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

identification of market trends with string and d2 brane maps abstract the multidimensional string objects are introduced as a new alternative for an application of string models for time series forecasting in trading on financial markets the objects are represented by open string with 2 endpoints and d2 brane which are continuous enhancement of 1 endpoint open string model we show how new object properties can change the statistics of the predictors which makes them the candidates for modeling a wide range of time series systems string angular momentum is proposed as another tool to analyze the stability of currency rates except the historical volatility to show the reliability of our approach with application of string models for time series forecasting we present the results of real demo simulations for four currency exchange pairs

stock return distributions tests of scaling and universality from three distinct stock markets define the log return of stock price st over a time interval t rrtt log st tlog st1 analyses of returns of individual stocks 2 3 and stock indices 4 have shown that the cumulative distribution of returns is well fit by a power law asymptotic behavior with tail exponent r pr x xr 1

scaling and memory in volatility return intervals in financial markets abstract for both stock and currency markets we study the return intervals between the daily volatilities of the price changes that are above a certain threshold q we find that the distribution function pq scales with the mean return interval as the scaling function f x is similar in form for all seven stocks and for all seven currency databases analyzed and f x is consistent with a power law form f x x with 2 we also quantify how the conditional distribution pq 0 depends on the previous return interval 0 and find that small or large return intervals are more likely to be followed by small or large return intervals this clustering of the volatility return intervals is a previously unrecognized phenomenon that we relate to the long term correlations known to be present in the volatility econophysics fluctuations extreme values long term correlations long term memory

relation between volatility correlations in financial markets and omori processes occurring on all scales we analyze the memory in volatility by studying volatility return intervals defined as the time between two consecutive fluctuations larger than a given threshold in time periods following stock market crashes such an aftercrash period is characterized by the omori law which describes the decay in the rate of aftershocks of a given size with time t by a power law with exponent close to 1 a shock followed by such a power law decay in the rate is here called omori process we find self similar features in the volatility specifically within the aftercrash period there are smaller shocks that themselves constitute omori processes on smaller scales similar to the omori process after the large crash we call these smaller shocks subcrashes which are followed by their own aftershocks we also show that the omori law holds not only after significant market crashes as shown by lillo and mantegna phys rev e 68 016119 2003 but also after intermediate shocks by appropriate detrending we remove the influence of the crashes and subcrashes from the data and find that this procedure significantly reduces the memory in the records moreover when studying long term correlated fractional brownian motion and autoregressive fractionally integrated moving average artificial models for volatilities we find omori type behavior after high volatilities thus our results support the hypothesis that the memory in the volatility is related to the omori processes present on different time scales

vc correlation analysis on the overnight and daytime return in japanese stock market abstract while most financial engineering and econophysics studies have focused in daytime trading much less investigation has been devoted to the non trading or night periods in this work the correlation between overnight and daytime return correlation nd and the correlation between daytime return and following over night return correlation df were investigated which led to several findings first a weak negative correlation between overnight and daytime return correlation nd was observed in japanese stocks market secondly the application of volatility constrained correlation vc correlation method led to a significant amplification of this signal which benefits for increasing predictability of day time return compared to standard correlation furthermore the analysis of the amplified signal derived from vc correlation for each stock revealed a linear scale relationship between the standard correlation and vc correlation therefore this result indicates that by using the vc correlation stronger correlation effect can be observed taking together these findings suggest that the combination of vc approach with financial trading data over night paves the way to improve market predictability

indication of multiscaling in the volatility return intervals of stock markets a certain trend with the mean interval we generate surrogate records using the schreiber method and find that their cumulative distributions almost collapse to a single curve and moments are almost constant for most ranges of those substantial differences suggest that nonlinear correlations in the original volatility sequence account for the deviations from a single scaling law we also find that the original and surrogate records exhibit slight tendencies for short and long due to the discreteness and finite size effects of the records respectively to avoid as possible those effects for testing the multiscaling behavior we investigate the moments in the range 10100 and find that the exponent from the power law fitting m has a narrow distribution around 0 which depends on m for the 500 stocks the distribution of for the surrogate records are very narrow and centered around 0 this suggests that the return interval distribution exhibits multiscaling behavior due to the nonlinear correlations in the original volatility

multifactor analysis of multiscaling in volatility return intervals we study the volatility time series of 1137 most traded stocks in the u s stock markets for the two year period 2001 2002 and analyze their return intervals which are time intervals between volatilities above a given threshold q we explore the probability density function of pq assuming a stretched exponential function pqe we find that the exponent depends on the threshold in the range between q 1 and 6 standard deviations of the volatility this finding supports the multiscaling nature of the return interval distribution to better understand the multiscaling origin we study how depends on four essential factors capitalization risk number of trades and return we show that depends on the capitalization risk and return but almost does not depend on the number of trades this suggests that relates to the portfolio selection but not on the market activity to further characterize the multiscaling of individual stocks we fit the moments of m s m 1 m in the range of 10 100 by a power law m the exponent is found also to depend on the capitalization risk and return but not on the number of trades and its tendency is opposite to that of moreover we show that decreases with increasing approximately by a linear relation the return intervals demonstrate the temporal structure of volatilities and our findings suggest that their multiscaling features may be helpful for portfolio optimization

statistical properties of deterministic threshold elements the case of market price abstract we analyze statistical properties of a set of deterministic threshold elements which is introduced as a model for the stock market the macroscopic variable of the stock market price shows seemingly stochastic fluctuation with a f 2 power spectrum consistent with real economic fluctuations the maximum lyapunov exponent is estimated to be zero indicating that the system is at the edge of chaos

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

effect of nonlinear filters on detrended fluctuation analysis when investigating the dynamical properties of complex multiple component physical and physiological systems it is often the case that the measurable system s output does not directly represent the quantity we want to probe in order to understand the underlying mechanisms instead the output signal is often a linear or nonlinear function of the quantity of interest here we investigate how various linear and nonlinear transformations affect the correlation and scaling properties of a signal using the detrended fluctuation analysis dfa which has been shown to accurately quantify power law correlations in nonstationary signals specifically we study the effect of three types of transforms i linear y i a x i b ii nonlinear polynomial y i a x k i and iii nonlinear logarithmic y i log x i delta filters we compare the correlation and scaling properties of signals before and after the transform we find that linear filters do not change the correlation properties while the effect of nonlinear polynomial and logarithmic filters strongly depends on a the strength of correlations in the original signal b the power k of the polynomial filter and c the offset delta in the logarithmic filter we further apply the dfa method to investigate the apparent scaling of three analytic functions i exponential exp x a ii logarithmic log x a and iii power law x a lambda which are often encountered as trends in physical and biological processes while these three functions have different characteristics we find that there is a broad range of values for parameter a common for all three functions where the slope of the dfa curves is identical we further note that the dfa results obtained for a class of other analytic functions can be reduced to these three typical cases we systematically test the performance of the dfa method when estimating long range power law correlations in the output signals for different parameter values in the three types of filters and the three analytic functions we consider

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

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

empirical regularities of opening call auction in chinese stock market abstract we study the statistical regularities of an opening call auction using the ultra high frequency data of 22 liquid stocks traded on the shenzhen stock exchange in 2003 the distribution of the relative price defined as the relative difference between the order price in the opening call auction and the closing price on the last trading day is asymmetric and that the distribution displays a sharp peak at the zero relative price and a relatively wide peak at the negative relative price the detrended fluctuation analysis dfa method is adopted to investigate the long term memory of relative order prices we further study the statistical regularities of order sizes in the opening call auction and observe a phenomenon of number preference known as order size clustering the probability density function pdf of order sizes could be well fitted by a q gamma function and the long term memory also exists in order sizes in addition both the average volume and the average number of orders decrease exponentially with the price level away from the best bid or ask price level in the limit order book lob established immediately after the opening call auction and a price clustering phenomenon is observed

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

human comment dynamics in on line social systems a b s t r a c t human comment is studied using data from tianya which is one of the most popular on line social systems in china we found that the time interval between two consecutive comments on the same topic called inter event time follows a power law distribution this result shows that there is no characteristic decay time on a topic it allows for very long periods without comments that separate bursts of intensive comments furthermore the frequency of a different id commenting on a topic also follows a power law distribution it indicates that there are some hubs in the topic who lead the direction of the public opinion based on the personal comments habit a model is introduced to explain these phenomena the numerical simulations of the model fit well with the empirical results our findings are helpful for discovering regular patterns of human behavior in on line society and the evolution of the public opinion on the virtual as well as real society

bayes theorem for choquet capacities we give an upper bound for the posterior probability of a measurable set a when the prior lies in a class of probability measures p the bound is a rational function of two choquet integrals if p is weakly compact and is closed with respect to majorization then the bound is sharp if and only if the upper prior probability is 2 alternating the result is used to compute bounds for several sets of priors used in robust bayesian inference the result may be regarded as a characterization of 2 alternating choquet capacities

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

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

sensitivity in bayesian statistics the prior and the likelihood abstract one paradigm for sensitivity analyses in bayesian statistics is to specify a reasonable class of priors and to compute the corresponding class of posterior inferences the class is chosen to represent uncertainty about the prior there is often additional uncertainty however about the family of sampling distributions this article introduces a method for computing ranges of posterior expectations over reasonable classes of sampling distributions that lie close to a given parametric family by treating the prior as a probability measure on the space of sampling distributions this article also gives a unified treatment to what are usually considered two separate problems sensitivity to the prior and sensitivity to the sampling model first the notion of close to is made explicit then an algorithm is given for turning ratio linear problems into sequences of linear problems in addition to solving the problem at hand the algorithm simplifies many other robust bayesian computational pro

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

local sensitivity of posterior expectations we investigate the degree to which posterior expectations are sensitive to prior distributions using a local method based on functional differentiation invariance considerations suggest a family of norms which can be used to measure perturbations to the prior the sensitivity measure is seen to depend heavily on the choice of norm asymptotic results suggest which norm will yield the most useful results in practice we find that to maintain asymptotically sensible behaviour it is necessary to reduce the richness of the class of prior perturbations as the dimension of the parameter space increases jeffreys prior is characterized as the prior to which inference is least sensitive

autoregressive conditional duration a new model for irregularly spaced transaction data this paper proposes a new statistical model for the analysis of data which arrive at irregular intervals the model treats the time between events as a stochastic process and proposes a new class of point processes with dependent arrival rates the conditional intensity is developed and compared with other self exciting processes because the model focuses on the expected duration between events it is called the autoregressive conditional duration acd model asymptotic properties of the quasi maximum likelihood estimator are developed as a corollary to arch model results strong evidence is provided for duration clustering for the financial transaction data analyzed both deterministic time of day effects and stochastic effects are important the model is applied to the arrival times of trades and therefore is a model of transaction volume and also to the arrival of other events such as price changes models for the volatility of prices are estimated with price based durations and examined from a market microstructure point of view

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

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

invariance properties of density ratio priors density ratio neighborhoods are classes of probabilities that are used in robust bayesian inference these classes are invariant under bayesian updating and marginalization this makes them computationally convenient in robust bayesian inference we show that this is the unique class of probabilities that has these invariance properties aside from its theoretical value this result has computational implications as well

monge ampere equations and moduli spaces of manifolds of circular type abstract a bounded manifold of circular type is a complex manifold m of dimension n admitting a bounded exhaustive real function u defined on m minus a point x o so that a it is a smooth solution on m x o to the monge ampere equation d d c u n 0 b x o is a singular point for u of logarithmic type and e u extends smoothly on the blow up of m at x o c d d c e u 0 at any point of m x o this class of manifolds naturally includes all smoothly bounded strictly linearly convex domains and all smoothly bounded strongly pseudoconvex circular domains of c n a set of modular parameters for bounded manifolds of circular type is considered in particular for each biholomorphic equivalence class of them it is proved the existence of an essentially unique manifold in normal form it is also shown that the class of normalizing maps for an n dimensional manifold m is a new holomorphic invariant with the following property it is parameterized by the points of a finite dimensional real manifold of dimension n 2 when m is a non convex circular domain while it is of dimension n 2 2 n when m is a strictly linearly convex domain new characterizations of the circular domains and of the unit ball are also obtained

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

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

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

symmetric upper probabilities as a first step toward developing statistical models based on upper and lower probabilities we study upper probabilities and upper expectations on the unit interval that are symmetric by which we mean invariant with respect to equimeasurability these upper probabilities are generalizations of uniform probability measures we give some characterizations of these upper probabilities specifically we show that symmetry of the upper expectation functional is equivalent to the underlying set of densities being closed under majorization we also show that a function is the upper distribution for a symmetric upper probability if and only if its lower graph is star shaped with respect to the origin and to the point 1 1 we derive inner and outer approximations to symmetric classes of probabilities based on the upper probability the class of symmetric upper expectations that are completely determined by their values on the indicator functions is characterized we provide a geometric characterization of a hierarchy of upper probabilities including fine s generalized upper probabilities and 2 alternating choquet capacities in particular we establish a 1 1 correspondence between symmetric 2 alternating capacities and nonincreasing density functions we prove that undominated generalized upper probabilities do not exist in the symmetric case examples from robust statistics are considered an example is given that shows that symmetry of upper probabilities does not imply symmetry of upper expectations a corollary is that symmetry of the choquet integral does not imply symmetry of the upper expectation functional

quantifying fluctuations in market liquidity analysis of the bid ask spread quantifying the statistical features of the bid ask spread offers the possibility of understanding some aspects of market liquidity using quote data for the 116 most frequently traded stocks on the new york stock exchange over the two year period 1994 1995 we analyze the fluctuations of the average bid ask spread s over a time interval dt we find that s is characterized by a distribution that decays as a power law phs x j x zs with an exponent zs 3 for all 116 stocks analyzed our analysis of the autocorrelation function of s shows long range power law correlations ksstdsst tdl t ms similar to those previously found for the volatility we next examine the relationship between the bid ask spread and the volume q and find that s ln q we find that a similar logarithmic relationship holds between the transaction level bid ask spread and the trade size we then study the relationship between s and other indicators of market liquidity such as the frequency of trades n and the frequency of quote updates u and finds ln n and s ln u lastly we show that the bid ask spread and the volatility are also related logarithmically

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

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

detrended minimum variance hedge ratio a new method for hedge ratio at different time scales abstract in this paper based on the detrended fluctuation analysis dfa method and the detrended cross correlation analysis dcca method we propose an improved method of minimum variance mv hedge ratio i e the detrended minimum variance d mv hedge ratio which can measure the hedge ratio at different time scales the proposed d mv hedge ratio is defined as the detrended covariance function between spot and futures returns divided by the detrended variance function of futures returns through the simulated and empirical analysis we find that i the outcomes of the hedge ratio and the corresponding hedging effectiveness for the d mv hedge ratio are diverse at different time scales which can meet needs of various hedging participants with different hedging horizons ii our proposed d mv hedge ratio has a better hedging performance and a greater potential to determine the hedge ratio because its results of hedging effectiveness at most of time scales are better than those of the traditional mv hedge ratio and iii as for the method of d mv hedge ratio for different polynomial orders m in the fitting procedure the d mv 1 hedge ratio i e the linear polynomial in the fitting procedure has the best hedging capability for determining the hedge ratio

a kahler structure on finsler spaces with nonzero constant flag curvature in this paper we obtain a kahler structure on the tangent bundle of a finsler manifold of positive constant flag curvature we show that there does not exist any finsler metric such that this structure became locally symmetric or einstein manifold similar results are obtained on a tube around zero section in the tangent bundle in the case of a finsler manifold of negative constant flag curvature

new dynamics between volume and volatility abstract understanding quantifying and predicting market fluctuation has become increasingly important in recent decades volatility and volume are the two commonly used quantities to study the market dynamics and the relationship between these two has been modeled and debated for years with several hypothesis been put forward using empirical data we investigate the causality and correlation between volume and volatility and find new ways in which they interact particularly when the levels of both are high we find that the volume conditional volatility distribution scales with volume as a power law function with an exponential cutoff we exploit the characteristics of a volume volatility scatterplot and find a strong correlation between logarithmic volume and a quantity we define as local maximum volatility lmv the highest volatility observed in a given range of volume this supports our empirical analysis showing that volume is an effective parameter for prediction of the maximum value of volatility for both same day and near future time periods the joint conditional probability of volume and volatility also indicates if we invoke both quantities the prediction of the largest next day volatility will be better than invoking either one alone this approach is thus a greatly improved method of risk assessment

probability of large movements in financial markets abstract based on empirical financial time series we show that the silence breaking probability follows a super universal power law the probability of observing a large movement is inversely proportional to the length of the on going low variability period such a scaling law has been previously predicted theoretically r kitt j kalda physica a 353 2005 480 assuming that the length distribution of the low variability periods follows a multi scaling power law

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

serial correlation of detrended time series a preliminary essential procedure in time series analysis is the separation of the deterministic component from the random one if the signal is the result of superposing a noise over a deterministic trend then the first one must estimate and remove the trend from the signal to obtain an estimation of the stationary random component the errors accompanying the estimated trend are conveyed as well to the estimated noise taking the form of detrending errors therefore the statistical errors of the estimators of the noise parameters obtained after detrending are larger than the statistical errors characteristic to the noise considered separately in this paper we study the detrending errors by means of a monte carlo method based on automatic numerical algorithms for nonmonotonic trends generation and for construction of estimated polynomial trends alike to those obtained by subjective methods for a first order autoregressive noise we show that in average the detrending errors of the noise parameters evaluated by means of the autocovariance and autocorrelation function are almost uncorrelated to the statistical errors intrinsic to the noise and they have comparable magnitude for a real time series with significant trend we discuss a recursive method for computing the errors of the estimated parameters after detrending and we show that the detrending error is larger than the half of the total error

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

computing bounds on expectations abstract one method for evaluating the sensitivity of a bayesian analysis is to embed the prior into a class of priors then bounds on prior and posterior quantities of interest must be computed this approach to inference often called robust bayesian inference has received much attention lately implementing robust bayesian methods entails difficult computations especially if the parameter space is high dimensional in this article we develop a monte carlo approach to computing these bounds and also explore some interesting theoretical properties of certain classes of priors the methods can be useful in other situations in which bounds on expectations are required

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memory effects in the statistics of interoccurrence times between large returns in financial records we study the statistics of the interoccurrence times between events above some threshold q in two kinds of multifractal data sets multiplicative random cascades and multifractal random walks with vanishing linear correlations we show that in both data sets the relevant quantities probability density functions and the autocorrelation function of the interoccurrence times as well as the conditional return period are governed by power laws with exponents that depend explicitly on the considered threshold by studying a large number of representative financial records market indices stock prices exchange rates and commodities we show explicitly that the interoccurrence times between large daily returns follow the same behavior in a nearly quantitative manner we conclude that this kind of behavior is a general consequence of the nonlinear memory inherent in the multifractal data sets

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

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

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