract complexity of time series is an important feature of dynamical systems such as financial systems in order to bring out the complete non linear behavior of financial time series non linear tools of complexity measurement like entropy measures are indispensable sample entropy sampen and distribution entropy disten are popular methods of assessing the complexity in various fields however both sample entropy and distribution entropy show some limitations in detecting the complexity of stock markets therefore we use two entropies as binary indices to analyze the complexity of time series and structure the entropy plane in order to further improve the accuracy of the research results we take the embedding dimension m as the variable expand the entropy point into the entropy curve for further research furthermore considering the shortcomings of sample entropy and distribution entropy in practical application we generalize them by i replacing sample entropy and distribution entropy with multi scale sample entropy and multi scale distribution entropy ii generalizing shannon entropy as tsallis entropy also scale factor and entropic index q are taken respectively as variables to get the entropy curves by using the artificial data we confirm the rationality of using entropy points and entropy curves to study the complexity of time series finally we apply this method to measure the complexity of real world financial time series the results show that the entropy curves plotted by the financial time series obtained from different areas have significant differences

autoregressive processes with anomalous scaling behavior applications to high frequency variations of a stock market index we employ autoregressive conditional heteroskedasticity processes to model the probability distribution function pdf of high frequency relative variations of the standard poors 500 market index data obtained at the time horizon of 1 min the model reproduces quantitatively the shape of the pdf characterized by a levy type power law decay around its center followed by a crossover to a faster decay at the tails furthermore it is able to reproduce accurately the anomalous decay of the central part of the pdf at larger time horizons and by the introduction of a short range memory also the crossover behavior of the corresponding standard deviations and the time scale of the exponentially decaying autocorrelation function of returns displayed by the empirical data

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

coarse graining and self similarity of price fluctuations abstract we propose a new approach for analyzing price fluctuations in their strongly correlated regime ranging from minutes to months this is done by employing a self similarity assumption for the magnitude of coarse grained price fluctuation or volatility the existence of a cramer function the characteristic function for self similarity is confirmed by analyzing real price data from a stock market we also discuss the close interrelation among our approach the scaling of moments method and the multifractal approach for price fluctuations

non poisson intermittent events in price formation in a ising spin model of market abstract the formation of price in a financial market is modelled as a chain of ising spin with three fundamental figures of trading we investigate the time behaviour of the model and we compare the results with the real euro usd change rate by using the test of local poisson hypothesis we show that this minimal model leads to clustering and declustering in the volatility signal typical of the real market data

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

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

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

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

statistical properties of the attendance time series in the minority game abstract we study the statistical properties of the attendance time series corresponding to the number of agents making a particular decision in the minority game mg we focus on the analysis of the probability distribution and the autocorrelation function of the attendance over a time interval in the efficient phase of the game in this regime both the probability distribution and the autocorrelation function are shown to have similar behaviour for time differences corresponding to multiples of 2 2m which is twice the number of possible history bit strings in a mg with agents making decisions based on the most recent m outcomes of the game

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

evidence of multifractality from cee exchange rates against euro abstract the multifractal spectrum of a time series can be ascertained with a number of techniques some based on wavelets others based on the much newer multifractal detrended fluctuation analysis mf dfa we test for the presence of multifractality in daily data on selected exchange rates from central and eastern european economies against euro the approach is based on a slight modification of the mf dfa analysis in that local trends are not allowed to be polynomially fitted but rather are estimated through a sifting process which is established through a so called empirical mode decomposition emd algorithm we assess the drivers of the multifractal spectrum strength like temporal correlations or distributions based on surrogate data another topic discussed is whether the entrance in the exchange rate mechanism erm ii influenced the multifractality of the exchange rates

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

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

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

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

the bulk of the stock market correlation matrix is not pure noise abstract we analyse the structure of the distribution of eigenvalues of the stock market correlation matrix with increasing length of the time series representing the price changes we use 100 highly capitalized stocks from the american market and relate the result to the corresponding ensemble of wishart random matrices it turns out that systematically more eigenvalues remain beyond the borders prescribed by this variant of the random matrix theory rmt this may indicate that even the bulk of the spectrum of the stock market correlation matrix carries some sort of correlations that are masked by a measurement noise when the time series used to construct the matrix are short we also study some other characteristics of the noisy eigensignals like their return distributions temporal correlations or their multifractal spectra and the results support the above conclusions

levels of complexity in scale invariant neural signals many physical and physiological signals exhibit complex scale invariant features characterized by 1 f scaling and long range power law correlations indicating a possibly common control mechanism specifically it has been suggested that dynamical processes influenced by inputs and feedback on multiple time scales may be sufficient to give rise to 1 f scaling and scale invariance two examples of physiologic signals that are the output of hierarchical multiscale physiologic systems under neural control are the human heartbeat and human gait here we show that while both cardiac interbeat interval and gait interstride interval time series under healthy conditions have comparable 1 f scaling they still may belong to different complexity classes our analysis of the multifractal scaling exponents of the fluctuations in these two signals demonstrates that in contrast to the multifractal behavior found in healthy heartbeat dynamics gait time series exhibit less complex close to monofractal behavior further we find strong anticorrelations in the sign and close to random behavior for the magnitude of gait fluctuations at short and intermediate time scales in contrast to weak anticorrelations in the sign and strong positive correlation for the magnitude of heartbeat interval fluctuations suggesting that the neural mechanisms of cardiac and gait control exhibit different linear and nonlinear features these findings are of interest because they underscore the limitations of traditional two point correlation methods in fully characterizing physiological and physical dynamics in addition these results suggest that different mechanisms of control may be responsible for varying levels of complexity observed in physiological systems under neural regulation and in physical systems that possess similar 1 f scaling

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

time dependent hurst exponent in financial time series abstract we calculate the hurst exponent h t of several time series by dynamical implementation of a recently proposed scaling technique the detrending moving average dma in order to assess the accuracy of the technique we calculate the exponent h t for artificial series simulating monofractal brownian paths with assigned hurst exponents h we next calculate the exponent h t for the return of high frequency tick by tick sampled every minute series of the german market we find a much more pronounced time variability in the local scaling exponent of financial series compared to the artificial ones the dma algorithm allows the calculation of the exponent h t without any a priori assumption on the stochastic process and on the probability distribution function of the random variables as happens for example in the case of the kitagawa grid and the extended kalmann filtering methods the present technique examines the local scaling exponent h t around a given instant of time this is a significant advance with respect to the standard wavelet transform or to the higher order power spectrum technique which instead operate on the global properties of the series by legendre or fourier transform of qth order moments

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

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

statistical analysis of the overnight and daytime return we investigate the two components of the total daily return close to close the overnight return close to open and the daytime return open to close as well as the corresponding volatilities of the 2215 new york stock exchange stocks for the 20 year period from 1988 to 2007 the tail distribution of the volatility the long term memory in the sequence and the cross correlation between different returns are analyzed our results suggest that i the two component returns and volatilities have features similar to that of the total return and volatility the tail distribution follows a power law for all volatilities and long term correlations exist in the volatility sequences but not in the return sequences ii the daytime return contributes more to the total return both the tail distribution and the long term memory of the daytime volatility are more similar to that of the total volatility compared to the overnight records in addition the cross correlation between the daytime return and the total return is also stronger iii the two component returns tend to be anticorrelated moreover we find that the cross correlations between the three different returns total overnight and daytime are quite stable over the entire 20 year period

scaling self similarity and multifractality in fx markets abstract this paper presents an empirical investigation of scaling and multifractal properties of us dollar deutschemark usd dem returns the data set is ten years of 5 min returns the cumulative return distributions of positive and negative tails at different time intervals are linear in the double logarithmic space this presents strong evidence that the usd dem returns exhibit power law scaling in the tails to test the multifractal properties of usd dem returns the mean moment of the absolute returns as a function of time intervals is plotted for different powers of absolute returns these moments show different slopes for these powers of absolute returns the nonlinearity of the scaling exponent indicates that the returns are multifractal

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

scale invariance and universality of economic fluctuations in recent years physicists have begun to apply concepts and methods of statistical physics to study economic problems and the neologism econophysics is increasingly used to refer to this work much recent work is focused on understanding the statistical properties of time series one reason for this interest is that economic systems are examples of complex interacting systems for which a huge amount of data exist and it is possible that economic time series viewed from a dierent perspective might yield new results this manuscript 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 economics we shall see that while scale invariance has been tested for many years universality is relatively less frequently discussed this article reviews the results of two recent studies i the probability distribution of stock price uctuations stock price uctuations occur in all magnitudes in analogy to earthquakes from tiny uctuations to drastic events such as market crashes the distribution of price uctuations decays with a power law tail well outside the levy stable regime and describes uctuations that dier in size by as much as eight orders of magnitude ii quantifying business rm uctuations we analyze the computstat database comprising all publicly traded united states manufacturing companies within the years 1974 1993 we nd that the distributions of growth rates is dierent for dierent bins of rm size with a width that varies inversely with a power of rm size similar variation is found for other complex organizations including country size university research budget size and size of species of bird populations c 2000 elsevier science 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

renyi s information transfer between financial time series a b s t r a c t in this paper we quantify the statistical coherence between financial time series by means of the renyi entropy with the help of campbell s coding theorem we show that the renyi entropy selectively emphasizes only certain sectors of the underlying empirical distribution while strongly suppressing others this accentuation is controlled with renyi s parameter q to tackle the issue of the information flow between time series we formulate the concept of renyi s transfer entropy as a measure of information that is transferred only between certain parts of underlying distributions this is particularly pertinent in financial time series where the knowledge of marginal events such as spikes or sudden jumps is of a crucial importance we apply the renyian information flow to stock market time series from 11 world stock indices as sampled at a daily rate in the time period 02 01 1990 31 12 2009 corresponding heat maps and net information flows are represented graphically a detailed discussion of the transfer entropy between the dax and s p500 indices based on minute tick data gathered in the period 02 04 2008 11 09 2009 is also provided our analysis shows that the bivariate information flow between world markets is strongly asymmetric with a distinct information surplus flowing from the asia pacific region to both european and us markets an important yet less dramatic excess of information also flows from europe to the us this is particularly clearly seen from a careful analysis of renyi information flow between the dax and s p500 indices

stochastic processes with power law stability and a crossover in power law correlations motivated by the goal of finding a more accurate description of the empirically observed dynamics of financial fluctuations we propose a stochastic process that yields three statistical properties i short range autocorrelations in the index changes ii long range correlations in the absolute values of the index changes with a crossover between two power law regimes at approximately one week and iii power law stability in the tails of the probability distributions of the index changes we find that this stochastic process can surprisingly well reproduce statistical properties observed in the high frequency data of the s p 500 stock index

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

relaxation dynamics of aftershocks after large volatility shocks in the ssec index abstract the relaxation dynamics of aftershocks after large volatility shocks are investigated based on two high frequency data sets of the shanghai stock exchange composite ssec index compared with previous relevant work we have defined main financial shocks based on large volatilities rather than large crashes we find that the occurrence rate of aftershocks with the magnitude exceeding a given threshold for both daily volatility constructed using 1 minute data and minutely volatility using intra minute data decays as a power law the power law relaxation exponent increases with the volatility threshold and is significantly greater than 1 taking financial volatility as the counterpart of seismic activity the power law relaxation in financial volatility deviates remarkably from the omori law in geophysics

dynamic fluctuations of cross correlations in multi time scale abstract with the empirical mode decomposition we investigate the dynamic fluctuations of cross correlations in multi time scale in this approach the time series of price returns in financial markets is decomposed into a small number of intrinsic mode functions and the corresponding time series of phases can be obtained with the hilbert transform through the empirical mode decomposition we uncover that the cross correlations between stocks change significantly for different time scales and exhibit singular behaviors during a financial crisis with the phase correlation analysis we observe that the cross correlations between market indices vary also for different time scales dividing the total time interval into two sub intervals by the year 2007 we detect that the market indices are much more correlated after 2007

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

extended aic model based on high order moments and its application in the financial market abstract in this paper an extended method of traditional akaike information criteria aic is proposed to detect the volatility of time series by combining it with higher order moments such as skewness and kurtosis since measures considering higher order moments are powerful in many aspects the properties of asymmetry and flatness can be observed furthermore in order to reduce the effect of noise and other incoherent features we combine the extended aic algorithm with multiscale wavelet analysis in which the newly extended aic algorithm is applied to wavelet coefficients at several scales and the time series are reconstructed by wavelet transform after that we create aic planes to derive the relationship among aic values using variance skewness and kurtosis respectively when we test this technique on the financial market the aim is to analyze the trend and volatility of the closing price of stock indices and classify them and we also adapt multiscale analysis to measure complexity of time series over a range of scales empirical results show that the singularity of time series in stock market can be detected via extended aic algorithm

persistence probabilities of the german dax and shanghai index abstract we present a relatively detailed analysis of the persistence probability distributions in financial dynamics compared with the auto correlation function the persistence probability distributions describe dynamic correlations nonlocal in time universal and non universal behaviors of the german dax and shanghai index are analyzed and numerical simulations of some microscopic models are also performed around the fixed point z 0 0 the interacting herding model produces the scaling behavior of the real markets

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

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

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