hurst entropy a method to determine predictability in a binary series based on a fractal related process shannon s concept of information is related to predictability in a binary series the value of information relies on the frequency of 0 s and 1 s or how it is expected to occur however information entropy does not consider the bias in randomness related to autocorrelation in fact it is possible for a binary temporal series to carry both short and long term memories related to the sequential distribution of 0 s and 1 s although the hurst exponent measures the range of autocorrelation there is a lack of mathematical connection between information entropy and autocorrelation present in the series to fill this important gap we combined numerical simulations and an analytical approach to determine how information entropy changes according to the frequency of 0 s and 1 s and the hurst exponent indeed we were able to determine how predictability depends on both parameters our findings are certainly useful to several fields when binary times series are applied such as neuroscience to econophysics

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

fractal properties of financial markets abstract we present an analysis of the usa stock market using a simple fractal function financial bubbles preceding the 1987 2000 and 2007 crashes are investigated using the besicovitch ursell fractal function fits show a good agreement with the s p 500 data when a complete financial growth is considered starting at the threshold of the abrupt growth and ending at the peak moving the final time of the fitting interval towards earlier dates causes growing discrepancy between two curves on the basis of a detailed analysis of the financial index behavior we propose a method for identifying the stage of the current financial growth and estimating the time in which the index value is going to reach the maximum

characterizing limit order prices abstract a computational model of a limit order book is used to study the effect of different limit order distribution offsets reference prices such as same side contra side best market prices and last traded price are considered in combination with different price offset distributions we show that when characterizing limit order prices varying the offset distribution only produces different behavior when the reference price is the contra side best price irrespective of the underlying mechanisms used in computing the limit order prices the shape of the price graph and the behavior of the average order book profile distribution are strikingly similar in all the considered reference prices offset distributions this implies that existing averaging methods can cancel variabilities in limit order book shape attributes and may be misleading

a derivative free optimization algorithm based on conditional moments in this paper we propose a derivative free optimization algorithm based on conditional moments for finding the maximizer of an objective function the proposed algorithm does not require calculation or approximation of any order derivative of the objective function the step size in iteration is determined adaptively according to the local geometrical feature of the objective function and a pre specified quantity representing the desired precision the theoretical properties including convergence of the method are presented numerical experiments comparing with the newton quasi newton and trust region methods are given to illustrate the effectiveness of the algorithm

exact results for the roughness of a finite size random walk abstract we consider the role of finite size effects on the value of the effective hurst exponent h this problem is motivated by the properties of the high frequency daily stock prices for a finite size random walk we derive some exact results based on spitzer s identity the conclusion is that finite size effects strongly enhance the value of h and the convergency to the asymptotic value h 1 2 is rather slow this result has a series of conceptual and practical implication which we discuss

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

investigating market efficiency through a forecasting model based on differential equations abstract a new differential equation based model for stock price trend forecast is proposed as a tool to investigate efficiency in an emerging market its predictive power showed statistically to be higher than the one of a completely random model signaling towards the presence of arbitrage opportunities conditions for accuracy to be enhanced are investigated and application of the model as part of a trading strategy is discussed

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

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

avalanche dynamics surface roughening and self organized criticality experiments on a three dimensional pile of rice we present a two dimensional system that exhibits features of self organized criticality the avalanches that occur on the surface of a pile of rice are found to exhibit finite size scaling in their probability distribution the critical exponents are ensuremath tau 1 21 2 for the avalanche size distribution and d 1 99 2 for the cutoff size furthermore the geometry of the avalanches is studied leading to a fractal dimension of the active sites of d b 1 58 2 using a set of scaling relations we can calculate the roughness exponent ensuremath alpha d ensuremath d b 0 41 3 and the dynamic exponent z d 2 ensuremath ensuremath tau 1 56 8 this result is compared with that obtained from a power spectrum analysis of the surface roughness which yields ensuremath alpha 0 42 3 and z 1 5 1 in excellent agreement with those obtained from the scaling relations

revisiting rainfall clustering and intermittency across different climatic regimes 1 one of the vexing questions in rainfall research is the role of intermittency and its nonuniversal signature in anomalous scaling functions whether this lack of universal behavior is due to the bursting patterns in rainfall intensity or the alternation between long dry periods and highly clustered wet phases or both remains an open issue to progress on a narrower scope of this problem the effects of intermittency originating from rainfall occurrence are first separated from rainfall intermittency induced by intensity variability across five climatic regimes considered here it was shown that the rainfall occurrence process op exhibits 1 a near constant spectral slope 2 a near constant clustering exponent and 3 a probability density function of dry phases displaying a power law behavior with an exponent 1 5 consistent with other studies for timescales commensurate with frontal and storm systems also for the op the scaling exponents of the normalized higher order structure functions reveal an extensive monofractal scaling at all five climatic regimes when taken together these intersite results are suggestive that rainfall intensity modulations are the main cause of the nonuniversal anomalous scaling and not the clustering properties associated with the support the nature of these modulations is markedly different when comparing rainfall to a familiar and often interrelated process such as scalar turbulence in the case of turbulence amplitude variability of scalar dissipation rates appear to mitigate the intermittency effects connected with anomalous scaling while for rainfall series intensity fluctuations seem to amplify them

statistical properties of the volatility of price fluctuations we study the statistical properties of volatility measured by locally averaging over a time window t the absolute value of price changes over a short time interval ensuremath delta t we analyze the s 500 stock index for the 13 year period jan 1984 to dec 1996 we find that the cumulative distribution of the volatility is consistent with a power law asymptotic behavior characterized by an exponent ensuremath mu ensuremath approx 3 similar to what is found for the distribution of price changes the volatility distribution retains the same functional form for a range of values of t further we study the volatility correlations by using the power spectrum analysis both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents also both methods show the presence of a crossover at approximately 1 5 days in addition we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 u s companies over the two year period jan 1994 to dec 1995

the effects of common risk factors on stock returns a detrended cross correlation analysis abstract in this paper we investigate the cross correlations between fama and french three factors and the return of american industries on the basis of cross correlation statistic test and multifractal detrended cross correlation analysis mf dcca qualitatively we find that the return series of fama and french three factors and american industries were overall significantly cross correlated based on the analysis of a statistic quantitatively we find that the cross correlations between three factors and the return of american industries were strongly multifractal and applying mf dcca we also investigate the cross correlation of industry returns and residuals we find that there exists multifractality of industry returns and residuals the result of correlation coefficients we can verify that there exist other factors which influence the industry returns except fama three factors

a polynomial time predictor corrector algorithm for a class of linear complementarity problems a polynomial time algorithm for a class of linear complementarity problems with positive semidefinite matrices is presented the method is based on a one step euler s prediction and one step newton s correction procedure to follow the homotopy path defined as the set x y in mathbb r n x i y i mu i 1 cdots n mu 0 y mx q and solves the problem in o n 3 5 l arithmetic operations moreover after one iteration the value x t y decreases with the ratio at least 1 2 5 sqrt n

a quadratically convergent o k 1 n l iteration algorithm for the p k matrix linear complementarity problem an interior point predictor corrector algorithm for thep matrix linear complementarity problem is proposed the algorithm is an extension of mizuno todd ye s predictor corrector algorithm for linear programming problem the extended algorithm is quadratically convergent with iteration complexity o kappa 1 sqrt n l it is the first polynomially and quadratically convergent algorithm for a class of lcps that are not necessarily monotone

on the scaling ranges of detrended fluctuation analysis for long term memory correlated short series of data abstract we examine the scaling regime for the detrended fluctuation analysis dfa the most popular method used to detect the presence of long term memory in data and the fractal structure of time series first the scaling range for dfa is studied for uncorrelated data as a function of time series length l and the correlation coefficient of the linear regression r 2 at various confidence levels next a similar analysis for artificial short series of data with long term memory is performed in both cases the scaling range is found to change linearly both with l and r 2 we show how this dependence can be generalized to a simple unified model describing the relation l r 2 h where h 1 2 h 1 stands for the hurst exponent of the long range autocorrelated signal our findings should be useful in all applications of dfa technique particularly for instantaneous local dfa where a huge number of short time series has to be analyzed at the same time without possibility of checking the scaling range in each of them separately

a sandpile model for the distribution of rainfall abstract recently peters et al phys rev lett 88 2002 018701 have found power law behaviour in the distribution of rain events here it is shown that the observed self similar features in both the reservoir level and the distribution of rain events can quantitatively be reproduced from an extension to two dimensions of the oslo model developed to describe the dynamics of a pile of rice furthermore it is argued that the sandpile model may be able to reproduce more detailed features such as the shape of cumulus clouds in addition many other systems which show self similarity in their time variations with the same quantitative characterizations are discussed

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

theoretical convergence of large step primal dual interior point algorithms for linear programming this paper proposes two sets of rules rule g and rule p for controlling step lengths in a generic primal dual interior point method for solving the linear programming problem in standard form and its dual theoretically rule g ensures the global convergence while rule p which is a special case of rule g ensures the o nl iteration polynomial time computational complexity both rules depend only on the lengths of the steps from the current iterates in the primal and dual spaces to the respective boundaries of the primal and dual feasible regions they rely neither on neighborhoods of the central trajectory nor on potential function these rules allow large steps without performing any line search rule g is especially flexible enough for implementation in practically efficient primal dual interior point algorithms

time varying hurst exponent for us stock markets abstract in this work the dynamical behavior of the us stock markets is characterized on the basis of the temporal variations of the hurst exponent estimated with detrended fluctuation analysis dfa over moving windows for the historical dow jones 1928 2007 and the s p 500 1950 2007 daily indices according to the results drawn i the hurst exponent displays an erratic dynamics with some episodes alternating low and high persistent behavior ii the major breakthrough of the long term trend of the scaling behavior occurred in 1972 at the end of the bretton woods system when the hurst exponent shifted form a positive to a negative long term trend other effects such as the 1987 crisis and the emergence of anti correlated behavior in the recent two years are also discussed

is the expression h 1 3 q valid for real financial data non extensive thermodynamics is one of the most intriguing physics new frontiers a large number of researchers have been successfully finding connections between the new concepts introduced by this new field and other complex systems already presented in particular borland phys rev e 57 1998 6634 6642 has introduced a very interesting relation between the entropic index q that arises in the non extensive entropy and the well known hurst exponent h used to measure long range dependence in complex systems in this paper we provide statistical support to borland results and test the validity of these results in real financial data

a continuation algorithm for a class of linear complementarity problems using an extrapolation technique abstract a polynomial time continuation algorithm is presented for a class of linear complementarity problems with positive semidefinite matrices the linear extrapolation technique is combined with the newton iteration in the predictor corrector procedure of the algorithm to numerically follow the solution curve of the homotopy equations arising from the perturbed karush kuhn tucker condition the convergence rate of the method is proved to be 1 4 7 n after each cycle consisting of one extrapolation between two newton steps

scaling and universality in animate and inanimate systems we illustrate the general principle that in biophysics econophysics and possibly even city growth the conceptual framework provided by scaling and universality may be of use in making sense of complex statistical data specifically we discuss recent work on dna sequences heartbeat intervals avalanche like lung inflation urban growth and company growth although our main focus is on data we also discuss statistical mechanical models

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

characterization of laser propagation through turbulent media by quantifiers based on the wavelet transform dynamic study abstract we analyze within the wavelet theory framework the wandering over a screen of the centroid of a laser beam after it has propagated through a time changing laboratory generated turbulence following a previous work fractals 12 2004 223 two quantifiers are used the hurst parameter h and the normalized total wavelet entropy the temporal evolution of both quantifiers obtained from the laser spot data stream is studied and compared this allows us to extract information on the stochastic process associated with the turbulence dynamics

a delay financial model with stochastic volatility martingale method abstract in this paper we extend a delayed geometric brownian model by adding a stochastic volatility term which is driven by a hidden process of fast mean reverting diffusion to the delayed model combining a martingale approach and an asymptotic method we develop a theory for option pricing under this hybrid model the core result obtained by our work is a proof that a discounted approximate option price can be decomposed as a martingale part plus a small term subsequently a correction effect on the european option price is demonstrated both theoretically and numerically for a good agreement with practical results

does the singular value decomposition entropy have predictive power for stock market evidence from the shenzhen stock market abstract this paper analyzes the predictive ability of the singular value decomposition entropy for the shenzhen component index based on different scales it is found that the predictive ability of the entropy for the index is affected by the width of moving time windows and the structural break in stock market by moving time windows with one year the predictive power of singular value decomposition entropy of shenzhen stock market for its component index is found after the reform of non tradable shares

detrended fluctuation analysis on spot and futures markets of west texas intermediate crude oil abstract in this paper we study the auto correlations and cross correlations of west texas intermediate wti crude oil spot and futures return series employing detrended fluctuation analysis dfa and detrended cross correlation analysis dcca scaling analysis shows that for time scales smaller than a month the auto correlations and cross correlations are persistent for time scales larger than a month but smaller than a year the correlations are anti persistent while for time scales larger than a year the series are neither auto correlated nor cross correlated indicating the efficient operation of the crude oil markets moreover for small time scales the degree of short term cross correlations is higher than that of auto correlations using the multifractal extension of dfa and dcca we find that for small time scales the correlations are strongly multifractal while for large time scales the correlations are nearly monofractal analyzing the multifractality of shuffled and surrogated series we find that both long range correlations and fat tail distributions make important contributions to the multifractality our results have important implications for market efficiency and asset pricing models

coherent and random sequences in financial fluctuations abstract the detrended fluctuation analysis dfa is used to sort out temporal correlations in financial data its usefulness for the investigations of long range power law correlations in economic sequences is shown our findings of persistent and antipersistent sequences are suprisingly similar to those for dna sequences which appeared as a mosaic of coding and non coding patches

asymmetric market efficiency using the index based asymmetric mfdfa abstract we explore the asymmetric market efficiency for various countries stock indices using the index based asymmetric mfdfa we divide market based on its trend within certain sub period then we test whether the overall up and down trend markets are efficient via the asymmetric generalized hurst exponent at first we provide the criteria for testing the asymmetric market efficiency based on the monte carlo simulation using the brownian motion secondly we analyze the asymmetric market efficiency of 34 countries for different sub periods by comparing the hurst exponents of original and shuffled time series we discover that the sources of inefficiency are different with respect to time periods by presenting the groups of countries based on the asymmetric market inefficiency lastly we discuss a time varying feature of market efficiency where the wider gap between the up and down trend efficiency and the stronger correlation between stock index and the asymmetric hurst exponent are discovered during the financial crisis

the use of the hurst exponent to investigate the global maximum of the warsaw stock exchange wig20 index abstract the wig20 index the index of the 20 biggest companies traded on the warsaw stock exchange reached the global maximum on 29th october 2007 i have used the local dfa detrended functional analysis to obtain the hurst exponent diffusion exponent and investigate the signature of anti correlation of share price evolution around the maximum the analysis was applied to the share price evolution for variable dfa parameters for many values of parameters the evidence of anti correlation near the wig20 maximum was pointed out

applications of statistical physics to economic and financial topics abstract problems in economy and finance have started to attract the interest of statistical physicists fundamental problems pertain to the existence or not of long medium short range power law correlations in economic systems as well as to the presence of financial cycles methods like the extended detrended fluctuation analysis and the multi affine analysis are recalled emphasizing their value in sorting out correlation ranges and predictability among spectacular results the possibility of crash predictions is indicated the well known financial analyst technique the so called moving average is shown to raise questions about fractional brownian motion properties finally the m k zipf method and the i variability diagram technique are presented for sorting out short range correlations analogies with other fields of modern applied statistical physics are also presented in view of some universal openess

the properties and mechanism of long term memory in nonparametric volatility abstract recent empirical literature documents the presence of long term memory in return volatility but the mechanism of the existence of long term memory is still unclear in this paper we investigate the origin and properties of long term memory with nonparametric volatility using high frequency time series data of the chinese shanghai composite stock price index we perform detrended fluctuation analysis dfa on three different nonparametric volatility estimators with different sampling frequencies for the same volatility series the hurst exponents reduce as the sampling time interval increases but they are still larger than 1 2 which means that no matter how the interval changes it still cannot change the existence of long memory rrv presents a relatively stable property on long term memory and is less influenced by sampling frequency rv and rbv have some evolutionary trends depending on time intervals which indicating that the jump component has no significant impact on the long term memory property this suggests that the presence of long term memory in nonparametric volatility can be contributed to the integrated variance component considering the impact of microstructure noise rbv and rrv still present long term memory under various time intervals we can infer that the presence of long term memory in realized volatility is not affected by market microstructure noise our findings imply that the long term memory phenomenon is an inherent characteristic of the data generating process not a result of microstructure noise or volatility clustering