detrended fluctuation analysis based on higher order moments of financial time series in this paper a generalized method of detrended fluctuation analysis dfa is proposed as a new measure to assess the complexity of a complex dynamical system such as stock market we extend dfa and local scaling dfa to higher moments such as skewness and kurtosis labeled smdfa and kmdfa so as to investigate the volatility scaling property of financial time series simulations are conducted over synthetic and financial data for providing the comparative study we further report the results of volatility behaviors in three american countries three chinese and three european stock markets by using dfa and lsdfa method based on higher moments they demonstrate the dynamics behaviors of time series in different aspects which can quantify the changes of complexity for stock market data and provide us with more meaningful information than single exponent and the results reveal some higher moments volatility and higher moments multiscale volatility details that cannot be obtained using the traditional dfa method

multifractal properties of the indian financial market abstract we investigate the multifractal properties of the logarithmic returns of the indian financial indices bse nse by applying the multifractal detrended fluctuation analysis the results are compared with that of the us s p 500 index numerically we find that q th order generalized hurst exponents h q and q change with the moments q the nonlinear dependence of these scaling exponents and the singularity spectrum f show that the returns possess multifractality by comparing the mf dfa results of the original series to those for the shuffled series we find that the multifractality is due to the contributions of long range correlations as well as the broad probability density function the financial markets studied here are compared with the binomial multifractal model bmfm and have a smaller multifractal strength than the bmfm

statistical properties of german dax and chinese indices abstract we investigate statistical properties of the german dax and chinese indices including the volatility distribution autocorrelation function dfa function and return volatility correlation function with both the daily data and minutely data at the minutely time scale the chinese indices may show irregular dynamic behavior at the daily time scale the volatility distribution autocorrelation function and dfa function of the chinese indices are qualitatively similar to those of the german dax while the return volatility correlation function exhibits an anti leverage effect different from the leverage effect of the german dax

multifractal property of chinese stock market in the csi 800 index based on mf dfa approach abstract csi 800 index consists of csi 500 index and csi 300 index aiming to reflect the performance of stocks with large mid and small size of china a share market in this paper we analyze the multifractal structure of chinese stock market in the csi 800 index based on the multifractal detrended fluctuation analysis mf dfa method we find that the fluctuation of the closing logarithmic returns have multifractal properties the shape and width of multifractal spectrum are depended on the weighing order q more interestingly we observe a bigger market crash in june august 2015 than the one in 2008 based on the local hurst exponents the result provides important information for further study on dynamic mechanism of return fluctuation and whether it would trigger a new financial crisis

statistical properties of daily ensemble variables in the chinese stock markets abstract we study dynamical behavior of the chinese stock markets by investigating the statistical properties of daily ensemble return and variety defined respectively as the mean and the standard deviation of the ensemble daily price return of a portfolio of stocks traded in china s stock markets on a given day the distribution of the daily ensemble return has an exponential form in the center and power law tails while the variety distribution is lognormal in the bulk followed by a power law tail for large variety based on detrended fluctuation analysis r s analysis and modified r s analysis we find evidence of long memory in the ensemble return and strong evidence of long memory in the evolution of variety

volatilities traded volumes and the hypothesis of price increments in derivative securities a detrended fluctuation analysis dfa is applied to the statistics of korean treasury bond ktb futures from which the logarithmic increments volatilities and traded volumes are estimated over a specific time lag in this study the logarithmic increment of futures prices has no long memory property while the volatility and the traded volume exhibit the existence of the long memory property to analyze and calculate whether the volatility clustering is due to a inherent higher order correlation not detected by with the direct application of the dfa to logarithmic increments of ktb futures it is of importance to shuffle the original tick data of future prices and to generate a geometric brownian random walk with the same mean and standard deviation it was found from a comparison of the three tick data that the higher order correlation inherent in logarithmic increments leads to volatility clustering particularly the result of the dfa on volatilities and traded volumes can be supported by the hypothesis of price changes

detrending moving average algorithm for multifractals the detrending moving average dma algorithm is a widely used technique to quantify the long term correlations of nonstationary time series and the long range correlations of fractal surfaces which contains a parameter ensuremath theta determining the position of the detrending window we develop multifractal detrending moving average mfdma algorithms for the analysis of one dimensional multifractal measures and higher dimensional multifractals which is a generalization of the dma method the performance of the one dimensional and two dimensional mfdma methods is investigated using synthetic multifractal measures with analytical solutions for backward ensuremath theta 0 centered ensuremath theta 0 5 and forward ensuremath theta 1 detrending windows we find that the estimated multifractal scaling exponent ensuremath tau q and the singularity spectrum f ensuremath alpha are in good agreement with the theoretical values in addition the backward mfdma method has the best performance which provides the most accurate estimates of the scaling exponents with lowest error bars while the centered mfdma method has the worse performance it is found that the backward mfdma algorithm also outperforms the multifractal detrended fluctuation analysis the one dimensional backward mfdma method is applied to analyzing the time series of shanghai stock exchange composite index and its multifractal nature is confirmed

comparison of detrending methods for fluctuation analysis abstract we examine several recently suggested methods for the detection of long range correlations in data series based on similar ideas as the well established detrended fluctuation analysis dfa in particular we present a detailed comparison between the regular dfa and two recently suggested methods the centered moving average cma method and a modified detrended fluctuation analysis mdfa we find that cma performs the same as dfa in long data with weak trends and is slightly superior to dfa in short data with weak trends when comparing standard dfa to mdfa we observe that dfa performs slightly better in almost all examples we studied we also discuss how several types of trends affect different types of dfa for weak trends in the data the new methods are comparable with dfa in these respects however if the functional form of the trend in data is not a priori known dfa remains the method of choice only a comparison of dfa results using different detrending polynomials yields full recognition of the trends a comparison with independent methods is recommended for proving long range correlations

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

microscopic models for long ranged volatility correlations we propose a general interpretation for long range correlation effects in the activity and volatility of financial markets this interpretation is based on the fact that the choice between active and inactive strategies is subordinated to random walk like processes we numerically demonstrate our scenario in the framework of simplified market models such as the minority game model with an inactive strategy or a more sophisticated version that includes some price dynamics we show that real market data can be surprisingly well accounted for by these simple models

asymptotically dense spherical codes ii laminated spherical codes for pt i see ibid vol 43 no 6 p 1774 85 1997 new spherical codes called laminated spherical codes are constructed in dimensions 2 49 using a technique similar to the construction of laminated lattices each spherical code is recursively constructed from existing spherical codes in one lower dimension laminated spherical codes outperform the best known spherical codes in the minimum distance sense for many code sizes the density of a laminated spherical code approaches the density of the laminated lattice in one lower dimension as the minimum distance approaches zero in particular the three dimensional laminated spherical code is asymptotically optimal in the sense that its density approaches the fejes toth 1959 upper bound as the minimum distance approaches zero laminated spherical codes perform asymptotically as well as wrapped spherical codes in those dimensions where laminated lattices are optimal sphere packings

constructing ordinary sum differential equations using polynomial networks data relations can define general sum partial differential equations of a composite function additive derivative model time series data observations can analogously describe an ordinary sum differential equation with time derivatives which is possible to be solved using partial derivative term substitutions of time dependent series differential polynomial neural network is a new type of neural network which constructs and substitutes for an unknown general partial differential equation from data observations developed by the author it generates sum series of convergent partial polynomial derivative terms which can describe an unknown complex function time series this type of non linear regression decomposes a system model described by the general differential equation into many partial low order derivative specifications of selected relative sum terms common soft computing techniques in general can apply input variables of only absolute interval values of a specific data range the character of relative data allows processing a wider range of test interval values than defined by a training set the characteristics of the composite sum differential equation solutions can facilitate a much greater variety of model forms than is allowed using standard soft computing methods recurrent neural network proved to form simple solid time series models most of which it is possible to describe using ordinary differential equations so the comparisons were done

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

research on the fractal structure in the chinese stock market abstract applying fractal theory this paper probes and discusses self similarity and scale invariance of the chinese stock market it analyses three kinds of scale indexes i e autocorrelation index hurst index and the scale index on the basis of detrended fluctuation analysis dfa algorithm and promotes dfa into a recursive algorithm using the three kinds of scale indexes we conduct empirical research on the chinese shanghai and shenzhen stock markets the results indicate that the rate of returns of the two stock markets does not obey the normal distribution a correlation exists between the stock price indexes over time scales the stock price indexes exhibit fractal time series it indicates that the policy guide hidden at the back influences the characteristic of the chinese stock market

inference of differential equation models by genetic programming this paper describes an evolutionary method for identifying a causal model from the observed time series data we use a system of ordinary differential equations odes as the causal model this approach is known to be useful for practical applications e g bioinformatics chemical reaction models control theory etc to explore the search space more effectively in the course of evolution the right hand sides of odes are inferred by genetic programming gp and the least mean square lms method is used along with the ordinary gp we apply our method to several target tasks and empirically show how successfully gp infers the systems of odes we also describe an extension of the approach to the inference of differential equation systems with transcendental functions

unbiased detrended fluctuation analysis long range correlations in very short time series abstract detrended fluctuation analysis dfa is a standard method to evaluate long range correlations embedded in non stationary time series to obtain a reliable estimation of scaling behavior it requires the length of a time series is long enough at least 10 000 which is not always the case in reality how to evaluate long range correlation behavior in a very short time series is still an open problem in the present paper we propose an improvement of dfa by correcting the bias in estimation of variance called unbiased detrended fluctuation analysis udfa extensive calculations show its high performance for instance from a fractional brownian motion fbm series with length 500 the estimated long range correlation exponent has negligible bias and acceptable confidence region standard deviation less than 0 05 as a typical example the proposed method is used to monitor evolution of fractal gait rhythm of a volunteer rich patterns are found in the evolutionary process

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

successive refinement lattice vector quantization lattice vector quantization lvq solves the complexity problem of lbg based vector quantizers yielding very general codebooks however a single stage lvq when applied to high resolution quantization of a vector may result in very large and unwieldy indices making it unsuitable for applications requiring successive refinement the goal of this work is to develop a unified framework for progressive uniform quantization of vectors without having to sacrifice the mean squared error advantage of lattice quantization a successive refinement uniform vector quantization methodology is developed where the codebooks in successive stages are all lattice codebooks each in the shape of the voronoi regions of the lattice at the previous stage such voronoi shaped geometric lattice codebooks are named voronoi lattice vqs vlvq measures of efficiency of successive refinement are developed based on the entropy of the indices transmitted by the vlvqs additionally a constructive method for asymptotically optimal uniform quantization is developed using tree structured subset vlvqs in conjunction with entropy coding the methodology developed here essentially yields the optimal vector counterpart of scalar bitplane wise refinement unfortunately it is not as trivial to implement as in the scalar case furthermore the benefits of asymptotic optimality in tree structured subset vlvqs remain elusive in practical nonasymptotic situations nevertheless because scalar bitplane wise refinement is extensively used in modern wavelet image coders we have applied the vlvq techniques to successively refine vectors of wavelet coefficients in the vector set partitioning vspiht framework the results are compared against spiht and the previous successive approximation wavelet vector quantization sa w vq results of sampson da silva and ghanbari 1996

application of multifractal measures to tehran price index we report an empirical study of tehran price index tepix to analyze our data we use various methods like as rescaled range analysis r s modified rescaled range analysis lo s method detrended fluctuation analysis dfa and generalized hurst exponents analysis based on numerical results the scaling range of tepix returns is specified long memory effect or long range correlation property in this market is investigated characteristic exponent for probability distribution function of tepix returns is derived and finally the stage of development in tehran stock exchange is determined

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

assessment of 48 stock markets using adaptive multifractal approach abstract in this paper stock market comovements are examined using cointegration granger causality tests and nonlinear approaches in context of mutual information and correlations since underlying data sets are affected by non stationarities and trends we also apply adaptive multifractal detrended fluctuation analysis amf dfa and adaptive multifractal detrended cross correlation analysis amf dxa we find only 170 pair of stock markets cointegrated and according to the granger causality and mutual information we realize that the strongest relations lies between emerging markets and between emerging and frontier markets according to scaling exponent given by amf dfa h q 2 1 we find that all underlying data sets belong to non stationary process according to efficient market hypothesis emh only 8 markets are classified in uncorrelated processes at 2 confidence interval 6 stock markets belong to anti correlated class and dominant part of markets has memory in corresponding daily index prices during january 1995 to february 2014 new zealand with h 0 457 0 004 and jordan with h 0 602 0 006 are far from emh the nature of cross correlation exponents based on amf dxa is almost multifractal for all pair of stock markets the empirical relation h x y h x x h y y 2 is confirmed mentioned relation for q 0 is also satisfied while for q 0 there is a deviation from this relation confirming behavior of markets for small fluctuations is affected by contribution of major pair for larger fluctuations the cross correlation contains information from both local internal and global external conditions width of singularity spectrum for auto correlation and cross correlation are x x 0 304 0 905 and x y 0 246 1 178 respectively the wide range of singularity spectrum for cross correlation confirms that the bilateral relation between stock markets is more complex the value of d c c a indicates that all pairs of stock market studied in this time interval belong to cross correlated processes

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

successive refinement of information the successive refinement of information consists of first approximating data using a few bits of information then iteratively improving the approximation as more and more information is supplied the goal is to achieve an optimal description at each stage in general an ongoing description which is rate distortion optimal whenever it is interrupted is sought it is shown that in order to achieve optimal successive refinement the necessary and sufficient conditions are that the solutions of the rate distortion problem can be written as a markov chain in particular all finite alphabet signals with hamming distortion satisfy these requirements it is also shown that the same is true for gaussian signals with squared error distortion and for laplacian signals with absolute error distortion a simple counterexample with absolute error distortion and a symmetric source distribution which shows that successive refinement is not always achievable is presented

power law and multiscaling properties of the chinese stock market abstract we investigate the cumulative probability density function pdf and the multiscaling properties of the returns in the chinese stock market by using returns data adjusted for thin trading we find that the distribution has power law tails at shorter microscopic timescales or lags however the distribution follows an exponential law for longer timescales furthermore we investigate the long range correlation and multifractality of the returns in the chinese stock market by the dfa and mfdfa methods we find that all the scaling exponents are between 0 5 and 1 by dfa method which exhibits the long range power law correlations in the chinese stock market moreover we find by mfdfa method that the generalized hurst exponents h q are not constants which shows the multifractality in the chinese stock market we also find that the correlation of shenzhen stock market is stronger than that of shanghai stock market

forecasting volatility in shanghai and shenzhen markets based on multifractal analysis abstract this paper analyzes the multifractality in shanghai and shenzhen stock markets using multifractal spectrum analysis and multifractal detrended fluctuation analysis we find that the main source of multifractality is long range correlations of large and small fluctuations then we introduce a multifractal volatility measure mv and find that by taking mv as daily conditional volatility the simulated series displayed similar stylized facts to the original daily return series by capturing the dynamics of mv using the arfima model we find that the out of sample forecasting performance of the arfima mv model is better than some garch class models and the arfima rv model under some criteria of loss function

discrete scale invariance in cross correlations between time series abstract the de trended cross correlation analysis dcca is converted to a new form which turns out to be a periodic function modulated power law to evaluate discrete scale long range cross correlation between time series if the modulator is dominated with one frequency the derived form will degenerate to a log periodic power law we investigate a total of five important stock markets distributing in different continents calculations show that the cross correlations between different stock markets may hint at log periodic oscillations this finding may be helpful for us to evaluate financial state in a global way

direct determination approach for the multifractal detrending moving average analysis in the canonical framework we propose an alternative approach for the multifractal analysis based on the detrending moving average method mf dma we define a canonical measure such that the multifractal mass exponent q is related to the partition function and the multifractal spectrum f can be directly determined the performances of the direct determination approach and the traditional approach of the mf dma are compared based on three synthetic multifractal and monofractal measures generated from the one dimensional p model the two dimensional p model and the fractional brownian motions we find that both approaches have comparable performances to unveil the fractal and multifractal nature in other words without loss of accuracy the multifractal spectrum f can be directly determined using the new approach with less computation cost we also apply the new mf dma approach to the volatility time series of stock prices and confirm the presence of multifractality

effect of trends on detrended fluctuation analysis scaling behavior we find that crossovers result from the competition between the scaling of the noise and the apparent scaling of the trend we study how the characteristics of these crossovers depend on i the slope of the linear trend ii the amplitude and period of the periodic trend iii the amplitude and power of the power law trend and iv the length as well as the correlation properties of the noise surprisingly we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws i e long range power law dependence of the position of the crossover on the parameters of the trends we show that the dfa result of noise with a trend can be exactly determined by the superposition of the separate results of the dfa on the noise and on the trend assuming that the noise and the trend are not correlated if this superposition rule is not followed this is an indication that the noise and the superposed trend are not independent so that removing the trend could lead to changes in the correlation properties of the noise in addition we show how to use dfa appropriately to minimize the effects of trends how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation or if the crossover is due to a trend without any transition in the dynamical properties of the noise

on the spectrum of fractional brownian motions fractional brownian motions fbms provide useful models for a number of physical phenomena whose empirical spectra obey power laws of fractional order however due to the nonstationary nature of these processes the precise meaning of such spectra remains generally unclear two complementary approaches are proposed which are intended to clarify this point the first one based on a time frequency analysis takes into account the nonstationary nature of fbm and puts emphasis on time averaged measurements the second one based on a time scale analysis is matched to self similarity properties of fbm and reveals an underlying stationary structure relative to each time scaling

detrended fluctuation analysis for fractals and multifractals in higher dimensions one dimensional detrended fluctuation analysis dfa and multifractal detrended fluctuation analysis mfdfa are widely used in the scaling analysis of fractal and multifractal time series because they are accurate and easy to implement in this paper we generalize the one dimensional dfa and mfdfa to higher dimensional versions the generalization works well when tested with synthetic surfaces including fractional brownian surfaces and multifractal surfaces the two dimensional mfdfa is also adopted to analyze two images from nature and experiment and nice scaling laws are unraveled

econophysics financial time series from a statistical physics point of view in recent years physicists have started applying concepts and methods of statistical physics to study economic problems the word econophysics is sometimes used to refer to this work much recent work is focused on understanding the statistical properties of nancial time series one reason for this interest is that nancial markets are examples of complex interacting systems for which a huge amount of data exist and it is possible that nancial time series viewed from a dierent perspective might yield new results this article reviews the results of three recent phenomenological studies i the probability distribution of stock price uctuations stock price uctuations occur in all magnitudes in analogy to earthquakes from tiny uctuations to drastic events such as market crashes 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 eight orders of magnitude in addition this distribution preserves its functional form for uctuations on time scales that dier by three orders of magnitude from 1 min up to approximately 10 d 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 and persist for several months iii correlations among dierent companies the third result bears on the application of random matrix theory to understand the correlations among price uctuations of any two dierent stocks from a study of the eigenvalue statistics of the cross correlation matrix constructed from price uctuations of the leading 1000 stocks we nd that the largest 1 of the eigenvalues and the corresponding eigenvectors show systematic deviations from the predictions for a random matrix whereas the rest of the eigenvalues conform to random matrix behavior suggesting that these 1 of the eigenvalues contain system specic information about correlated time evolution of dierent companies c 2000 published by elsevier science b v all rights reserved

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

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

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

design performance and complexity analysis of residual trellis coded vector quantizers multistage trellis coded vector quantization ms tcvq is developed as a constrained trellis source coding technique the performance of the two stage tcvq is studied for gaussian sources issues of stage by stage design output alphabet selection and complexity are addressed with emphasis on selecting and partitioning the stage codebooks for a given rate ms tcvq achieves low encoding and storage complexity compared to tcvq and comparisons with same dimensional multistage vector quantization indicate a 0 5 3 db improvement in signal to quantization noise ratio

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

uniform and piecewise uniform lattice vector quantization for memoryless gaussian and laplacian sources lattice vector quantizer design procedures for nonuniform sources are presented the procedures yield lattice vector quantizers with excellent performance and retaining the structure required for fast quantization analytical methods for truncating and scaling lattices to be used in vector quantizations are given and their utility is demonstrated for independent and identically distributed i i d gaussian and laplacian sources an analytical technique for piecewise linear multidimensional compandor designs is evaluated for i i d gaussian and laplacian sources by comparing its performance to that of the other vector quantizers

multifractal moving average analysis and test of multifractal model with tuned correlations we address two common major problems in the study of time series characterizing fluctuations in complex systems multifractal analysis and multifractal modeling specifically we introduce a multi fractal centered moving average mf cma analysis which is computationally easier but equivalently performing compared with the well established multi fractal detrended fluctuation analysis mf dfa with linear detrending in addition we study in detail a generalized binomial multi fractal model gb mfm to conveniently and reliably generate multifractal surrogate data with arbitrary singularity strengths and arbitrary long term persistence we use the data generated by this model as well as realistic by construction monofractal data series with crossovers and trends to test and compare the multifractal analysis methods and discuss finite size effects as well as limitations due to spurious multifractality

nth order fuzzy linear differential equations in this paper a numerical method for solving nth order linear differential equations with fuzzy initial conditions is considered the idea is based on the collocation method the existence theorem of the fuzzy solution is considered this method is illustrated by solving several examples

gaussian source coding with spherical codes a fixed rate shape gain quantizer for the memoryless gaussian source is proposed the shape quantizer is constructed from wrapped spherical codes that map a sphere packing in spl ropf sup k 1 onto a sphere in spl ropf sup k and the gain codebook is a globally optimal scalar quantizer a wrapped leech lattice shape quantizer is used to demonstrate a signal to quantization noise ratio within 1 db of the distortion rate function for rates above 1 bit per sample and an improvement over existing techniques of similar complexity an asymptotic analysis of the tradeoff between gain quantization and shape quantization is also given

multifractal properties of chinese stock market in shanghai abstract in this article we apply three methods of multifractal analysis partition function method singular spectrum method and multifractal detrended fluctuation analysis method to analyze the closing index fluctuations of shanghai stock market during the past seven years we have found that shanghai stock market has weak multifractal features and there are long range power law correlations between index series the shapes of singular spectrums do not change with time scales and their strengths weaken when the scales shorten but when the orders of partition function increase the strengths of multifractal increase the singular spectrums become rougher and the general hurst exponents decrease these results provide solid and important values for further study on the dynamic mechanism of stock market price fluctuation

design and analysis of a successively refinable lattice quantizer for i i d gaussian sources a successively refinable quantizer is proposed for independent identically distributed i i d gaussian sources our quantizer is a successively refinable extension of the gaussian source coding algorithm based on wrapped spherical codes designed by hamkins and zeger in ldquogaussian source coding with spherical codes rdquo ieee transactions on information theory vol 4 no 11 pp 2980 2989 november 2002 the proposed successively refinable quantizer is analyzed for the case of high resolution and optimum bit allocation is computed our simulation results show that our proposed quantizer outperforms other successively refinable quantizers designed for gaussian sources

product code vector quantizers for waveform and voice coding memory and computation requirements imply fundamental limitations on the quality that can be achieved in vector quantization systems used for speech waveform coding and linear predictive voice coding lpc one approach to reducing storage and computation requirements is to organize the set of reproduction vectors as the cartesian product of a vector codebook describing the shape of each reproduction vector and a scalar codebook describing the gain or energy such shape gain vector quantizers can be applied both to waveform coding using a quadratic error distortion measure and to voice coding using an itakura saito distortion measure in each case the minimum distortion reproduction vector can be found by first selecting a shape code word and then based on that choice selecting a gain codeword several algorithms are presented for the design of shape gain vector quantizers based on a traning sequence of data or a probabilistic model the algorithms are used to design shape gain vector quantizers for both the waveform coding and voice coding application the quantizers are simulated and their performance is compared to that of previously reported vector quantization systems

time series forecasting using a system of ordinary differential equations this paper presents a hybrid evolutionary method for identifying a system of ordinary differential equations odes to predict the small time scale traffic measurements data we used the tree structure based evolutionary algorithm to evolve the architecture and a particle swarm optimization pso algorithm to fine tune the parameters of the additive tree models for the system of ordinary differential equations we also illustrate some experimental comparisons with genetic programming gene expression programming and a feedforward neural network optimized using pso algorithm experimental results reveal that the proposed method is feasible and efficient for forecasting the small scale traffic measurements data

long range correlations and nonstationarity in the brazilian stock market abstract we report an empirical study of the ibovespa index of the sao paulo stock exchange in which we detect the existence of long range correlations to analyze our data we introduce a rescaled variant of the usual detrended fluctuation analysis that allows us to obtain the hurst exponent through a one parameter fitting we also compute a time dependent hurst exponent h t using 3 year moving time windows in particular we find that before the launch of the collor plan in 1990 the curve h t remains in general well above 1 2 while afterwards it stays close to 1 2 we thus argue that the structural reforms set off by the collor plan has lead to a more efficient stock market in brazil we also suggest that the time dependence of the ibovespa hurst exponent could be described in terms of a multifractional brownian motion

price volume multifractal analysis of the moroccan stock market abstract in this paper we analyzed price volume multifractal cross correlations of moroccan stock exchange we chose the period from january 1st 2000 to january 20th 2017 to investigate the multifractal behavior of price change and volume change series then we used multifractal detrended cross correlations analysis method mf dcca and multifractal detrended fluctuation analysis mf dfa to analyze the series we computed bivariate generalized hurst exponent renyi exponent and spectrum of singularity for each pair of indices to measure quantitatively cross correlations furthermore we used detrended cross correlations coefficient dcca and cross correlation test q m to analyze cross correlation quantitatively and qualitatively by analyzing results we found existence of price volume multifractal cross correlations the spectrum width has a strong multifractal cross correlation we remarked that volume change series is anti persistent when we analyzed the generalized hurst exponent for all moments q the cross correlation test showed the presence of a significant cross correlation however dcca coefficient had a small positive value which means that the level of correlation is not very significant finally we analyzed sources of multifractality and their degree of contribution in the series

comparing the structure of an emerging market with a mature one under global perturbation a b s t r a c t in this paper we investigate the tehran stock exchange tse and dow jones industrial average djia in terms of perturbed correlation matrices to perturb a stock market there are two methods namely local and global perturbation in the local method we replace a correlation coefficient of the cross correlation matrix with one calculated from two gaussian distributed time series whereas in the global method we reconstruct the correlation matrix after replacing the original return series with gaussian distributed time series the local perturbation is just a technical study we analyze these markets through two statistical approaches random matrix theory rmt and the correlation coefficient distribution by using rmt we find that the largest eigenvalue is an influence that is common to all stocks and this eigenvalue has a peak during financial shocks we find there are a few correlated stocks that make the essential robustness of the stock market but we see that by replacing these return time series with gaussian distributed time series the mean values of correlation coefficients the largest eigenvalues of the stock markets and the fraction of eigenvalues that deviate from the rmt prediction fall sharply in both markets by comparing these two markets we can see that the djia is more sensitive to global perturbations these findings are crucial for risk management and portfolio selection

asymptotically dense spherical codes i wrapped spherical codes a new class of spherical codes called wrapped spherical codes is constructed by wrapping any sphere packing spl lambda in euclidean space onto a finite subset of the unit sphere in one higher dimension the mapping preserves much of the structure of spl lambda and unlike previously proposed maps the density of the wrapped spherical codes approaches the density of spl lambda as the minimum distance approaches zero we show that this implies that the asymptotically maximum spherical coding density is achieved by wrapped spherical codes whenever spl lambda is the densest possible sphere packing

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