the trading time risks of stock investment in stock price drop abstract this article investigates the trading time risk ttr of stock investment in the case of stock price drop of dow jones industrial average dji and hushen300 data csi300 respectively the escape time of stock price from the maximum to minimum in a data window length dwl is employed to measure the absolute ttr the ratio of the escape time to data window length is defined as the relative ttr empirical probability density functions of the absolute and relative ttrs for the dji and csi300 data evidence that i whenever the dwl increases the absolute ttr increases the relative ttr decreases otherwise ii there is the monotonicity or non monotonicity for the stability of the absolute or relative ttr iii there is a peak distribution for shorter trading days and a two peak distribution for longer trading days for the pdf of ratio iv the trading days play an opposite role on the absolute or relative ttr and its stability between dji and csi300 data

can one make any crash prediction in finance using the local hurst exponent idea abstract we apply the hurst exponent idea for investigation of djia index time series data the behavior of the local hurst exponent prior to drastic changes in financial series signal is analyzed the optimal length of the time window over which this exponent can be calculated in order to make some meaningful predictions is discussed our prediction hypothesis is verified with examples of 1929 and 1987 crashes as well as with more recent phenomena in stock market from the period 1995 to 2003 some interesting agreements are found

multiscale multifractal diffusion entropy analysis of financial time series abstract this paper introduces a multiscale multifractal diffusion entropy analysis mmdea method to analyze long range correlation then applies this method to stock index series the method combines the techniques of diffusion process and renyi entropy to focus on the scaling behaviors of stock index series using a multiscale which allows us to extend the description of stock index variability to include the dependence on the magnitude of the variability and time scale compared to multifractal diffusion entropy analysis the mmdea can show more details of scale properties and provide a reliable analysis in this paper we concentrate not only on the fact that the stock index series has multifractal properties but also that these properties depend on the time scale in which the multifractality is measured this time scale is related to the frequency band of the signal we find that stock index variability appears to be far more complex than reported in the studies using a fixed time scale

signatures of noise enhanced stability in metastable states the lifetime of a metastable state in the transient dynamics of an overdamped brownian particle is analyzed both in terms of the mean first passage time and by means of the mean growth rate coefficient both quantities feature nonmonotonic behaviors as a function of the noise intensity and are independent signatures of the noise enhanced stability effect they can therefore be alternatively used to evaluate and estimate the presence of this phenomenon which characterizes metastability in nonlinear physical systems

tta a new approach to estimate hurst exponent with less estimation error and computational time abstract investigation of long memory processes in signals can give us an important information about how signals have behaved so far and how will it behave in future hurst exponent estimation is a proper tool to show memory in signals rescaled range analysis r s detrended fluctuation analysis dfa and generalized hurst exponent ghe are most known methods for estimation of hurst exponent which introduced in literature in this paper we propose a new algorithm to estimate hurst exponent based on triangles total areas tta that can be made out of three samples of different lag in time series to test our algorithm performance we used two kinds of synthetic waveforms with known hurst exponents results indicates that the proposed method is superior with respect to data length estimation error computational time and noise sensitivity we also apply our proposed method in epilepsy detection and compare our results with previous works to show outperformance of our algorithm with accuracy of 94 5 in classification between interictal and ictal eeg signals

role of the initial conditions on the enhancement of the escape time in static and fluctuating potentials we present a study of the noise driven escape of an overdamped brownian particle moving in a cubic potential profile with a metastable state we analyze the role of the initial conditions of the particle on the enhancement of the average escape time as a function of the noise intensity for fixed and fluctuating potentials we observe the noise enhanced stability effect for all the initial unstable states investigated for a fixed potential we find a peculiar initial condition xc which separates the set of the initial unstable states in two regions those which give rise to divergences from those which show nonmonotonic behavior of the average escape time for fluctuating potential at this particular initial condition and for low noise intensity we find large fluctuations of the average escape time

option pricing formulas based on a non gaussian stock price model options are financial instruments that depend on the underlying stock we explain their non gaussian fluctuations using the nonextensive thermodynamics parameter q a generalized form of the black scholes bs partial differential equation and some closed form solutions are obtained the standard bs equation q 1 which is used by economists to calculate option prices requires multiple values of the stock volatility known as the volatility smile using q 1 5 which well models the empirical distribution of returns we get a good description of option prices using a single volatility

fractional calculus and continuous time finance in this paper we present a rather general phenomenological theory of tick by tick dynamics in financial markets many well known aspects such as the levy scaling form follow as particular cases of the theory the theory fully takes into account the non markovian and non local character of financial time series predictions on the long time behaviour of the waiting time probability density are presented finally a general scaling form is given based on the solution of the fractional diffusion equation

hitting time distributions in financial markets we analyze the hitting time distributions of stock price returns in different time windows characterized by different levels of noise present in the market the study has been performed on two sets of data from us markets the first one is composed by daily price of 1071 stocks trade for the 12 year period 1987 1998 the second one is composed by high frequency data for 100 stocks for the 4 year period 1995 1998 we compare the probability distribution obtained by our empirical analysis with those obtained from different models for stock market evolution specifically by focusing on the statistical properties of the hitting times to reach a barrier or a given threshold we compare the probability density function pdf of three models namely the geometric brownian motion the garch model and the heston model with that obtained from real market data we will present also some results of a generalized heston model r 2007 elsevier b v all rights reserved

noise enhanced stability in fluctuating metastable states we derive general equations for the nonlinear relaxation time of brownian diffusion in randomly switching potential with a sink for piece wise linear dichotomously fluctuating potential with metastable state we obtain the exact average lifetime as a function of the potential parameters and the noise intensity our result is valid for arbitrary white noise intensity and for arbitrary fluctuation rate of the potential we find noise enhanced stability phenomenon in the system investigated the average lifetime of the metastable state is greater than the time obtained in the absence of additive white noise we obtain the parameter region of the fluctuating potential where the effect can be observed the system investigated also exhibits a maximum of the lifetime as a function of the fluctuation rate of the potential

power law cross correlations between price change and volume change of indian stocks abstract we study multifractal long range correlations and cross correlations of daily price change and volume change of 50 stocks that comprise nifty index of national stock exchange mumbai using mf dfa and mf dcca methods we find that the time series of price change are uncorrelated whereas anti persistent long range multifractal correlations are found in volume change series we also find antipersistent long range multifractal cross correlations between the time series of price change and volume change as multifractality is a signature of complexity we estimate complexity parameters of the time series of price change volume change and cross correlated price volume change by fitting the fourth degree polynomials to their multifractal spectra our results indicate that the time series of price change display high complexity whereas the time series of volume change and cross correlated price volume change display low complexity

mean escape time in a system with stochastic volatility we study the mean escape time in a market model with stochastic volatility the process followed by the volatility is the cox ingersoll and ross process which is widely used to model stock price fluctuations the market model can be considered as a generalization of the heston model where the geometric brownian motion is replaced by a random walk in the presence of a cubic nonlinearity we investigate the statistical properties of the escape time of the returns from a given interval as a function of the three parameters of the model we find that the noise can have a stabilizing effect on the system as long as the global noise is not too high with respect to the effective potential barrier experienced by a fictitious brownian particle we compare the probability density function of the return escape times of the model with those obtained from real market data we find that they fit very well

financial time series modeling using the hurst exponent abstract this study aims to enhance the understanding of logarithmic asset returns in particular more emphasis is given to the long memory property of financial returns a well documented stylized fact however in the presence of structural breaks other studies suggest that statistical tools such as the autocorrelation function acf can wrongly indicate long memory we propose an insensitive to structural breaks method to test for dependence between distant observations furthermore a model which combines memory in returns and memory in absolute returns is developed in two stages first return series are segmented with respect to changes in the volatility and then the two parameters of the model are estimated to assess the capabilities of the model historical prices of the standard and poor 500 index s p500 financial time stocks exchange 100 index ftse100 deutsche boerse ag german stock index dax and crude oil are used 1 given the estimated parameters and the volatility within each regime 10000 vectors are generated and compared to the original data in terms of the kolmogorov smirnov k s statistical test the obtained results suggest that long memory is present and provide evidence that the additional memory information captured by the model improves financial returns modeling

blocks with cyclic defect groups and clifford extensions abstract we prove that the residual clifford extension of any non exceptional character belonging to a p block with cyclic defect groups of a twisted group algebra is naturally isomorphic to the clifford extension of any simple module belonging to that block we also show that dade s inductive conjecture holds for blocks with cyclic defect groups

are the optimum problems in structural design well posed from the examples considered above it can be seen that the area of the cross section minimizing the total weight of a simple rod under a given load is in general not unique only under particular assumptions on the constraints and the distribution of axial loads is the optimal solution uniquely determined by the principle of minimum weight another feature of the optimal solutions is that their properties of regularity number and location of discontinuities of the solutions and its derivatives are in general not at all obvious from the beginning

on hurst exponent estimation under heavy tailed distributions abstract in this paper we show how the sampling properties of the hurst exponent methods of estimation change with the presence of heavy tails we run extensive monte carlo simulations to find out how rescaled range analysis r s multifractal detrended fluctuation analysis m f d f a detrending moving average d m a and generalized hurst exponent approach g h e estimate hurst exponent on independent series with different heavy tails for this purpose we generate independent random series from stable distribution with stability exponent changing from 1 1 heaviest tails to 2 gaussian normal distribution and we estimate the hurst exponent using the different methods r s and g h e prove to be robust to heavy tails in the underlying process g h e provides the lowest variance and bias in comparison to the other methods regardless the presence of heavy tails in data and sample size utilizing this result we apply a novel approach of the intraday time dependent hurst exponent and we estimate the hurst exponent on high frequency data for each trading day separately we obtain hurst exponents for s p500 index for the period beginning with year 1983 and ending by november 2009 and we discuss the surprising result which uncovers how the market s behavior changed over this long period

multifractal detrended fluctuation analysis of nonstationary time series abstract we develop a method for the multifractal characterization of nonstationary time series which is based on a generalization of the detrended fluctuation analysis dfa we relate our multifractal dfa method to the standard partition function based multifractal formalism and prove that both approaches are equivalent for stationary signals with compact support by analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series by comparing the multifractal dfa results for original series with those for shuffled series we can distinguish multifractality due to long range correlations from multifractality due to a broad probability density function we also compare our results with the wavelet transform modulus maxima method and show that the results are equivalent

assessing market uncertainty by means of a time varying intermittency parameter for asset price fluctuations abstract maximum likelihood estimation techniques for multifractal processes are applied to high frequency data in order to quantify intermittency in the fluctuations of asset prices from time records as short as one month these methods permit extraction of a meaningful intermittency parameter characterising the degree of volatility clustering we can therefore study the time evolution of volatility clustering and test the statistical significance of this variability by analysing data from the oslo stock exchange and comparing the results with the investment grade spread we find that the estimates of are lower at times of high market uncertainty

theoretical analysis and simulations of the generalized lotka volterra model the dynamics of generalized lotka volterra systems is studied by theoretical techniques and computer simulations these systems describe the time evolution of the wealth distribution of individuals in a society as well as of the market values of firms in the stock market the individual wealths or market values are given by a set of time dependent variables w i i 1 dots n the equations include a stochastic autocatalytic term representing investments a drift term representing social security payments and a time dependent saturation term due to the finite size of the economy the w i mathrm mathrm s turn out to exhibit a power law distribution of the form p w ensuremath sim w ensuremath 1 ensuremath ensuremath alpha it is shown analytically that the exponent ensuremath alpha can be expressed as a function of one parameter which is the ratio between the constant drift component social security and the fluctuating component investments this result provides a link between the lower and upper cutoffs of this distribution namely between the resources available to the poorest and those available to the richest in a given society the value of ensuremath alpha is found to be insensitive to variations in the saturation term which represent the expansion or contraction of the economy the results are of much relevance to empirical studies that show that the distribution of the individual wealth in different countries during different periods in the 20th century has followed a power law distribution with 1l ensuremath alpha l2

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

multifractal behavior in the dynamics of brazilian inflation indices abstract in this paper we applied the multifractal detrended fluctuations analysis mf dfa to investigate the components of the observed multifractality in time series of 6 brazilian inflation indices we found the generalized hurst exponent h q for each brazilian inflation indices and quantify their statistical properties which allowed us to observe separately the small scale contributing primarily via the negative moments q and the large scale via the positive moments q we also calculated the multifractal spectrum f and used a fourth degree polynomial regression fit to estimate the complexity parameters that describe the degree of multifractality of the underlying process we compared the mf dfa results for the original time series with those for shuffled series we found that its multifractal nature is due to two factors broadness of probability density function of the times series and different correlations in small and large scale fluctuations

power law distributions in empirical data power law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man made phenomena unfortunately the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution the part of the distribution representing large but rare events and by the difficulty of identifying the range over which power law behavior holds commonly used methods for analyzing power law data such as least squares fitting can produce substantially inaccurate estimates of parameters for power law distributions and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all here we present a principled statistical framework for discerning and quantifying power law behavior in empirical data our approach combines maximum likelihood fitting methods with goodness of fit tests based on the kolmogorov smirnov ks statistic and likelihood ratios we evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches we also apply the proposed methods to twenty four real world data sets from a range of different disciplines each of which has been conjectured to follow a power law distribution in some cases we find these conjectures to be consistent with the data while in others the power law is ruled out

stochastic resonance of drawdown risk in energy market prices abstract we investigate the stochastic resonance dynamic behavior characteristics of price drawdown time series driven by internal and external periodic information and discuss the influence of information resonance on price drawdown risk based on price drawdown periodic heston model and signal power amplification a theoretical model of the periodic price drawdown time series is proposed to describe the energy price drawdown time series with the periodic heston model then the signal power amplification spa is employed to measure the stochastic resonance phenomenon in the internal and external periodic information environment of complex energy dynamics system combined with the real data of wti spot price of nymex the least square method of drawdown time series distribution is used to estimate the parameters of the model the probability density functions of drawdown between the theoretical model and the real data are compared and a good agreement can be found between both the simulated data from the proposed model and the real data after the stochastic simulation of signal power amplification under internal and external periodic information respectively the results show that i in the functions of spa versus price volatility parameters noise correlation strength or periodic information strength inverse resonance phenomenon can be observed that is to say there is the best system price volatility parameter noise correlation strength and information strength corresponding to the least risk of the price drawdown ii in the spa versus amplitude of volatility fluctuations the correlation induce multiple inverse stochastic resonance phenomenon can be observed iii the increase of growth rate strengthens spa and weakens drawdown risk of energy market prices

forbidden patterns permutation entropy and stock market inefficiency abstract in this paper we introduce two new quantifiers for the stock market inefficiency the number of forbidden patterns and the normalized permutation entropy they are model independent measures thus they have more general applicability we find robust evidence that degree of market inefficiency is positively correlated with the number of forbidden patterns and negatively correlated with the permutation entropy our empirical results suggest that these two physical tools are useful to discriminate the stage of stock market development and can be easily implemented

dynamic behaviors and measurements of financial market crash rate abstract this paper proposes the conditional crash rate ccr to study the degree of financial market crisis and evaluate the risk of financial market crash based on maximum drawdown and escape rate it is found that the ccr of stock price in financial market is equivalent to the escape rate of the drawdown time series corresponding to price series based on the mean escape rate the analytical solution of ccr of financial market of stock price described by black scholes model is obtained for the ccr empirical researches show that the theoretical results of the heston model are in good agreement with the results of the real financial data of the sp ii we can find critical phenomena resonance and inverse resonance behaviors in the function of ccr vs mean reversion of volatility ii the parameter variation induces the appearance of noise enhancement stability in the function of ccr vs amplitude of volatility fluctuation

multiple change point detection for auto regressive conditional heteroscedastic processes the emergence of the recent financial crisis during which markets frequently underwent changes in their statistical structure over a short period of time illustrates the importance of non stationary modelling in financial time series motivated by this observation we propose a fast well performing and theoretically tractable method for detecting multiple change points in the structure of an auto regressive conditional heteroscedastic model for financial returns with piecewise constant parameter values our method termed basta binary segmentation for transformed auto regressive conditional heteroscedasticity proceeds in two stages process transformation and binary segmentation the process transformation decorrelates the original process and lightens its tails the binary segmentation consistently estimates the change points we propose and justify two particular transformations and use simulation to fine tune their parameters as well as the threshold parameter for the binary segmentation stage a comparative simulation study illustrates good performance in comparison with the state of the art and the analysis of the financial times stock exchange ftse 100 index reveals an interesting correspondence between the estimated change points and major events of the recent financial crisis although the method is easy to implement ready made r software is provided

when noise decreases deterministic diffusion dynamical noise acting homogeneously in each time step can enhance the stability of an unstable fixed point however if dynamical noise is added locally in state space additional clear enhancement can be achieved if this restriction is chosen properly a systematic analysis of the influence of local and global dynamical noise on the residence time of an unstable state is presented and optimal parameters for the stabilizing mechanisms are discussed as a consequence it is demonstrated that local dynamical noise can yield increased localization in deterministic diffusion models

correspondence between temporal correlations in time series inverse problems and the spherical model in this paper we employ methods from statistical mechanics to model temporal correlations in time series we put forward a methodology based on the maximum entropy principle to generate ensembles of time series constrained to preserve part of the temporal structure of an empirical time series of interest we show that a constraint on the lag one autocorrelation can be fully handled analytically and corresponds to the well known spherical model of a ferromagnet we then extend such a model to include constraints on more complex temporal correlations by means of perturbation theory showing that this leads to substantial improvements in capturing the lag one autocorrelation in the variance we apply our approach on synthetic data and illustrate how it can be used to formulate expectations on the future values of a data generating process

the detection and estimation of long memory in stochastic volatility abstract we propose a new time series representation of persistence in conditional variance called a long memory stochastic volatility lmsv model the lmsv model is constructed by incorporating an arfima process in a standard stochastic volatility scheme strongly consistent estimators of the parameters of the model are obtained by maximizing the spectral approximation to the gaussian likelihood the finite sample properties of the spectral likelihood estimator are analyzed by means of a monte carlo study an empirical example with a long time series of stock prices demonstrates the superiority of the lmsv model over existing short memory volatility models

exponential distribution of financial returns at mesoscopic time lags a new stylized fact we study the probability distribution of stock returns at mesoscopic time lags return horizons ranging from about an hour to about a month while at shorter microscopic time lags the distribution has power law tails for mesoscopic times the bulk of the distribution more than 99 of the probability follows an exponential law the slope of the exponential function is determined by the variance of returns which increases proportionally to the time lag at longer times the exponential law continuously evolves into gaussian distribution the exponential to gaussian crossover is well described by the analytical solution of the heston model with stochastic volatility r 2004 elsevier b v all rights reserved

optimal design of elastic rods extension of a minimum energy solution an optimal design problem solved previously for an elastic rod which is a mixture of two materials and which hangs under its own weight is solved here for a different parameter range on the product of elastic stiffness and density of the materials the problem is also considered when the parameters are at the junction of the two ranges and the possibility of an infinite number of solutions arises raising questions of well posedness of the problem there the method used is the maximum principle of pontryagin and hestenes

fractionally integrated generalized autoregressive conditional heteroskedasticity abstract the new class of fractionally integrated generalized autoregressive conditionally heteroskedastic figarch processes is introduced the conditional variance of the process implies a slow hyperbolic rate of decay for the influence of lagged squared innovations unlike i d processes for the mean maximum likelihood estimates mle of the figarch parameters are argued to be t 1 2 consistent the small sample behavior of an approximate mle procedure is assessed through a simulation study which also documents how the estimation of a standard garch model tends to produce integrated or igarch like estimates an empirical example with daily deutschmark u s dollar exchange rates illustrates the practical relevance of the new figarch specification

long term memory in stock market prices a test for long term memory that is robust to short range dependence is developed it is a modification of the r s statistic and the relevant asymptotic sampling theory is derived via functional central limit theory contrary to previous findings when applied to daily and monthly stock returns indexes over several time periods this test yields no evidence of long range dependence once short range dependence is accounted for monte carlo experiments show that the modified r s test has power against at least two specific models of long term memory suggesting that models with short range dependence may adequately capture the behavior of historical stock returns copyright 1991 by the econometric society

topology of correlation based minimal spanning trees in real and model markets we compare the topological properties of the minimal spanning tree obtained from a large group of stocks traded at the new york stock exchange during a 12 year trading period with the one obtained from surrogated data simulated by using simple market models we find that the empirical tree has features of a complex network that cannot be reproduced even as a first approximation by a random market model and by the widespread one factor model

the influences of delay time on the stability of a market model with stochastic volatility abstract the effects of the delay time on the stability of a market model are investigated by using a modified heston model with a cubic nonlinearity and cross correlated noise sources these results indicate that i there is an optimal delay time o which maximally enhances the stability of the stock price under strong demand elasticity of stock price and maximally reduces the stability of the stock price under weak demand elasticity of stock price ii the cross correlation coefficient of noises and the delay time play an opposite role on the stability for the case of the delay time o and the same role for the case of the delay time o moreover the probability density function of the escape time of stock price returns the probability density function of the returns and the correlation function of the returns are compared with other literatures

varieties of long memory models long memory is defined as a series having a slowly declining correlogram or equivalently an infinite spectrum at zero frequency fractional integrated processes have such properties but here it is pointed out that a number of other processes can also be long memory including generalized fractionally integrated models arising from aggregation time changing coefficient models and possibly nonlinear models it seems that there are many classes of processes that deserve further study the relevance of long memory is illustrated using absolute returns from a daily stock market index

fractionally integrated process for transition economics we analyze the european transition economics and show that many time series of major indices exhibit i power law correlations in their values ii power law correlations in their magnitudes and iii an asymmetric probability distribution applying the phase randomization procedure to these time series we show that magnitude correlations completely vanish we propose a stochastic model that can generate time series with features i ii and iii and we show by means of numerical simulations that this model is capable of reproducing these three features found in the empirical data

long term memory and volatility clustering in high frequency price changes abstract we studied the long term memory in diverse stock market indices and foreign exchange rates using detrended fluctuation analysis dfa for all high frequency market data studied no significant long term memory property was detected in the return series while a strong long term memory property was found in the volatility time series the possible causes of the long term memory property were investigated using the return data filtered by the ar 1 model reflecting the short term memory property the garch 1 1 model reflecting the volatility clustering property and the figarch model reflecting the long term memory property of the volatility time series the memory effect in the ar 1 filtered return and volatility time series remained unchanged while the long term memory property diminished significantly in the volatility series of the garch 1 1 filtered data notably there is no long term memory property when we eliminate the long term memory property of volatility by the figarch model for all data used although the hurst exponents of the volatility time series changed considerably over time those of the time series with the volatility clustering effect removed diminish significantly our results imply that the long term memory property of the volatility time series can be attributed to the volatility clustering observed in the financial time series

the in efficiency of nymex energy futures a multifractal analysis abstract we performed a systematic analysis to investigate the multifractal properties and efficient market hypothesis emh in time series of volatility for nymex new york mercantile exchange energy futures using the multifractal detrended fluctuations analysis mf dfa we studied the generalized hurst exponent h q and the renyi exponent q for each record and quantify their statistical properties which allowed us to observe separately the contributing small scale primarily via the negative moments q and the large scale via the positive moments q we also calculated the multifractal spectrum f and used a fourth degree polynomial regression fit to estimate the complexity parameters that describe the degree of multifractality of the underlying process the results obtained from our fitting procedure show that the volatility time series of nymex energy futures display overall persistent behavior 0 0 5 a higher degree of multifractality and the dominance of large fluctuations in this sense our empirical results related to 0 0 5 categorically reject the emh furthermore our results presented that crude oil light sweet cushing oklahoma the no 2 heating oil new york harbor and propane mont belvieu texas energy futures are highly concentrated with behavior more closely associated to oligopolistic market

hurst exponent footprints from activities on a large structural system abstract this paper presents hurst exponent footprints from pseudo dynamic measurements of significantly varied activities on a damaged bridge structure during rehabilitation through continuous monitoring the system is interesting due to associated uncertainty in large scale structures and significant presence of human intervention arising from fundamentally different processes investigations into the variation of computed hurst exponents on time series of limited lengths are carried out in this regard the hurst exponents are compared with respect to specific events during the rehabilitation as well as with the data collection locations the variations of local hurst exponents about the values computed for each activity are presented the scaling of hurst exponents for different activities is also investigated these are representative of the extent of multifractality for each event the extent of multifractality is assessed along with its source and time dependency

morita equivalences related to the glauberman correspondence abstract starting with p interior algebras where p is a finite p group we prove two theorems establishing certain group graded morita equivalences these apply in particular to the case of blocks with normal defect groups and defect zero blocks of normal subgroups respectively

algorithm to estimate the hurst exponent of high dimensional fractals we propose an algorithm to estimate the hurst exponent of high dimensional fractals based on a generalized high dimensional variance around a moving average low pass filter as working examples we consider rough surfaces generated by the random midpoint displacement and by the cholesky levinson factorization algorithms the surrogate surfaces have hurst exponents ranging from 0 1 to 0 9 with step 0 1 and different sizes the computational efficiency and the accuracy of the algorithm are also discussed

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

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

use of cumulative sums of squares for retrospective detection of changes of variance abstract this article studies the problem of multiple change points in the variance of a sequence of independent observations we propose a procedure to detect variance changes based on an iterated cumulative sums of squares icss algorithm we study the properties of the centered cumulative sum of squares function and give an intuitive basis for the icss algorithm for series of moderate size i e 200 observations and beyond the icss algorithm offers results comparable to those obtained by a bayesian approach or by likelihood ratio tests without the heavy computational burden required by these approaches simulation results comparing the icss algorithm to other approaches are presented

multifractal diffusion entropy analysis optimal bin width of probability histograms abstract in the framework of multifractal diffusion entropy analysis we propose a method for choosing an optimal bin width in histograms generated from underlying probability distributions of interest the method presented uses techniques of renyi s entropy and the mean squared error analysis to discuss the conditions under which the error in the multifractal spectrum estimation is minimal we illustrate the utility of our approach by focusing on a scaling behavior of financial time series in particular we analyze the s p500 stock index as sampled at a daily rate in the time period 1950 2013 in order to demonstrate a strength of the method proposed we compare the multifractal spectrum for various bin widths and show the robustness of the method especially for large values of q for such values other methods in use e g those based on moment estimation tend to fail for heavy tailed data or data with long correlations connection between the spectrum and renyi s q parameter is also discussed and elucidated on a simple example of multiscale time series

scaling in the market of futures the price time series of the italian government bonds btp futures is studied by means of scaling concepts originally developed for random walks in statistical physics the series of overnight price differences is mapped onto a one dimensional random walk the bond walk the analysis of the root mean square fluctuation function and of the auto correlation function indicates the absence of both short and long range correlations in the bond walk a simple monte carlo simulation of a random walk with trinomial probability distribution is able to reproduce the main features of the bond walk

true and apparent scaling the proximity of the markov switching multifractal model to long range dependence in this paper we consider daily financial data of a collection of different stock market indices exchange rates and interest rates and we analyze their multi scaling properties by estimating a simple specification of the markov switching multifractal msm model in order to see how well the estimated model captures the temporal dependence of the data we estimate and compare the scaling exponents h q for q 1 2 for both empirical data and simulated data of the msm model in most cases the multifractal model appears to generate apparent long memory in agreement with the empirical scaling laws

evaluating volatile stock markets using information theoretic measures abstract in this paper we broaden the entropy concept for indian financial markets to make a collation between markets which are highly volatile we have considered seven different estimators of shannon entropy tsallis entropy and renyi entropy for various values of their parameters and also approximate entropy and sample entropy for all these entropies we provide computational results for minute wise and day wise data in terms of nifty stock and nifty sector indices we conclude that in context of sector wise indices and stock wise indices nifty pharma and nifty50 are the most volatile among other indices respectively

ar p based detrended fluctuation analysis abstract autoregressive models are commonly used for modeling time series from nature economics and finance this work explored simple autoregressive ar p models to remove long term trends in detrended fluctuation analysis dfa crude oil prices and bitcoin exchange rate were considered with the former corresponding to a mature market and the latter to an emergent market results showed that ar p based dfa performs similar to traditional dfa however the former dfa provides information on stability of long term trends which is valuable for understanding and quantifying the dynamics of complex time series from financial systems

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

the maximum potential energy of elastic rods under axial gravitational load an optimal design problem solved previously for an elastic rod hanging under its own weight found the distribution of the cross sectional area that minimized the total potential energy stored in an equilibrium state with the admissible designs bounded above and below and also subject to the constraint of prescribed total volume this work solves the companion problem of the design that stores the maximum potential energy under the same constraint conditions the method used is based on a comparison theorem for sandwich structures

estimation of time dependent hurst exponents with variational smoothing and application to forecasting foreign exchange rates abstract hurst exponents depict the long memory of a time series for human dependent phenomena as in finance this feature may vary in the time it justifies modelling dynamics by multifractional brownian motions which are consistent with time dependent hurst exponents we improve the existing literature on estimating time dependent hurst exponents by proposing a smooth estimate obtained by variational calculus this method is very general and not restricted to the sole hurst framework it is globally more accurate and easier than other existing non parametric estimation techniques besides in the field of hurst exponents it makes it possible to make forecasts based on the estimated multifractional brownian motion the application to high frequency foreign exchange markets gbp chf sek usd cad aud jpy cny and sgd all against eur shows significantly good forecasts when the hurst exponent is higher than 0 5 what depicts a long memory feature the accuracy is higher

optimal design of elastic rods under axial gravitational load using the maximum principle abstract optimal design problems for structural elements in equilibrium often come in pairs in which the cost function for one problem becomes a constraint for the second in particular the problem of minimizing structural volume or weight under size and stress constraints has a dual in which potential energy is minimized for fixed volume of material these dual problems are solved here for a linearly elastic rod hanging from a rigid support the design variable is the cross sectional area of the rod the method used is the maximum principle of pontryagin and hestenes rather than the function space methods used by others for similar problems

linear and nonlinear experimental regimes of stochastic resonance we investigate the stochastic resonance phenomenon in a physical system based on a tunnel diode the experimental control parameters are set to allow the control of the frequency and amplitude of the deterministic modulating signal over an interval of values spanning several orders of magnitude we observe both a regime described by the linear response theory and the nonlinear deviation from it in the nonlinear regime we detect saturation of the power spectral density of the output signal detected at the frequency of the modulating signal and a dip in the noise level of the same spectral density when these effects are observed we detect a phase and frequency synchronization between the stochastic output and the deterministic input

multiscale shannon entropy and its application in the stock market abstract in this paper we perform a multiscale entropy analysis on the dow jones industrial average index using the shannon entropy the stock index shows the characteristic of multi scale entropy that caused by noise in the market the entropy is demonstrated to have significant predictive ability for the stock index in both long term and short term and empirical results verify that noise does exist in the market and can affect stock price it has important implications on market participants such as noise traders

non stationary multifractality in stock returns abstract we perform an extensive empirical analysis of scaling properties of equity returns suggesting that financial data show time varying multifractal properties this is obtained by comparing empirical observations of the weighted generalised hurst exponent wghe with time series simulated via multifractal random walk mrw by bacry et al e bacry j delour j f muzy multifractal random walk physical review e 64 2 2001 026103 while dynamical wghe computed on synthetic mrw series is consistent with a scenario where multifractality is constant over time fluctuations in the dynamical wghe observed in empirical data are not in agreement with a mrw with constant intermittency parameter we test these hypotheses of constant multifractality considering different specifications of mrw model with fatter tails in all cases considered although the thickness of the tails accounts for most of the anomalous fluctuations of multifractality it still cannot fully explain the observed fluctuations

scaling behaviors in differently developed markets scaling properties of four di erent stock market indices are studied in terms of a generalized hurst exponent approach we nd that the deviations from pure brownian motion behavior are associated with the degrees of development of the markets and we observe strong di erentiations in the scaling properties of markets at di erent development stage c

source algebras and source modules the aim of this article is to give a self contained approach in module theoretic terms to two fundamental results in block theory due to puig 6 14 6 first there is an embedding of the source algebra of the brauer correspondent of a block of some finite group into a source algebra of that block and second the source algebras of the brauer correspondence can be described explicitly our proof of the first result theorem 5 and its corollary 6 below is essentially the translation to our terminology of the proof in 1 4 10 the second result describing the source algebras of the brauer correspondent follows also from 3 but the proofs in 3 use both the main result on the structure of nilpotent blocks in 5 as well as techniques from 6 sects 4 6 while our approach from proposition 9 onwards requires only some classical results on the structure of blocks with a central defect group an account of the results in 6 on source algebras of blocks with a normal defect group can also be found in 7 sect 45 except for the explicit description of the central extension e see section 10 below as being defined in terms of the multiplicity algebra of the block which is quoted in 7 45 10 b without proof referring back to 6 at the end of 7 sect 45

estimating long range dependence finite sample properties and confidence intervals abstract a major issue in financial economics is the behavior of asset returns over long horizons various estimators of long range dependence have been proposed even though some have known asymptotic properties it is important to test their accuracy by using simulated series of different lengths we test r s analysis detrended fluctuation analysis and periodogram regression methods on samples drawn from gaussian white noise the dfa statistics turns out to be the unanimous winner unfortunately no asymptotic distribution theory has been derived for this statistics so far we were able however to construct empirical i e approximate confidence intervals for all three methods the obtained values differ largely from heuristic values proposed by some authors for the r s statistics and are very close to asymptotic values for the periodogram regression method

noise enhanced stability of periodically driven metastable states we study the effect of noise enhanced stability of periodically driven metastable states in a system described by piecewise linear potential we find that the growing of the average escape time with the intensity of the noise is depending on the initial condition of the system we analytically obtain the condition for the noise enhanced stability effect and verify it by numerical simulations

roles of capital flow on the stability of a market system abstract the roles of capital flow in an ensemble composed of sub markets are investigated a modified heston model and recycled noises are employed to describe the dynamics of stock price and capital flow in the ensemble respectively the mean escape times of two sub markets with a cubic nonlinearity are calculated by using numerical simulation the results evidence that i there is a worst delay time or rate of capital inflow concerning the minimal stability of stock price and an optimal delay time or rate of capital outflow concerning the maximal stability of stock price when 0 denotes strength of correlation between two wiener processes of the stock price and the volatility ii when 0 the stability of stock price is maximally enhanced by an optimal delay time or rate of capital inflow and reduced by a worst rate of capital outflow but monotonously strengthened by delay time of capital outflow

volatility driven market in a generalized lotka voltera formalism abstract the generalized lotka voltera glv formalism has been introduced in order to explain the power law distributions in the individual wealth w i t pareto law and financial markets returns fluctuations r as a result of the auto catalytic multiplicative random character of the individual capital dynamics as long as the multiplicative random factor is extracted from the same probability distribution for all the individuals the exponent of the power laws turns out to be independent on the time variations of the average this explains also the stability over the past century of experimentally measured pareto exponent in contrast to the scaling properties of the single time unconditional probability distributions the auto correlations between observables measured at different times are not correctly reproduced by the original glv if the variance 2 of is time independent in the glv formalism the volatility r 2 auto correlations decay exponentially while the measurements in real markets indicate a power law with a very small exponent we show in the present paper that by making the variance of the individual wealth changes 2 a function of the market volatility r 2 one correctly reproduces the market volatility long range correlations moreover we show that this non trivial feedback loop between the market price volatility and the variance of the investors wealth leads to non trivial patterns in the overall market trends if the feedback is too strong it may even endanger the market stability

relationship between efficiency and predictability in stock price change abstract in this study we evaluate the relationship between efficiency and predictability in the stock market the efficiency which is the issue addressed by the weak form efficient market hypothesis is calculated using the hurst exponent and the approximate entropy apen the predictability corresponds to the hit rate this is the rate of consistency between the direction of the actual price change and that of the predicted price change as calculated via the nearest neighbor prediction method we determine that the hurst exponent and the apen value are negatively correlated however predictability is positively correlated with the hurst exponent

fractional calculus and continuous time finance ii the waiting time distribution we complement the theory of tick by tick dynamics of financial markets based on a continuous time random walk ctrw model recently proposed by scalas et al 4 and we point out its consistency with the behaviour observed in the waiting time distribution for bund future prices traded at liffe london

on the relationship between the hurst exponent the ratio of the mean square successive difference to the variance and the number of turning points abstract the long range dependence of the fractional brownian motion fbm fractional gaussian noise fgn and differentiated fgn dfgn is described by the hurst exponent h considering the realizations of these three processes as time series they might be described by their statistical features such as half of the ratio of the mean square successive difference to the variance a and the number of turning points t this paper investigates the relationships between a and h and between t and h it is found numerically that the formulae a h a e b h in case of fbm and a h a b h c for fgn and dfgn describe well the a h relationship when t h is considered no simple formula is found and it is empirically found that among polynomials the fourth and second order description applies best the most relevant finding is that when plotted in the space of a t the three process types form separate branches hence it is examined whether a and t may serve as hurst exponent indicators some real world data stock market indices sunspot numbers chaotic time series are analyzed for this purpose and it is found that the h s estimated using the h a relations expressed as inverted a h functions are consistent with the h s extracted with the well known wavelet approach this allows to efficiently estimate the hurst exponent based on fast and easy to compute a and t given that the process type fbm fgn or dfgn is correctly classified beforehand finally it is suggested that the a h relation for fgn and dfgn might be an exact shifted 3 2 power law

invariant lattices and modular decomposition of irreducible representations let p be a prime let h be a finite group and let c be an absolutely irreducible character of h any thorough study of the p modular decom position of c requires passage to some integral representation if s is a finite group acting on h and leaving invariant such an integral represen tation will not be s invariant in general it is important to have invariant integral representations for purposes of clifford theory in fact modular decomposition often gives new insights in such classical questions like extendability of characters for this reason we consider the more general situation that h is a normal subgroup of some group g and let s g h s still acts on the characters of h and the isomorphism types of h modules we also fix a p modular system k r k where

dynamical generalized hurst exponent as a tool to monitor unstable periods in financial time series we investigate the use of the hurst exponent dynamically computed over a weighted moving time window to evaluate the level of stability instability of financial firms financial firms bailed out as a consequence of the 2007 2008 credit crisis show a neat increase with time of the generalized hurst exponent in the period preceding the unfolding of the crisis conversely firms belonging to other market sectors which suffered the least throughout the crisis show opposite behaviors we find that the multifractality of the bailed out firms increase at the crisis suggesting that the multi fractal properties of the time series are changing these findings suggest the possibility of using the scaling behavior as a tool to track the level of stability of a firm in this paper we introduce a method to compute the generalized hurst exponent which assigns larger weights to more recent events with respect to older ones in this way large fluctuations in the remote past are less likely to influence the recent past we also investigate the scaling associated with the tails of the log returns distributions and compare this scaling with the scaling associated with the hurst exponent observing that the processes underlying the price dynamics of these firms are truly multi scaling