a trilinear form for the third janko group abstract in this paper we describe the action of the sporadic simple group j3 on a vector space m of dimension 85 over q 3 19 in doing so we shall prove that j3 is uniquely determined up to isomorphism by the conditions given by z janko ist naz alta math 1 1968 25 64 in 1967 we also describe a j3 invariant symmetric trilinear form on m this form which is uniquely determined up to scalar multiplication can be used to define a multiplication on a m m that makes a into a non associative algebra

time independent models of asset returns revisited abstract in this study we investigate various well known time independent models of asset returns being simple normal distribution student t distribution levy truncated levy general stable distribution mixed diffusion jump and compound normal distribution for this we use standard and poor s 500 index data of the new york stock exchange helsinki stock exchange index data describing a small volatile market and artificial data the results indicate that all models excluding the simple normal distribution are at least quite reasonable descriptions of the data furthermore the use of differences instead of logarithmic returns tends to make the data looking visually more levy type distributed than it is this phenomenon is especially evident in the artificial data that has been generated by an inflated random walk process

incidence of nonextensive thermodynamics in temporal scaling at feigenbaum points abstract recently in phys rev lett 95 2005 140601 grassberger addresses the interesting issue of the applicability of q statistics to the renowned feigenbaum attractor he concludes there is no genuine connection between the dynamics at the critical attractor and the generalized statistics and argues against its usefulness and correctness yet several points are not in line with our current knowledge nor are his interpretations we refer here only to the dynamics on the attractor to point out that a correct reading of recent developments invalidates his basic claim

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

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

path probability of stochastic motion a functional approach the path probability of a particle undergoing stochastic motion is studied by the use of functional technique and the general formula is derived for the path probability distribution functional the probability of finding paths inside a tube band the center of which is stipulated by a given path is analytically evaluated in a way analogous to continuous measurements in quantum mechanics then the formalism developed here is applied to the stochastic dynamics of stock price in finance

visibility graph network analysis of gold price time series abstract mapping time series into a visibility graph network the characteristics of the gold price time series and return temporal series and the mechanism underlying the gold price fluctuation have been explored from the perspective of complex network theory the network degree distribution characters which change from power law to exponent law when the series was shuffled from original sequence and the average path length characters which change from l ln n into ln l ln n as the sequence was shuffled demonstrate that price series and return series are both long rang dependent fractal series the relations of hurst exponent to the power law exponent of degree distribution demonstrate that the logarithmic price series is a fractal brownian series and the logarithmic return series is a fractal gaussian series power law exponents of degree distribution in a time window changing with window moving demonstrates that a logarithmic gold price series is a multifractal series the power law average clustering coefficient demonstrates that the gold price visibility graph is a hierarchy network the hierarchy character in light of the correspondence of graph to price fluctuation means that gold price fluctuation is a hierarchy structure which appears to be in agreement with elliot s experiential wave theory on stock price fluctuation and the local rule growth theory of a hierarchy network means that the hierarchy structure of gold price fluctuation originates from persistent short term factors such as short term speculation

financial multifractality and its subtleties an example of dax abstract detailed study of multifractal characteristics of the financial time series of asset values and of its returns is performed using a collection of the high frequency deutsche aktienindex data the tail index the renyi exponents based on the box counting algorithm for the graph d q and the generalized hurst exponents h q are computed in parallel for short and daily return times the results indicate a more complicated nature of the stock market dynamics than just consistent multifractal

an empirical investigation of australian stock exchange data we present an empirical study of high frequency australian equity data examining the behaviour of distribution tails and the existence of long memory a method is presented that allows us to deal with australian stock exchange data by splitting it into two separate data series representing an intraday and overnight component power law exponents for the empirical density functions are estimated and compared with results from other studies using the autocorrelation and variance plots we nd there to be a strong indication of long memory type behaviour in the absolute return volume and transaction frequency

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

fitting the empirical distribution of intertrade durations based on the analysis of a tick by tick data set used in the previous work by one of the authors djia stocks traded at nyse in october 1999 in this paper we reject the hypothesis that tails of the empirical intertrade distribution are described by a power law we further argue that the tsallis q exponentials are a viable tool for fitting and describing the unconditional distribution of empirical intertrade durations and they compare well to the weibull distribution

empirical distributions of chinese stock returns at different microscopic timescales abstract we study the distributions of event time returns and clock time returns at different microscopic timescales using ultra high frequency data extracted from the limit order books of 23 stocks traded in the chinese stock market in 2003 we find that the returns at the one trade timescale obey the inverse cubic law for larger timescales 2 32 trades and 1 5 min the returns follow the student distribution with power law tails with the decrease in timescale the tail becomes fatter which is consistent with the variational theory in turbulence

scale invariant distribution and multifractality of volatility multipliers in stock markets abstract the statistical properties of the multipliers of the absolute returns are investigated using 1 min high frequency data of financial time series the multiplier distribution is found to be independent of the box size s when s is larger than some crossover scale providing direct evidence of the existence of scale invariance in financial data the multipliers with base a 2 are well approximated by a normal distribution and the most probable multiplier scales as a power law with respect to the base a we unravel that the volatility multipliers possess multifractal nature which is independent of construction of the multipliers that is the values of s and a

possibility between earthquake and explosion seismogram differentiation by discrete stochastic non markov processes and local hurst exponent analysis the basic scientific point of this paper is to draw the attention of researchers to new possibilities of differentiation of similar signals having different nature one example of such kinds of signals is presented by seismograms containing recordings of earthquakes eq s and technogenic explosions te s eq s are among the most dramatic phenomena in nature we propose here a discrete stochastic model for possible solution of a problem of strong eq forecasting and differentiation of te s from the weak eq s theoretical analysis is performed by two independent methods by using statistical theory of discrete non markov stochastic processes phys rev e 62 6178 2000 and the local hurst exponent the following earth states have been considered among them before ib and during i strong eq during weak eq ii and during te iii and in a calm state of earth s core iv the estimation of states i ii and iii has been made on the particular examples of turkey 1999 eq s state iv has been taken as an example of earth s state before underground te time recordings of seismic signals of the first four dynamic orthogonal collective variables six various planes of phase portrait of four dimensional phase space of orthogonal variables and the local hurst exponent have been calculated for the dynamic analysis of states of systems i char21 iv the analysis of statistical properties of seismic time series i char21 iv has been realized with the help of a set of discrete time dependent functions time correlation function and first three memory functions their power spectra and the first three points in the statistical spectrum of non markovity parameters in all systems studied we have found a bizarre combination of the following spectral characteristics the fractal frequency spectra adjustable by phenomena of usual and restricted self organized criticality spectra of white and color noises and unusual alternation of markov and non markov effects of long range memory detected earlier j phys a 27 5363 1994 only for hydrodynamic systems our research demonstrates that discrete non markov stochastic processes and long range memory effects play a crucial role in the behavior of seismic systems i char21 iv the approaches permitting us to obtain an algorithm of strong eq forecasting and to differentiate te s from weak eq s have been developed

decomposing the stock market intraday dynamics abstract the correlation matrix formalism is used to study temporal aspects of the stock market evolution this formalism allows to decompose the financial dynamics into noise as well as into some coherent repeatable intraday structures the present study is based on the high frequency deutsche aktienindex dax data over the time period between november 1997 and september 1999 and makes use of both the corresponding returns as well as volatility variations one principal conclusion is that a bulk of the stock market dynamics is governed by the uncorrelated noise like processes there exists however a small number of components of coherent short term repeatable structures in fluctuations that may generate some memory effects seen in the standard autocorrelation function analysis laws that govern fluctuations associated with those various components are different which indicates an extremely complex character of the financial fluctuations

neo classical theory of competition or adam smith s hand as mathematized ideology abstract orthodox economic theory utility maximization rational agents efficient markets in equilibrium is based on arbitrarily postulated nonempiric notions the disagreement between economic reality and a key feature of neo classical economic theory was criticized empirically by osborne i show that the orthodox theory is internally self inconsistent for the very reason suggested by osborne lack of invertibility of demand and supply as functions of price to obtain price as functions of supply and demand the reason for the noninvertibililty arises from nonintegrable excess demand dynamics a feature of their theory completely ignored by economists

analytic solutions for optimal statistical arbitrage trading abstract in this paper we derive analytic formulae for statistical arbitrage trading where the security price follows an ornstein uhlenbeck process by framing the problem in terms of the first passage time of the process we derive expressions for the mean and variance of the trade length and the return we examine the problem of choosing an optimal strategy under two different objective functions the expected return and the sharpe ratio an exact analytic solution is obtained for the case of maximising the expected return

statistical properties of derivatives a journey in term structures abstract this article presents an empirical study of 13 derivative markets for commodities and financial assets the study goes beyond statistical analysis by including the maturity as a variable for the daily returns of futures contracts from 1998 to 2010 and for delivery dates up to 120 months we observe that the mean and variance of the commodities follow a scaling behavior in the maturity dimension with an exponent characteristic of the samuelson effect the comparison between the tails of the probability distribution according to the expiration dates shows that there is a segmentation in the fat tails exponent term structure above the levy stable region finally we compute the average tail exponent for each maturity and we observe two regimes of extreme events for derivative markets reminiscent of a phase diagram with a sharp transition at the 18th delivery month

the ctrw in finance direct and inverse problems with some generalizations and extensions we study financial distributions within the framework of the continuous time random walk ctrw we review earlier approaches and present new results related to overnight effects as well as the generalization of the formalism which embodies a non markovian formulation of the ctrw aimed to account for correlated increments of the return

the first 20 min in the hong kong stock market based on the minute by minute data of the hang seng index in hong kong and the analysis of probability distribution and autocorrelations we nd that the index uctuations for the rst few minutes of daily opening show behaviors very dierent from those of the other times in particular the properties of tail distribution which will show the power law scaling with exponent about four or an exponential type decay the volatility and its correlations depend on the opening eect of each trading day c 2000 elsevier science b v all rights reserved

quantifying the dynamics of financial correlations abstract a novel application of the correlation matrix formalism to study dynamics of the financial evolution is presented this formalism allows to quantify the memory effects as well as some potential repeatable intraday structures in the financial time series the present study is based on the high frequency deutsche aktienindex dax data over the time period between november 1997 and december 1999 and demonstrates a power of the method in this way two significant new aspects of the dax evolution are identified i the memory effects turn out to be sizably shorter than what the standard autocorrelation function analysis seems to indicate and ii there exist short term repeatable structures in fluctuations that are governed by a distinct dynamics the former of these results may provide an argument in favour of the market efficiency while the latter one may indicate origin of the difficulty in reaching a gaussian limit expected from the central limit theorem in the distribution of returns on longer time horizons

modeling of the financial market using the two dimensional anisotropic ising model we have used the two dimensional classical anisotropic ising model in an external field and with an ion single anisotropy term as a mathematical model for the price dynamics of the financial market the model presented allows us to test within the same framework the comparative explanatory power of rational agents versus irrational agents with respect to the facts of financial markets we have obtained the mean price in terms of the strong of the site anisotropy term which reinforces the sensitivity of the agent s sentiment to external news

a characterization and another construction of janko s group graphs r with the following properties are classified i f is g s transitive for some s 4 and some group g g 1 2 where g is the girth of f and ii f is connected a new construction of j3 is given

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

scaling and correlation in financial time series we discuss the results of three recent phenomenological studies focussed on understanding the distinctive statistical properties of nancial time series i the probability distribution of stock price uctuations stock price uctuations occur in all magnitudes in analogy to earthquakes from tiny uctuations to very drastic events such as the crash of 19 october 1987 sometimes referred to as black monday the distribution of price uctuations decays with a power law tail well outside the levy stable regime and describes uctuations that dier by as much as 8 orders of magnitude in addition this distribution preserves its functional form for uctuations on time scales that dier by 3 orders of magnitude from 1 min up to approximately 10 days ii correlations in nancial time series while price uctuations themselves have rapidly decaying correlations the magnitude of uctuations measured by either the absolute value or the square of the price uctuations has correlations that decay as a power law persisting for several months iii volatility and trading activity we quantify the relation between trading activity measured by the number of transactions nt and the price change gt for a given stock over a time interval t t t we nd that nt displays long range power law correlations in time which leads to the interpretation that the long range correlations previously found for jgtj are connected to those of nt c 2000 elsevier science b v all rights reserved

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

a threshold model for australian stock exchange equities abstract in this paper we present a threshold model to describe the phenomena of zero return enhancement that is present in australian stock exchange data we examine the intraday behaviour of the asx data and construct a new measure for the market activity using principal component analysis we use this measure to create a business time scale that keeps the level of zero return enhancement constant throughout trading hours operating in this new time scale we fit the model to data for small and large time scales and find that the model affords an excellent approximation of the distribution of stock returns

stochastic cellular automata model for stock market dynamics in the present work we introduce a stochastic cellular automata model in order to simulate the dynamics of the stock market a direct percolation method is used to create a hierarchy of clusters of active traders on a two dimensional grid active traders are characterized by the decision to buy ensuremath sigma i t 1 or sell ensuremath sigma i t ensuremath 1 a stock at a certain discrete time step the remaining cells are inactive ensuremath sigma i t 0 the trading dynamics is then determined by the stochastic interaction between traders belonging to the same cluster extreme intermittent events such as crashes or bubbles are triggered by a phase transition in the state of the bigger clusters present on the grid where almost all the active traders come to share the same spin orientation most of the stylized aspects of the financial market time series including multifractal proprieties are reproduced by the model a direct comparison is made with the daily closures of the s index

violation of the scaling relation and non markovian nature of earthquake aftershocks abstract the statistical properties of earthquake aftershocks are studied the scaling relation for exponents of the omori law and the power law calm time distribution i e the interoccurrence time distribution which is valid if a sequence of aftershocks is a singular markovian process is carefully examined data analysis shows significant violation of the scaling relation implying the non markovian nature of aftershocks

finite time singularity in the dynamics of the world population economic and financial indices contrary to common belief both the earth s human population and its economic output have grown faster than exponential i e in a super malthusian mode for most of the known history these growth rates are compatible with a spontaneous singularity occurring at the same critical time 2052 10 signaling an abrupt transition to a new regime the degree of abruptness can be infered from the fact that the maximum of the world population growth rate was reached in 1970 i e about 80 years before the predicted singular time corresponding to approximately 4 of the studied time interval over which the acceleration is documented this rounding off of the finite time singularity is probably due to a combination of well known finite size effects and friction and suggests that we have already entered the transition region to a new regime as theoretical support a multivariate analysis coupling population capital r d and technology shows that a dramatic acceleration in the population growth during most of the timespan can occur even though the isolated dynamics do not exhibit it possible scenarios for the cross over and the new regime are discussed

coupled continuous time random walks in finance continuous time random walks ctrws are used in physics to model anomalous diffusion by incorporating a random waiting time between particle jumps in finance the particle jumps are log returns and the waiting times measure delay between transactions these two random variables log return and waiting time are typically not independent for these coupled ctrw models we can now compute the limiting stochastic process just like brownian motion is the limit of a simple random walk even in the case of heavy tailed power law price jumps and or waiting times the probability density functions for this limit process solve fractional partial differential equations in some cases these equations can be explicitly solved to yield descriptions of long term price changes based on a high resolution model of individual trades that includes the statistical dependence between waiting times and the subsequent log returns in the heavy tailed case this involves operator stable space time random vectors that generalize the familiar stable models in this paper we will review the fundamental theory and present two applications with tick by tick stock and futures data

scaling in the norwegian stock market the main objective of this paper is to investigate the validity of the much used assumptions that stock market returns follow a random walk and are normally distributed for this purpose the concepts of chaos theory and fractals are applied two independent models are used to examine price variations in the norwegian and us stock markets the first model used is the range over standard deviation or r s statistic which tests for persistence or antipersistence in the time series both the norwegian and us stock markets show significant persistence caused by long run memory components in the series in addition an average non periodic cycle of four years is found for the us stock market these results are not consistent with the random walk assumption the second model investigates the distributional scaling behaviour of the high frequency price variations in the norwegian stock market the results show a remarkable constant scaling behaviour between different time intervals this means that there is no intrinsic time scale for the dynamics of stock price variations the relationship can be expressed through a scaling exponent describing the development of the distributions as the time scale changes this description may be important when constructing or improving pricing models such that they coincide more closely with the observed market behaviour the empirical distributions of high frequency price variations for the norwegian stock market is then compared to the levy stable distribution with the relevant scaling exponent found by using the r s and distributional scaling analysis good agreement is found between the levy profile and the empirical distribution for price variations less than 6 standard deviations covering almost three orders of magnitude in the data for probabilities larger than 6 standard deviations there seem to be an exponential fall off from the levy profile in the tails which indicates that the second moment may be finite

scaling of the distribution of fluctuations of financial market indices up to more than one month we find that the distributions for dt 4d 1560 min are consistent with a power law asymptotic behavior characterized by an exponent a 3 well outside the stable levy regime 0 a 2 to test the robustness of the s p result we perform a parallel analysis on two other financial market indices database iv contains 3560 daily records of the nikkei index for the 14 year period 1984 1997 and database v contains 4649 daily records of the hang seng index for the 18 year period 1980 1997 we find estimates ofa consistent with those describing the distribution of s p 500 daily returns one possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility for time scales longer than dt 3 4 d our results are consistent with a slow convergence to gaussian behavior s1063 651x 99 11211 x pacs number s 05 40 fb 05 45 tp 89 90 1n

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

optimal trading strategies for ito diffusion processes abstract in this paper we present a method for determining optimal trading strategies for ito diffusion processes by framing the problem in terms of the first passage time for the process we derive distribution and density functions for the trade length and use these functions to calculate the expected trading frequency for the strategy the expected value and the variance of the rate of profit are obtained as functions of the return per trade and trading frequency we present two measures for trade drawdown which may be used as constraints when determining an optimal strategy the optimal strategy is calculated for the ornstein uhlenbeck process by maximising the expected rate of profit

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

pseudofractals and the box counting algorithm we show that for sets with the hausdorff besicovitch dimension equal to zero the box counting bc algorithm commonly used to calculate the renyi exponents dq can exhibit perfect scaling suggesting non zero dq the properties of these pathological sets pseudofractals are investigated numerical as well as analytical estimates for dq are obtained a simple indicator is given to distinguish pseudofractals and fractals in practical applications of the bc method histograms made of pseudofractal sets are shown to have pareto tails