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

on the syntactic transformation semigroup of a language generated by a finite biprefix code abstract let p be a finite biprefix code and let x q s be the syntactic transformation semigroup ts of p we show that if e s is an idempotent then the ts x e qe eqe consists of partial one to one maps we also show that any ts of partial one to one maps divides a ts of partial one to one maps which is the syntactic ts of a finite biprefix code

several types of enriched l m fuzzy convergence spaces abstract in this paper several types of enriched l m fuzzy convergence spaces are introduced including enriched l m fuzzy kent convergence spaces enriched l m fuzzy limit spaces pretopological enriched l m fuzzy convergence spaces topological enriched l m fuzzy convergence spaces and enriched l m fuzzy choquet convergence spaces these concepts generalize the concepts of kent convergence spaces of limit spaces of pretopological convergence spaces of topological convergence spaces and of choquet convergence spaces in general topology to the setting of l m fuzzy topology also their categorical properties and their mutual categorical relations are investigated

bilateral locally testable languages we give an algebraic characterization of a new variety of languages that will be called bilateral locally testable languages and denoted as blt given k 0 the membership of a word x to a blt k bt language can be decided by means of exploring the segments of length k of x as well as considering the order of appearance of those segments when we scan the prefixes and the suffixes of x in this paper we also characterize the syntactic semigroup of blt languages in terms of the equations of the variety they belong to as well as in terms of the join of two previously studied varieties

covers for monoids a monoid m is an extension of a submonoid t by a group g if there is a morphism from m onto g such that t is the inverse image of the identity of g our first main theorem gives descriptions of such extensions in terms of groups acting on categories the theory developed is also used to obtain a second main theorem which answers the following question given a monoid m and a submonoid t under what conditions can we find a monoid m and a morphism f from m onto m such that m is an extension of a submonoid t by a group and f maps t isomorphically onto t these results can be viewed as generalisations of two seminal theorems of mcalister in inverse semigroup theory they are also closely related to ash s celebrated solution of the rhodes conjecture in finite semigroup theory mcalister proved that each inverse monoid admits an e unitary inverse cover and gave a structure theorem for e unitary inverse monoids many researchers have extended one or both of these results to wider classes of semigroups almost all these generalisations can be recovered from our two main theorems

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

fuzzy initial convergence structure abstract we introduce the notion of fuzzy initial convergence structure induced by family of functions the notion of fuzzy initial convergence structure is shown to be a generalization of fuzzy product convergence structure

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

expansions free inverse semigroups and schutzenberger product in this paper we shall present a new construction of the free inverse monoid on a set x contrary to the previous constructions of 9 11 our construction is symmetric and originates from classical ideas of language theory the ingredients of this construction are the free group on x and the relation that associates to a word w of the free monoid on x the set of all pairs u v such that uv w it follows at once from our construction that the free inverse monoid on x can be naturally embedded into the schutzenberger product of two free groups of basis x we shall also give some connections with the theory of expansions as developed by rhodes and birget 2 3

on the varieties of languages associated with some varieties of finite monoids with commuting idempotents abstract eilenberg has shown that there is a one to one correspondence between varieties of finite monoids and varieties of recognizable languages in this paper we give a description of a variety of languages close to the class of piecewise testable languages considered by i simon the corresponding variety of monoids is the variety of j trivial monoids with commuting idempotents this result is then generalized to the case of finite monoids with commuting idempotents whose regular d classes are groups from a given variety of groups

fuzzy closure spaces abstract fuzzy topological spaces do not constitute a natural boundary for the validity of theorems but many results can be extended to what are called fuzzy closure spaces or fcs s for short the notions of a subspace a sum and a product are extended to fcs s the hereditary additivity and productivity behaviour of compactness in fcs s is investigated and some weak forms of compactness and fuzzy continuous functions in fcs s are introduced the interaction between fuzzy proximity spaces and fcs s is investigated a necessary background is included for completeness

t prefilter theory abstract in the first part of this paper the notion of t prefilter is introduced and studied as are the applications t and t their properties and relations between them we characterize the minimal prime t prefilters finer than a given t prefilter by using ultrafilters on x and we give equivalents conditions of the t maximality in the second part we define t convergence and we obtain a characterization of t compactness gantner steinlage by means of the maximal t prefilters finally some applications of these concepts related to the continuity separation axioms and fuzzy compactness are studied

on l m fuzzy convergence spaces this paper presents a definition of l m fuzzy convergence spaces it is shown that the category l m fc of l m fuzzy convergence spaces which embeds the category l m ftop of l m fuzzy topological spaces as a reflective subcategory is a cartesian closed topological category further it is proved that the category of topological pretopological l m fuzzy convergence spaces is isomorphic to the category of topological l m fuzzy quasi coincident neighborhood spaces moreover the relations among l m fuzzy convergence spaces pretopological l m fuzzy convergence spaces and topological l m fuzzy convergence spaces are investigated in the categorical sense

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

separation axioms of fuzzy initial convergence spaces abstract we define a fuzzy t 0 t 1 hausdorff regular and symmetric convergence space and we investigate some properties of fuzzy initial convergence structure with respect to separation axioms

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

convergence in i fuzzy topological spaces the purpose of this work is to combine the fuzzy q neighborhood system of fuzzy points introduced by sostak with the convergence structures of lee et al using the l filter approach of gahler and eklund

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

semi interior and semi closure of a fuzzy set on definit le semi interieur et la semi fermeture d un ensemble flou d une facon semblable a celle utilisee dans les espaces topologiques ordinaires

detrending the realized volatility in the global fx market abstract there has been growing interest in realized volatility rv of financial assets that is calculated using intra day returns the choice of optimal time grid for these calculations is not trivial and generally requires analysis of rv dependence on the grid spacing so called rv signature typical rv signatures have a maximum at the finest time grid spacing available which is attributed to the microstructure effects this maximum decays into a plateau at lower frequencies which implies almost stationary return variance we found that the rv signatures in the modern global fx market may have no plateau or even have a maximum at lower frequencies simple averaging methods used to address the microstructure effects in equities have no practical effect on the fx rv signatures we show that local detrending of the high frequency fx rate samples yields rv signatures with a pronounced plateau this implies that fx rates can be described with a brownian motion having non stationary trend and stationary variance we point at a role of algorithmic trading as a possible cause of micro trends in fx rates

biprefix codes inverse semigroups and syntactic monoids of injective automata abstract we prove for injective automata an analogue of pin s result 1978 that any finite monoid divides the syntactic monoid of p for some finite prefix code p pin s result for arbitrary automata is strengthened in that we show divides can be replaced by is a subsemigroup of we give some conditions sufficient to guarantee that if a syntactic monoid is inverse then the automaton is injective a direct proof is given of reutenaur s result 1979 1981 that if the language recognized by an injective automaton is a subsemigroup then it is of the form b for some biprefix code b

fuzzy hausdorff topological spaces abstract we introduce the notion of a fuzzy hausdorff topological space and make a few observations to establish the appropriateness of this notion

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

fuzzy sets and functions on fuzzy spaces abstract we generally follow the terminology of azad j math anal appl 82 1981 14 32 and ming j math anal appl 76 1980 571 599 in addition to the fundamental concepts for fuzzy sets we emphasize the usefulness of the concepts of fuzzy point fuzzy elementhood for fuzzy sets a and b a new characterization is given for relations a b and a b this knowledge permits us to combine the two definitions of fuzzy point fuzzy elementhood in the third section some results are given concerning various special types of fuzzy sets in fuzzy topological spaces and the fuzzy semi regular fuzzy regular spaces defined by azad in the last section the definitions of h almost continuous w almost open functions urysohn space which are defined by hussain wilansky and noiri respectively are extended to fuzzy sets furthermore some results are obtained in the functions of the fuzzy topological spaces defined by azad and those are defined here

forecasting volatility of fuel oil futures in china garch type sv or realized volatility models abstract in most previous works on forecasting oil market volatility squared daily returns were taken as the proxy of unobserved actual volatility however as demonstrated by andersen and bollerslev 1998 22 this proxy with too high measurement noise could be perfectly outperformed by a so called realized volatility rv measure calculated by the cumulative sum of squared intraday returns with this motivation we further extend earlier works by employing intraday high frequency data to compare the performance of three typical volatility models in the daily out of sample volatility forecasting of fuel oil futures on the shanghai futures exchange shfe the garch type stochastic volatility sv and realized volatility models by taking rv as the proxy of actual daily volatility and then computing forecasting errors we find that the realized volatility model based on intraday high frequency data produces significantly more accurate volatility forecasts than the garch type and sv models based on daily returns furthermore the sv model outperforms many linear and nonlinear garch type models that capture long memory volatility and or the asymmetric leverage effect in volatility these results also prove that abundant volatility information is available in intraday high frequency data and can be used to construct more accurate oil volatility forecasting models

on separation axioms and ti fuzzy continuity abstract we introduce and generalise concepts of t continuous functions in a fuzzy setting and study them in connection with the fuzzy continuity and fuzzy separation axioms some fuzzy topological properties are also investigated under such functions

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

right and left locally testable languages the aim of this paper is to give a denition as well as an algebraic characterization of two new varieties of languages that will be referred to as right respectively left locally testable languages and denoted as rlt resp llt both families strictly contain the class of locally testable languages given k 0 the membership of a word x to a rlt k rt language can be decided by means of exploring the prex and sux of length k 1o fx and the segments of length k as well as considering the order of appearance of those segments when we scan the prexes of x membership of x to a k lt can be decided in a similar way but we have to change the word prexes for suxes in the above description in this paper we also show that s is a syntactic semigroup of a k rt resp k lt language if and only if the local subsemigroups of s are idempotents and right resp left repetition free c 2000 elsevier science b v all rights reserved

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

designing realised kernels to measure the ex post variation of equity prices in the presence of noise this paper shows how to use realised kernels to carry out efficient feasible inference on the expost variation of underlying equity prices in the presence of simple models of market frictions the issue is subtle with only estimators which have symmetric weights delivering consistent estimators with mixed gaussian limit theorems the weights can be chosen to achieve the best possible rate of convergence and to have an asymptotic variance which is close to that of the maximum likelihood estimator in the parametric version of this problem realised kernels can also be selected to i be analysed using endogenously spaced data such as that in databases on transactions ii allow for market frictions which are endogenous iii allow for temporally dependent noise the finite sample performance of our estimators is studied using simulation while empirical work illustrates their use in practice

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

fuzzy regular convergence structures we define a fuzzy regular modification and fuzzy regular series and we investigate some properties of fuzzy regular modification with respect to fuzzy initial convergence structure

fuzzy convergence structures abstract we define a fuzzy convergence structure which is a correspondence between the prefilters on a given set x and the fuzzy subsets of x the notion of fuzzy convergence structure is shown to be a generalization of a fuzzy topology

over testable languages abstract in this paper we give a combinatorial description of the languages that are both locally and piecewise testable we call such languages over testable the locally testable semigroups were discovered in the study of finite automata the definition of locally testable semigroup is similar to that of locally testable language if we consider words over the alphabet which is the set of all elements of a semigroup s then such a word determines an element of s the product of the letters of the word a semigroup s is locally testable if whenever two words over the alphabet s have the same factors of a fixed length k and the same prefix and suffix of length k 1 then the products of the letters of these words are equal a natural extension of locally testable semigroups is obtained by dropping the condition about the prefix and suffix we call such semigroups strongly locally testable we prove in this paper that the family of strongly locally testable semigroups is exactly the intersection of the variety of locally idempotent and commutative semigroups and that of j trivial semigroups in particular a language is over testable if and only if its syntactic semigroup is strongly locally testable we use this algebraic characterization to derive a simple family of generators for the variety of over testable languages

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

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

econometric analysis of realized volatility and its use in estimating stochastic volatility models summary the availability of intraday data on the prices of speculative assets means that we can use quadratic variation like measures of activity in financial markets called realized volatility to study the stochastic properties of returns here under the assumption of a rather general stochastic volatility model we derive the moments and the asymptotic distribution of the realized volatility error the difference between realized volatility and the discretized integrated volatility which we call actual volatility these properties can be used to allow us to estimate the parameters of stochastic volatility models without recourse to the use of simulation intensive methods

effect of nonstationarities on detrended fluctuation analysis detrended fluctuation analysis dfa is a scaling analysis method used to quantify long range power law correlations in signals many physical and biological signals are noisy heterogeneous and exhibit different types of nonstationarities which can affect the correlation properties of these signals we systematically study the effects of three types of nonstationarities often encountered in real data specifically we consider nonstationary sequences formed in three ways i stitching together segments of data obtained from discontinuous experimental recordings or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts a cutting procedure commonly used in preparing data prior to signal analysis ii adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitudes and iii generating a signal comprised of segments with different properties e g different standard deviations or different correlation exponents we compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities we find that introducing nonstationarities to stationary correlated signals leads to the appearance of crossovers in the scaling behavior and we study how the characteristics of these crossovers depend on a the fraction and size of the parts cut out from the signal b the concentration of spikes and their amplitudes c the proportion between segments with different standard deviations or different correlations and d the correlation properties of the stationary signal we show how to develop strategies for preprocessing raw data prior to analysis which will minimize the effects of nonstationarities on the scaling properties of the data and how to interpret the results of dfa for complex signals with different local characteristics

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

l fuzzy q convergence structures abstract in this paper we construct a topological category of pretopological l fuzzy q convergence spaces which contains the category of topological l fuzzy q convergence spaces as a bireflective full subcategory considering the connections with l fuzzy topology it is proved that the category of topological l fuzzy q convergence spaces is isomorphic to the category of topological l fuzzy quasi coincident neighborhood spaces and the latter is isomorphic to the category of l fuzzy topological spaces moreover we find that our pretopological l fuzzy q convergence spaces can be characterized as a kind of l fuzzy quasi coincident neighborhood spaces which is called strong l fuzzy quasi coincident neighborhood space

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