detrended fluctuation analysis of intertrade durations abstract the intraday pattern long memory and multifractal nature of the intertrade durations which are defined as the waiting times between two consecutive transactions are investigated based upon the limit order book data and order flows of 23 liquid chinese stocks listed on the shenzhen stock exchange in 2003 an inverse u shaped intraday pattern in the intertrade durations with an abrupt drop in the first minute of the afternoon trading is observed based on a detrended fluctuation analysis we find a crossover of power law scaling behaviors for small box sizes trade numbers in boxes and large box sizes and strong evidence in favor of long memory in both regimes in addition the multifractal nature of intertrade durations in both regimes is confirmed by a multifractal detrended fluctuation analysis for individual stocks with a few exceptions in the small duration regime the intraday pattern has little influence on the long memory and multifractality

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

asymptotic integration of some nonlinear differential equations with fractional time derivative we establish that under some simple integral conditions regarding the nonlinearity the 1 order fractional differential equation 0d t x f t x 0 t 0 has a solution with which can be expanded asymptotically as a bt o t 1 when t for given real numbers a b our arguments are based on fixed point theory here 0d t designates the riemann liouville derivative of order 0 1

multifractal analysis of chinese stock volatilities based on the partition function approach abstract we have performed a detailed multifractal analysis on the 1 min volatility of two indexes and 1139 stocks in the chinese stock markets based on the partition function approach the partition function q s scales as a power law with respect to the box size s the scaling exponents q form a nonlinear function of q statistical tests based on bootstrapping show that the extracted multifractal nature is significant at the 1 significance level the individual securities can be well modeled by the p model in turbulence with p 0 40 0 02 based on the idea of ensemble averaging including quenched and annealed average we treat each stock exchange as a whole and confirm the existence of multifractal nature in the chinese stock markets

multifractal analysis of visualized room impulse response for detecting early reflections this paper describes an improved method for detecting early reflections in the initial part of the room impulse response using multifractals the proposed method uses the two dimensional multifractal analysis the room impulse response is visualized as a spectrogram image which is then subjected to the multifractal analysis the algorithm is based on describing local regularity in the image using distribution of holder exponents the time positions of the selected holder exponents in the image are utilized in detecting early reflections the obtained results show better efficiency of the proposed algorithm compared to the previous one dimensional multifractal analysis based algorithm

stability analysis of a fractional order model for the hiv aids epidemic in a patchy environment abstract a multi patch hiv aids epidemic model with fractional order derivative is formulated to investigate the effect of human movement on the spread of hiv aids epidemic among patches we derive the basic reproduction number r 0 and prove that if r 0 1 the disease free equilibrium dfe is locally and globally asymptotically stable in the case of r 0 1 we obtain sufficient conditions under which the endemic equilibrium is unique and globally asymptotically stable we also formulate a fractional optimal control problem focp in which the state and co state equations are given in terms of the left fractional derivatives we incorporate into the model time dependent controls aimed at controlling the spread of hiv aids epidemic the necessary conditions for fractional optimal control of the disease are obtained the simulation of the model is done with two patches the numerical results show that implementing all the control efforts decreases significantly the number of hiv infected and aids people in both patches in addition the value of r c the control reproduction number for a long time is at its minimum level and the value of objective functional j u increases when the fractional derivative order is reduced from 1 0 8 1

when human walking becomes random walking fractal analysis and modeling of gait rhythm fluctuations abstract we present a random walk fractal analysis of the stride to stride fluctuations in the human gait rhythm the gait of healthy young adults is scale free with long range correlations extending over hundreds of strides this fractal scaling changes characteristically with maturation in children and older adults and becomes almost completely uncorrelated with certain neurologic diseases stochastic modeling of the gait rhythm dynamics based on transitions between different neural centers reproduces distinctive statistical properties of the gait pattern by tuning one model parameter the hopping transition range the model can describe alterations in gait dynamics from childhood to adulthood including a decrease in the correlation and volatility exponents with maturation

the bulk of the stock market correlation matrix is not pure noise abstract we analyse the structure of the distribution of eigenvalues of the stock market correlation matrix with increasing length of the time series representing the price changes we use 100 highly capitalized stocks from the american market and relate the result to the corresponding ensemble of wishart random matrices it turns out that systematically more eigenvalues remain beyond the borders prescribed by this variant of the random matrix theory rmt this may indicate that even the bulk of the spectrum of the stock market correlation matrix carries some sort of correlations that are masked by a measurement noise when the time series used to construct the matrix are short we also study some other characteristics of the noisy eigensignals like their return distributions temporal correlations or their multifractal spectra and the results support the above conclusions

general formulation for the numerical solution of optimal control problems a new improved computational method for a class of optimal control problems is presented the state and the costate adjoint variables are approximated using a set of basis functions a method similar to a variational virtual work approach with weighing coefficients is used to transform the canonical equations into a set of algebraic equations the method allows approximating functions that need not satisfy the initial conditions a priori a lagrange multiplier technique is used to enforce the terminal conditions this enlarges the space from which the approximating functions can be chosen orthogonal polynomials are used to obtain a set of simultaneous equations with fewer non zero entries such a sparse system results in substantial computational economy two examples a time invariant system and a time varying system with quadratic performance index are solved using three different sets of orthogonal polynomials and the power series to demonstrate the feasibility and efficiency of this method

research on the relationship between the multifractality and long memory of realized volatility in the sseci abstract we examine the multifractal properties of the realized volatility rv and realized bipower variation rbv series in the shanghai stock exchange composite index sseci by using the multifractal detrended fluctuation analysis mf dfa method we find that there exist distinct multifractal characteristics in the volatility series the contributions of two different types of source of multifractality namely fat tailed probability distributions and nonlinear temporal correlations are studied by using the unit root test we also find the strength of the multifractality of the volatility time series is insensitive to the sampling frequency but that the long memory of these series is sensitive

the non standard finite difference scheme for linear fractional pdes in fluid mechanics a non standard finite difference scheme is developed to solve the linear partial differential equations with time and space fractional derivatives the grunwald letnikov method is used to approximate the fractional derivatives numerical illustrations that include the linear inhomogeneous time fractional equation linear space fractional telegraph equation linear inhomogeneous fractional burgers equation and the fractional wave equation are investigated to show the pertinent features of the technique numerical results are presented graphically and reveal that the non standard finite difference scheme is very effective and convenient for solving linear partial differential equations of fractional order

mechanics with fractional derivatives lagrangian and hamiltonian mechanics can be formulated to include derivatives of fractional order f riewe phys rev 53 1890 1996 lagrangians with fractional derivatives lead directly to equations of motion with nonconservative classical forces such as friction the present work continues the development of fractional derivative mechanics by deriving a modified hamilton s principle introducing two types of canonical transformations and deriving the hamilton jacobi equation using generalized mechanics with fractional and higher order derivatives the method is illustrated with a frictional force proportional to velocity in contrast to conventional mechanics with integer order derivatives quantization of a fractional derivative hamiltonian cannot generally be achieved by the traditional replacement of momenta with coordinate derivatives instead a quantum mechanical wave equation is proposed that follows from the hamilton jacobi equation by application of the correspondence principle

the fractional finite hankel transform and its applications in fractal space in the present work a generalized finite hankel transform is derived which is useful in solving equations in fractal dimension df and involving a fractal diffusion coefficient d0r the corresponding inversion formula is established and some properties are given then the transform is successfully used to solve a class of time fractional diffusion equations in fractional spatial dimension with an absorbent term and schrodinger equation in fractional dimensional space green s functions and exact wave function of the above problems are found

analysis and optimal control of time varying linear systems via block pulse functions succinct and clear sighted operational properties of block pulse functions are fully applied to the analysis and optimal control of time varying linear systems with quadratic performance index piecewise constant solutions equally distributed which are simple in form and convenient for use or implementation are consequently obtained another advantage of this method is that any positive integer can be chosen as the number of sub intervals whereas in the case of walsh function approximation the choice can only be made from 2 4 8 16 32 and so on the algorithms developed in the paper are illustrated by appropriate examples

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

block pulse series analysis of linear systems incorporating observers the paper considers the analysis of linear systems incorporating observers via block pulse functions and presents recursive algorithms convenient for computers compared with walsh function approaches the results are much simpler in form an example is given to illustrate the use of the method

application of shifted chebyshev series to the optimal control of linear distributed parameter systems by use of a particular property of the shifted chebyshev series the optimal control of a distributed parameter system is simplified into the optimal control of a linear time invariant lumped parameter system next a directly computational formulation for evaluating the optimal control and trajectory of a linear distributed parameter system is developed the formulation is straightforward and convenient for digital computation an illustrative example is given to demonstrate the applicability of the proposed method

long range dependencies in heart rate signals revisited abstract the arguments are given that local exponents obtained in multifractal analysis by two methods wavelet transform modulus maxima wtmm and multifractal detrended fluctuation analysis mdfa allow to separate statistically hearts of healthy people and subjects suffering from reduced left ventricle systolic function nyha i iii class proposed indices of fractality suggest that a signal of human heart rate is a mixture of two processes monofractal and multifractal ones

on the linear quadratic regulator problem in one dimensional linear fractional stochastic systems in this paper for one dimensional stochastic linear fractional systems in terms of the riemann liouville fractional derivative the optimal control is derived it is assumed that the state is completely observable and all the information regarding this is available the formulation leads to a set of stochastic fractional forward and backward equation in the riemann liouville sense the proposed method has been checked via some numerical simulations which show the effectiveness of the fractional stochastic optimal algorithm

on lp solutions for a class of sequential fractional differential equations abstract under some simple conditions on the coefficient a t we establish that the initial value problem 0 d t x a t x 0 t 0 lim t 0 t 1 x t 0 has no solution in l p 1 r where p 1 p 1 p and 0 d t designates the riemann liouville derivative of order our result might be useful for developing a non integer variant of h weyl s limit circle limit point classification of differential equations

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

the thermodynamics of fractals revisited with wavelets abstract the multifractal formalism originally introduced to describe statistically the scaling properties of singular measures is revisited using the wavelet transform this new approach is based on the definition of partition functions from the wavelet transform modulus maxima we demonstrate that very much like thermodynamic functions the generalized fractal dimensions d q and the f singularity spectrum can be readily determined from the scaling behavior of these partition functions we show that this method provides a natural generalization of the classical box counting techniques to fractal signals the wavelets playing the role of generalized boxes we illustrate our theoretical considerations on pedagogical examples e g devil s staircases and fractional brownian motions we also report the results of some recent application of the wavelet transform modulus maxima method to fully developed turbulence data that we emphasize the wavelet transform as a mathematical microscope that can be further used to extract microscopic informations about the scaling properties of fractal objects in particular we show that a dynamical system which leaves invariant such an object can be uncovered form the space scale arrangement of its wavelet transform modulus maxima we elaborate on a wavelet based tree matching algorithm that provides a very promising tool for solving the inverse fractal problem this step towards a statistical mechanics of fractals is illustrated on discrete period doubling dynamical systems where the wavelet transform is shown to reveal the renormalization operation which is essential to the understanding of the universal properties of this transition to chaos finally we apply our technique to analyze the fractal hierarchy of dla azimuthal cantor sets defined by intersecting the inner frozen region of large mass off lattice diffusion limited aggregates dla wit a circle this study clearly lets out the existence of an underlying multiplicative process that is likely to account for the fibonacci structural ordering recently discovered in the apparently disordered arborescent dla morphology

application of chebyshev polynomials to the optimal control of time varying linear systems the operational matrix of backward integration for the shifted chebyshev polynomials is introduced in this study the general expression of the shifted chebyshev polynomial approximation for any two arbitrary functions is also presented a linear time varying optimal control system with a quadratic performance measure is solved by using the shifted chebyshev polynomials only a small number of chebyshev polynomials is needed to produce an excellent result and the outcome is much better than the solution obtained by using the block pulse function so computer memory capacity and computing time can be saved considerably

multifractals embedded in short time series an unbiased estimation of probability moment an exact estimation of probability moments is the base for several essential concepts such as the multifractals the tsallis entropy and the transfer entropy by means of approximation theory we propose a new method called factorial moment based estimation of probability moments theoretical prediction and computational results show that it can provide us an unbiased estimation of the probability moments of continuous order calculations on probability redistribution model verify that it can extract exactly multifractal behaviors from several hundred recordings its powerfulness in monitoring evolution of scaling behaviors is exemplified by two empirical cases i e the gait time series for fast normal and slow trials of a healthy volunteer and the closing price series for shanghai stock market by using short time series with several hundred lengths a comparison with the well established tools displays significant advantages of its performance over the other methods the factorial moment based estimation can evaluate correctly the scaling behaviors in a scale range about three generations wider than the multifractal detrended fluctuation analysis and the basic estimation the estimation of partition function given by the wavelet transform modulus maxima has unacceptable fluctuations besides the scaling invariance focused in the present paper the proposed factorial moment of continuous order can find its various uses such as finding nonextensive behaviors of a complex system and reconstructing the causality relationship network between elements of a complex system

multifractality in the stock market price increments versus waiting times abstract by applying the multifractal detrended fluctuation analysis to the high frequency tick by tick data from deutsche borse both in the price and in the time domains we investigate multifractal properties of the time series of logarithmic price increments and inter trade intervals of time we show that both quantities reveal multiscaling and that this result holds across different stocks the origin of the multifractal character of the corresponding dynamics is among others the long range correlations in price increments and in inter trade time intervals as well as the non gaussian distributions of the fluctuations since the transaction to transaction price increments do not strongly depend on or are almost independent of the inter trade waiting times both can be sources of the observed multifractal behaviour of the fixed delay returns and volatility the results presented also allow one to evaluate the applicability of the multifractal model of asset returns in the case of tick by tick data

asymptotic integration of 1 α order fractional differential equations we establish the long time asymptotic formula of solutions to the 1 a order fractional differential equation 0 io t 1 ax a t x 0 t 0 under some simple restrictions on the functional coefficient a t where 0 io t 1 a is one of the fractional differential operators 0d t a x 0d t ax 0d t 1 ax and 0d t a tx x here 0d t a designates the riemann liouville derivative of order a 0 1 the asymptotic formula reads as b o 1 x s m a l l c x l a r g e as t for given b c r where x s m a l l and x l a r g e represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation 0 io t 1 ax 0 t 0

multifractal detrended cross correlation analysis in the mena area abstract in this paper we investigated multifractal cross correlations qualitatively and quantitatively using a cross correlation test and the multifractal detrended cross correlation analysis method mf dcca for markets in the mena area we used cross correlation coefficients to measure the level of this correlation the analysis concerns four stock market indices of morocco tunisia egypt and jordan the countries chosen are signatory of the agadir agreement concerning the establishment of a free trade area comprising arab mediterranean countries we computed the bivariate generalized hurst exponent renyi exponent and spectrum of singularity for each pair of indices to measure quantitatively the cross correlations by analyzing the results we found the existence of multifractal cross correlations between all of these markets we compared the spectrum width of these indices we also found which pair of indices has a strong multifractal cross correlation

detrended fluctuation analysis of time series of a firing fusimotor neuron abstract we study the interspike intervals isi time series of the spontaneous fusimotor neuron activity by applying the detrended fluctuation analysis that is a modification of the random walk model analysis thus we have found evidence for the white noise characteristics of the isi time series which means that the fusimotor activity does not possess temporal correlations we conclude that such an activity represents the requisite noisy component for occurrence of the stochastic resonance mechanism in the neural coordination of muscle spindles

performance of multifractal detrended fluctuation analysis on short time series the performance of the multifractal detrended analysis on short time series is evaluated for synthetic samples of several mono and multifractal models the reconstruction of the generalized hurst exponents is used to determine the range of applicability of the method and the precision of its results as a function of the decreasing length of the series as an application the series of the daily exchange rate between the us dollar and the euro is studied sets with known fractal and multifractal behavior the results are applied to the analysis of the daily exchange rate between the us dollar and the euro this time se ries is relatively short around 3500 entries given that the euro currency debuted at the beginning of 1999 further more in its short life the euro has gone through a dubita tive start followed by a strong couple of years and since around 2008 it has been immersed in a crisis which has threatened its existence this turbulent history makes it interesting to ask if its dynamics have changed with time the paper is organized as follows in the next section the mfdfa method is briefly described and the notation used in the rest of the paper is introduced section iii presents the analysis of the mono and multifractal syn thetic data section iv discusses the application of the results to a time series from finance namely the daily ex change rate between the us dollar and the euro finally the conclusions of this work are presented in section v

a nagumo like uniqueness theorem for fractional differential equations we extend to fractional differential equations a recent generalization of the nagumo uniqueness theorem for ordinary differential equations of first order

quantifying sound field diffuseness in small rooms using multifractals with the aim of quantifying sound field uniformity in spaces of relatively low volume four different configurations in terms of acoustic treatment and sound field diffuseness were constructed and tested in a diffuse sound field reflections are not strongly correlated both to the original sound and to earlier reflections the degree of correlation is embedded in the impulse response structure but is not trivial to identify the room impulse responses exhibit self similarity and therefore may be treated as multifractal signals characterized by a singularity spectrum the singularity spectrum contains a wealth of information about the acoustic field established in the room the width of the singularity spectrum in particular is directly related to the complexity of the impulse response structure the uniformity of the sound field in the room can be evaluated by examining the variation of the singularity spectra with position a new definition for sound field diffuseness is given that is not based on the concept of the energy density the proposed method is simple to apply statistically robust and provides a measure of diffusion independent of the room reverberation

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

effect of linear and nonlinear filters on multifractal analysis in this paper we investigate how various linear and nonlinear transformations affect the multifractal properties of both artificial and traffic signals using the multifractal analysis based on partition function with comparison with the multifractal detrended fluctuation analysis specifically we study the effect of three types of transforms which are often encountered in physical and biological processes linear nonlinear polynomial and logarithmic filters we compare the multifractal scaling properties of signals before and after the transform it is shown that linear filters do not change the multifractal properties while the effect of nonlinear polynomial depends on the power of the polynomial filter in addition the maximum value of the multifractal spectrum remains almost unchanged after the logarithmic filter however we find that the width of the multifractal spectrum changes significantly even for much smaller value of the offset parameter

on the multifractal effects generated by monofractal signals we study quantitatively the level of false multifractal signal one may encounter while ana lyzing multifractal phenomena in time series within multifractal detrended fluctuation analysis mf dfa the investigated effect appears as a result of finite length of used data series and is additionally amplified by the long term memory the data eventually may contain we pro vide the detailed quantitative description of such apparent multifractal background signal as a threshold in spread of generalized hurst exponent valuesh or a threshold in the width of multifractal spectrum below which multifractal properties of the system are only apparent i e do not exist despite 6 0 orh 6 0 we find this effect quite important for shorter or persistent series and we argue it is linear with respect to autocorrelation exponent its strength decays according to power law with respect to the length of time series the influ ence of basic linear and nonlinear transformations applied to initial data in finite time series with various levels of long memory is also investigated this provides additional set of semi analytical results the obtained formulas are significant in any interdisciplinary application of multifractality including physics financial data analysis or physiology because they allow to separate the true multifractal phenomena from the apparent artificial multifractal effects they should be a helpful tool of the first choice to decide whether we do in particular case with the signal with real multiscaling properties or not

nonextensive statistical features of the polish stock market fluctuations the statistics of return distributions on various time scales constitutes one of the most informative characteristics of the financial dynamics here we present a systematic study of such characteristics for the polish stock market index wig20 over the period 04 01 1999 31 10 2005 for the time lags ranging from 1min1min up to 1 h this market is commonly classified as emerging still on the shortest time scales studied we find that the tails of the return distributions are consistent with the inverse cubic power law as identified previously for majority of the mature markets within the time scales studied a quick and considerable departure from this law towards a gaussian can however be traced interestingly all the forms of the distributions observed can be comprised by the single q gaussians which provide a satisfactory and at the same time compact representation of the distribution of return fluctuations over all magnitudes of their variation the corresponding nonextensivity parameter q was found to systematically decrease when increasing the time scales the temporal correlations quantified here in terms of multifractality provide further arguments in favor of nonextensivity

an approximate method for numerically solving fractional order optimal control problems of general form in this article we discuss fractional order optimal control problems focps and their solutions by means of rational approximation the methodology developed here allows us to solve a very large class of focps linear nonlinear time invariant time variant siso mimo state input constrained free terminal conditions etc by converting them into a general rational form of optimal control problem ocp the fractional differentiation operator used in the focp is approximated using oustaloup s approximation into a state space realization form the original problem is then reformulated to fit the definition used in general purpose optimal control problem ocp solvers such as riots 95 a solver created as a matlab toolbox illustrative examples from the literature are reproduced to demonstrate the effectiveness of the proposed methodology and a free final time ocp is also solved

critical scale invariance in a healthy human heart rate we demonstrate the robust scale invariance in the probability density function pdf of detrended healthy human heart rate increments which is preserved not only in a quiescent condition but also in a dynamic state where the mean level of the heart rate is dramatically changing this scale independent and fractal structure is markedly different from the scale dependent pdf evolution observed in a turbulentlike cascade heart rate model these results strongly support the view that a healthy human heart rate is controlled to converge continually to a critical state

hermite series approach to optimal control a general expression for the operational matrix of integration p in the case of hermite polynomials is derived the structure of p is simple and it is therefore computationally attractive using this p the optimal control with quadratic index problem and the singularly perturbed optimal control problem are studied some numerical examples are also included

multifractal characterization of gold market a multifractal detrended fluctuation analysis abstract the multifractal detrended fluctuation analysis technique is employed to analyze the time series of gold consumer price index cpi and the market trend of three world s highest gold consuming countries namely china india and turkey for the period 1993 july 2013 various multifractal variables such as the generalized hurst exponent the multifractal exponent and the singularity spectrum are calculated and the results are fitted to the generalized binomial multifractal gbm series that consists of only two parameters special emphasis is given to identify the possible source s of multifractality in these series our analysis shows that the cpi series and all three market series are of multifractal nature the origin of multifractality for the cpi time series and indian market series is found due to a long range time correlation whereas it is mostly due to the fat tailed probability distributions of the values for the chinese and turkey markets the gbm model series more or less describes all the time series analyzed here

multiscale aspects of cardiac control abstract we report some recent attempts to understand the dynamics of complex physiologic fluctuations by adapting and extending concepts and methods developed very recently in statistical physics we first review recent progress using wavelet based multifractal analysis magnitude and sign decomposition analysis and a new segmentation algorithm to quantify multiscale features of heartbeat interval series we then investigate how heartbeat dynamics change with circadian influences and under pathologic conditions and we discuss their possible relation to the underlaying cardiac control mechanisms the analytic tools we discuss may be used on a wider range of physiologic signals

efficiency and multifractality analysis of csi 300 based on multifractal detrending moving average algorithm abstract we apply the multifractal detrending moving average mfdma to investigate and compare the efficiency and multifractality of 5 min high frequency china securities index 300 csi 300 the results show that the csi 300 market becomes closer to weak form efficiency after the introduction of csi 300 future we find that the csi 300 is featured by multifractality and there are less complexity and risk after the csi 300 index future was introduced with the shuffling surrogating and removing extreme values procedures we unveil that extreme events and fat distribution are the main origin of multifractality besides we discuss the knotting phenomena in multifractality and find that the scaling range and the irregular fluctuations for large scales in the f q s vs s plot can cause a knot

multifractal detrended fluctuation analysis of sheep livestock prices in origin abstract the multifractal detrended fluctuation analysis mf dfa is used to verify whether or not the returns of time series of prices paid to farmers in original markets can be described by the multifractal approach by way of example 5 weekly time series of prices of different breeds slaughter weight and market differentiation from 2000 to 2012 are analyzed results obtained from the multifractal parameters and multifractal spectra show that the price series of livestock products are of a multifractal nature the hurst exponent shows that these time series are stationary signals some of which exhibit long memory merino milk fed in seville and segurena paschal in jaen short memory merino paschal in cordoba and segurena milk fed in jaen or even are close to an uncorrelated signals merino paschal in seville mf dfa is able to discern the different underlying dynamics that play an important role in different types of sheep livestock markets such as degree and source of multifractality in addition the main source of multifractality of these time series is due to the broadness of the probability function instead of the long range correlation properties between small and large fluctuations which play a clearly secondary role

robustness and perturbation in the modeled cascade heart rate variability in this study numerical experiments are conducted to examine the robustness of using cascade to describe the multifractal heart rate variability hrv by perturbing the hierarchical time scale structure and the multiplicative rule of the cascade it is shown that a rigid structure of the multiple time scales is not essential for the multifractal scaling in healthy hrv so long as there exists a tree structure for the multiplication to take place a multifractal hrv and related properties can be captured by using the cascade but the perturbation of the multiplicative rule can lead to a qualitative change in particular a multifractal to monofractal hrv transition can result after the product law is perturbed to an additive one at the fast time scale we suggest that this explains the similar hrv scaling transition in the parasympathetic nervous system blockade

thermodynamics of fractal signals based on wavelet analysis application to fully developed turbulence data and dna sequences we use the continuous wavelet transform to generalize the multifractal formalism to fractal functions we report the results of recent applications of the so called wavelet transform modulus maxima wtmm method to fully developed turbulence data and dna sequences we conclude by briey describing some works currently under progress which are likely to be the guidelines for future research c 1998 elsevier science b v all rights reserved

multifractal formalism for fractal signals the structure function approach versus the wavelet transform modulus maxima method several attempts have been made recently to generalize the multifractal formalism originally introduced for singular measures to fractal signals we report on a systematic comparison between the structure function approach pioneered by parisi and frisch in 2 proceedings of the international school on turbulence and predictability in geophysical fluid dynamics and climate dynamics edited by m ghil r benzi and g parisi north holland amsterdam 1985 p 84 to account for the multifractal nature of fully developed turbulent signals and an alternative method we have developed within the framework of the wavelet transform analysis we comment on the intrinsic limitations of the structure function approach this technique has fundamental drawbacks and does not provide a full characterization of the singularities of a signal in many cases we demonstrate that our method based on the wavelet transform modulus maxima representation works in most situations and is likely to be the ground of a unified multifractal description of self affine distributions our theoretical considerations are both illustrated on pedagogical examples and supported by numerical simulations

on the asymptotic integration of nonlinear differential equations the aim of the present paper is twofold firstly the paper surveys the literature concerning a specific topic in asymptotic integration theory of ordinary differential equations the class of second order equations with bihari like nonlinearity secondly some general existence results are established with regard to a condition that has been found recently to be of significant use in the theory of elliptic partial differential equations

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

using renyi parameter to improve the predictive power of singular value decomposition entropy on stock market abstract this paper generalizes the method of traditional singular value decomposition entropy by incorporating orders q of renyi entropy we analyze the predictive power of the entropy based on trajectory matrix using shanghai composite index and dow jones index data in both static test and dynamic test in the static test on sci results of global granger causality tests all turn out to be significant regardless of orders selected but this entropy fails to show much predictability in american stock market in the dynamic test we find that the predictive power can be significantly improved in sci by our generalized method but not in dji this suggests that noises and errors affect sci more frequently than dji in the end results obtained using different length of sliding window also corroborate this finding

low order variability diagrams for short range correlation evidence in financial data bgl usd exchange rate dow jones industrial average gold ounce price a method to sort out short range correlations and decorrelations in financial data is tested on three typical sets the bulgarian lev usa dollar bgl usd exchange rate the dow jones industrial average the gold ounce price the method makes use of the so called variability diagram technique three toys are used as models in order to understand features our findings indicate that some predictability can be found at short range time intervals c 1999 elsevier science b v all rights reserved

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

investigating detrended fluctuation analysis with structural breaks abstract detrended fluctuation analysis has been used in several fields of science to study the statistical properties of trend stationary and nonstationary time series its application to financial data has produced important results concerning long range correlations and long memory however these results may be contaminated if the researcher attributes to nonstationary trends the effect of stationary trends with endogenous structural breaks our paper proposes a modified dfa model where boxes to determine local trends are replaced by endogenous structural break windows we also allow local trends fitted by quadratic functions and use squared residuals in place of patchy standard deviations to study the magnitude of the power law exponent the results show that our modified dfa model performs better than the fixed length alternatives originally proposed and is therefore a suitable model to fit with financial data consistently with previous findings our results show positive long range correlation in all indices with the higher value for emerging markets

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

quantitative approach to multifractality induced by correlations and broad distribution of data abstract we analyze quantitatively the effect of spurious multifractality induced by the presence of fat tailed symmetric and asymmetric probability distributions of fluctuations in time series in the presented approach different kinds of symmetric and asymmetric broad probability distributions of synthetic data are examined starting from levy regime up to those with finite variance we use nonextensive tsallis statistics to construct all considered data in order to have good analytical description of frequencies of fluctuations in the whole range of their magnitude and simultaneously the full control over exponent of power law decay for tails of probability distribution the semi analytical compact formulas are then provided to express the level of spurious multifractality generated by the presence of fat tails in terms of tsallis parameter q and the scaling exponent of the asymptotic decay of cumulated probability density function cdf the results are presented in hurst and holder languages more often used in study of multifractal phenomena according to the provided semi analytical relations it is argued how one can make a clear quantitative distinction for any real data between true multifractality caused by the presence of nonlinear correlations spurious multifractality generated by fat tailed shape of distributions eventually with their asymmetry and the correction due to linear autocorrelations in analyzed time series of finite length in particular the spurious multifractal effect of fat tails is found basic for proper quantitative estimation of all spurious multifractal effects examples from stock market data are presented to support these findings

on shifted jacobi spectral approximations for solving fractional differential equations in this paper a new formula of caputo fractional order derivatives of shifted jacobi polynomials of any degree in terms of shifted jacobi polynomials themselves is proved we discuss a direct solution technique for linear multi order fractional differential equations fdes subject to nonhomogeneous initial conditions using a shifted jacobi tau approximation a quadrature shifted jacobi tau q sjt approximation is introduced for the solution of linear multi order fdes with variable coefficients we also propose a shifted jacobi collocation technique for solving nonlinear multi order fractional initial value problems the advantages of using the proposed techniques are discussed and we compare them with other existing methods we investigate some illustrative examples of fdes including linear and nonlinear terms we demonstrate the high accuracy and the efficiency of the proposed techniques

long term correlations and multifractal nature in the intertrade durations of a liquid chinese stock and its warrant abstract the intertrade duration of equities is an important financial measure characterizing trading activities it is defined as the waiting time between successive trades of an equity using the ultrahigh frequency data of a liquid chinese stock and its associated warrant we perform a comparative investigation of the statistical properties of their intertrade duration time series the distributions of the two equities can be better described by the shifted power law form than the weibull form and their scaled distributions do not collapse onto a single curve although the intertrade durations of the two equities have very different magnitude their intraday patterns exhibit very similar shapes both detrended fluctuation analysis dfa and detrending moving average analysis dma show that the 1 min intertrade duration time series of the two equities are strongly correlated in addition both multifractal detrended fluctuation analysis mfdfa and multifractal detrending moving average analysis mfdma unveil that the 1 min intertrade durations possess multifractal nature however the difference between the two singularity spectra of the two equities obtained from the mfdma is much smaller than that from the mfdfa

analysis and optimal control of time varying linear systems via shifted legendre polynomials this paper extends the application of shifted legendre polynomial expansion to time varying systems the extension is achieved through representing the product of two shifted legendre series in a new shifted legendre series with this treatment of the product of two time functions the operational properties of the shifted legendre polynomials are fully applied to the analysis and optimal control of time varying linear systems with quadratic performance index

on the solution set for a class of sequential fractional differential equations we establish here that under some simple restrictions on the functional coefficient a t the solution set of the fractional differential equation 0d tx a t x 0 splits between eventually small and eventually large solutions as t where 0d t designates the riemann liouville derivative of the order 0 1

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

economic fluctuations and anomalous diffusion we quantify the relation between trading activity measured by the number of transactions n deltat and the price change g deltat for a given stock over a time interval t t deltat to this end we analyze a database documenting every transaction for 1000 u s stocks for the two year period 1994 1995 we find that price movements are equivalent to a complex variant of classic diffusion where the diffusion constant fluctuates drastically in time we relate the analog for stock price fluctuations of the diffusion constant known in economics as the volatility to two microscopic quantities i the number of transactions n deltat in deltat which is the analog of the number of collisions and ii the variance w 2 deltat of the price changes for all transactions in deltat which is the analog of the local mean square displacement between collisions our results are consistent with the interpretation that the power law tails of p g deltat are due to p w deltat and the long range correlations in g deltat are due to n deltat

detection of early reflections using multifractals early reflections are not always strong and sparse enough on the timeline to be easily identified when reviewing the impulse response diagram this paper presents a method for the detection of early reflection in the room impulse response using multifractals the proposed method uses the distribution of holder s exponent calculated for the acoustic impulse response for early reflection detection the obtained results confirm the assumption that impulse response signals exhibit self similarity and that fractal theory can be used for the detection of early reflections

scaling and universality in heart rate variability distributions we find that a universal homogeneous scaling form describes the distribution of cardiac variations for a group of healthy subjects which is stable over a wide range of time scales however a similar scaling function does not exist for a group with a common cardiopulmonary instability associated with sleep apnea subtle differences in the distributions for the day and night phase dynamics for healthy subjects are detected