identification of systems containing linear dynamic and static nonlinear elements identification of nonlinear systems which can be represented by combinations of linear dynamic and static nonlinear elements are considered previous results by the authors based on correlation analysis are combined to provide a unified treatment for this class of systems it is shown that systems composed of cascade feedforward feedback and multiplicative connections of linear dynamic and zero memory nonlinear elements can be identified in terms of the individual component subsystems from measurements of the system input and output only

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

coupling detrended fluctuation analysis for analyzing coupled nonstationary signals when many variables are coupled to each other a single case study could not give us thorough and precise information when these time series are stationary different methods of random matrix analysis and complex networks can be used but in nonstationary cases the multifractal detrended cross correlation analysis mf dxa method was introduced for just two coupled time series in this article we have extended the mf dxa to the method of coupling detrended fluctuation analysis cdfa for the case when more than two series are correlated to each other here we have calculated the multifractal properties of the coupled time series and by comparing cdfa results of the original series with those of the shuffled and surrogate series we can estimate the source of multifractality and the extent to which our series are coupled to each other we illustrate the method by selected examples from air pollution and foreign exchange rates

lacunarity and multifractal analysis of the large dla mass distribution abstract we show the methodology used to analyze fractal and mass multifractal properties of very large diffusion limited aggregation dla clusters with a maximum of 10 9 particles for 2d aggregates and 10 8 particles for 3d clusters to support our main result the scaling behavior obtained by our experimental results corresponds to the expected performance of monofractal objects in order to estimate lacunarity measures for large dla clusters we develop a variant of the gliding box algorithm which reduces the computer time needed to obtain experimental results we show how our mass multifractal data have a tendency to present monofractal behavior for the mass distribution of the cases presented in this paper in the limit of very large clusters lacunarity analysis shows provided we study small clusters mass distributions data which might be interpreted as two different values of fractal dimensions while the cluster grows however this effect tends to vanish when the cluster size increases further in such a way that monofractality is achieved the outcomes of this paper lead us to conclude that the previously reported mass multifractality behavior vicsek et al 1990 13 detected for dla clusters is a consequence of finite size effects and floating point precision limitations and not an intrinsic feature of the phenomena since the scaling behavior of our dla clusters space corresponds to monofractal objects being this situation remarkably noticeable in the limit of very large clusters

a blind approach to hammerstein model identification this paper discusses the hammerstein model identification using a blind approach by fast sampling at the output it is shown that identification of the linear part can be achieved based only on the output measurements that makes the hammerstein model identification possible without knowing the structure of the nonlinearity and the internal variables

dynamical model and nonextensive statistical mechanics of a market index on large time windows the shape and tails of partial distribution functions pdf for a financial signal i e the s and the turbulent nature of the markets are linked through a model encompassing tsallis nonextensive statistics and leading to evolution equations of the langevin and fokker planck type a model originally proposed to describe the intermittent behavior of turbulent flows describes the behavior of normalized log returns for such a financial market index for small and large time windows and both for small and large log returns these turbulent market volatility of normalized log returns distributions can be sufficiently well fitted with a ensuremath chi 2 distribution the transition between the small time scale model of nonextensive intermittent process and the large scale gaussian extensive homogeneous fluctuation picture is found to be at ca a 200 day time lag the intermittency exponent ensuremath kappa in the framework of the kolmogorov log normal model is found to be related to the scaling exponent of the pdf moments thereby giving weight to the model the large value of ensuremath kappa points to a large number of cascades in the turbulent process the first kramers moyal coefficient in the fokker planck equation is almost equal to zero indicating no restoring force a comparison is made between normalized log returns and mere price increments

brief paper convergence of the iterative algorithm for a general hammerstein system identification the convergence of the iterative identification algorithm for a general hammerstein system has been an open problem for a long time in this paper it is shown that the convergence can be achieved by incorporating a regularization procedure on the nonlinearity in addition to a normalization step on the parameters

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

parametric and nonparametric identification of linear systems in the presence of nonlinear distortions a frequency domain approach this paper studies the asymptotic behavior of nonparametric and parametric frequency domain identification methods to model linear dynamic systems in the presence of nonlinear distortions under some general conditions for random multisine excitations in the first part a related linear dynamic system rlds approximation to the nonlinear system nls is defined and it is shown that the differences between the nls and the rlds can be modeled as stochastic variables with known properties in the second part a parametric model for the rlds is identified convergence in probability of this model to the rlds is proven a function of dependency is defined to detect and separate the presence of unmodeled dynamics and nonlinear distortions and to bound the bias error on the transfer function estimate

a discussion on embedding the black scholes option pricing model in a quantum physics setting abstract in this paper we consider the implications of embedding the black scholes option pricing model within a quantum physical setting the option price is considered to be a state function and a potential function is found which allows the option price to satisfy the schrodinger differential equation once this arbitrage free potential function is obtained we argue for the construction of a so called arbitrage potential function this functional is instrumental in determining the existence of a financial state function we show the existence of an arbitrage free price when the potential function converges to one the existence of arbitrage hinges on the non zero value of the planck constant this constant is then linked to a parameter which regulates the probability of occurence of strategy paths we call this parameter the belief parameter we argue that it is the belief parameter which may indeed proxy arbitrage the outcome of this paper shows that the black scholes model can be captured within a quantum physical setting and that the advantages of doing so may indeed provide for a first step to include arbitrage in a natural way in an otherwise arbitrage free model

statistical properties of deterministic threshold elements the case of market price abstract we analyze statistical properties of a set of deterministic threshold elements which is introduced as a model for the stock market the macroscopic variable of the stock market price shows seemingly stochastic fluctuation with a f 2 power spectrum consistent with real economic fluctuations the maximum lyapunov exponent is estimated to be zero indicating that the system is at the edge of chaos

a multifractal detrended fluctuation description of iranian rial us dollar exchange rate the miltifractal properties and scaling behaviour of the exchange rate variations of the iranian rial against the us dollar from a daily perspective is numerically investigated for this purpose the multifractal detrended fluctuation analysis mf dfa is used through multifractal analysis the scaling exponents generalized hurst exponents generalized fractal dimensions and singularity spectrum are derived moreover contribution of two major sources of multifractality that is fat tailed probability distributions and nonlinear temporal correlations are studied

identification of mimo hammerstein models using least squares support vector machines this paper studies a method for the identification of hammerstein models based on least squares support vector machines ls svms the technique allows for the determination of the memoryless static nonlinearity as well as the estimation of the model parameters of the dynamic arx part this is done by applying the equivalent of bai s overparameterization method for identification of hammerstein systems in an ls svm context the siso as well as the mimo identification cases are elaborated the technique can lead to significant improvements with respect to classical overparameterization methods as illustrated in a number of examples another important advantage is that no stringent assumptions on the nature of the nonlinearity need to be imposed except for a certain degree of smoothness

a logistic map approach to economic cycles i the best adapted companies abstract a birth death lattice gas model about the influence of an environment on the fitness and concentration evolution of economic entities is analytically examined the model can be mapped onto a high order logistic map the control parameter is a scalar business plan conditions are searched for growth and decay processes stable states upper and lower bounds bifurcations periodic and chaotic solutions the evolution equation of the economic population for the best fitted companies indicates microscopic conditions for cycling the evolution of a dynamic exponent is shown as a function of the business plan parameters

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

decoupling the linear and nonlinear parts in hammerstein model identification the main result of this paper is to show that the linear part can be made decoupled from the nonlinear part in hammerstein model identification therefore identification of the linear part for a hammerstein model becomes a linear problem and accordingly enjoys the same convergence and consistency results as if the unknown nonlinearity is absent

statistical properties of the yuan exchange rate index abstract we choice the yuan exchange rate index based on a basket of currencies as the effective exchange rate of the yuan and investigate the statistical properties of the yuan exchange rate index after china s exchange rate system reform on the 21st july 2005 after dividing the time series into two parts according to the change in the yuan exchange rate regime in july 2008 we compare the statistical properties of the yuan exchange rate index during these two periods we find that the distribution of the two return series has the exponential form we also perform the detrending moving average analysis dma and the multifractal detrending moving average analysis mfdma the two periods possess different degrees of long range correlations and the multifractal nature is also unveiled in these two time series significant difference is found in the scaling exponents q and singularity spectra f of the two periods obtained from the mfdma analysis besides in order to detect the sources of multifractality shuffling and phase randomization procedures are applied to destroy the long range temporal correlation and fat tailed distribution of the yuan exchange rate index respectively we find that the fat tailedness plays a critical role in the sources of multifractality in the first period while the long memory is the major cause in the second period the results suggest that the change in china s exchange rate regime in july 2008 gives rise to the different multifractal properties of the yuan exchange rate index in these two periods and thus has an effect on the effective exchange rate of the yuan after the exchange rate reform on the 21st july 2005

an optimal two stage identification algorithm for hammerstein wiener nonlinear systems abstract an optimal two stage identification algorithm is presented for hammerstein wiener systems where two static nonlinear elements surround a linear block the proposed algorithm consists of two steps the first one is the recursive least squares and the second one is the singular value decomposition of two matrices whose dimensions are fixed and do not increase as the number of the data point increases moreover the algorithm is shown to be convergent in the absence of noise and convergent with probability one in the presence of white noise

identification of non linear stochastic systems by state dependent parameter estimation the paper outlines how improved estimates of time variable parameters in models of stochastic dynamic systems can be obtained using recursive filtering and fixed interval smoothing techniques with the associated hyper parameters optimized by maximum likelihood based on prediction error decomposition it then shows how by exploiting special data re ordering and back fitting procedures similar recursive parameter estimation techniques can be utilized to estimate much more rapid state dependent parameter sdp variations in this manner it is possible to identify and estimate a widely applicable class of nonlinear stochastic systems as illustrated by several examples that include simulated and real data from chaotic processes finally the paper points out that such sdp models can form the basis for new methods of signal processing automatic control and state estimation for nonlinear stochastic systems

the infinite number of generalized dimensions of fractals and strange attractors abstract we show that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions dq q 0 to this aim we develop a rescaling transformation group which yields analytic expressions for all the quantities dq we prove that lim q 0 dq fractal dimension d limq 1dq information dimension and dq 2 correlation exponent v dq with other integer q s correspond to exponents associated with ternary quaternary and higher correlation functions we prove that generally dq dq for any q q for homogeneous fractals dq dq a particularly interesting dimension is dq for two examples feigenbaum attractor generalized baker s transformation we calculate the generalized dimensions and find that d is a non trivial number all the other generalized dimensions are bounded between the fractal dimension and d

multiscaling in multifractals multiscaling is shown to be a consequence of multifractality when a lower cutoff is introduced in calculations of correlation functions after a suitable rescaling the correlation function data for different values of seem to fall onto a single curve in the multiscaling regime however we show that there is not a unique functional form at varying but a spread very close to a single curve for each this curve can be computed analytically in terms of the f a spectrum which characterizes the multifractal part of this spectrum can thus be obtained by computing only one moment of the weights at 0

illusion of persistence in nba 1995 2018 regular season data abstract among the sports fans beliefs about hot hands and winning streaks are widely spread while the scientific debate about these effects is still ongoing recently in a paper by ferreira 2018 detrended fluctuation analysis was applied to the nba teams win records it was shown that 28 considered nba teams exhibit persistence in the win record time series in this paper we take the same data set and compare the obtained results against various random models we find that the empirical results are consistent with the results obtained from various simple random models

p exponent and p leaders part ii multifractal analysis relations to detrended fluctuation analysis multifractal analysis studies signals functions images or fields via the fluctuations of their local regularity along time or space which capture crucial features of their temporal spatial dynamics it has become a standard signal and image processing tool and is commonly used in numerous applications of different natures in its common formulation it relies on the h older exponent as a measure of local regularity which is by nature restricted to positive values and can hence be used for locally bounded functions only in this contribution it is proposed to replace the h older exponent with a collection of novel exponents for measuring local regularity the p exponents one of the major virtues of p exponents is that they can potentially take negative values the corresponding wavelet based multiscale quantities the p leaders are constructed and shown to permit the definition of a new multifractal formalism yielding an accurate practical estimation of the multifractal properties of real world data moreover theoretical and practical connections to and comparisons against another multifractal formalism referred to as multifractal detrended fluctuation analysis are achieved the performance of the proposed p leader multifractal formalism is studied and compared to previous formalisms using synthetic multifractal signals and images illustrating its theoretical and practical benefits the present contribution is complemented by a companion article studying in depth the theoretical properties of p exponents and the rich classification of local singularities it permits

dimensions and entropies of strange attractors from a fluctuating dynamics approach abstract it is shown that the fluctuations in the divergence of near by trajectories on strictly deterministic strange attractors can be modelled by stochastic concepts in particular we propose kramers moyal type equations for correlation functions between points on the attractor the drift terms are the lyapunov exponents the diffusion terms depend on the above fluctuations from this we obtain bounds on generalized dimensions and entropies numerical results show that in nearly all studied cases henon map zaslavskii map mackey glass eq the attractors are fractal measures in the sense of farmer information dimension hausdorff dimension metric entropy topological entropy

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

how to quantify deterministic and random influences on the statistics of the foreign exchange market it is shown that price changes of the u s dollar german mark exchange rates upon different delay times can be regarded as a stochastic marcovian process furthermore we show how kramers moyal coefficients can be estimated from the empirical data finally we present an explicit fokker planck equation which models very precisely the empirical probability distributions in particular their non gaussian heavy tails

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

hammerstein system identification through best linear approximation inversion and regularisation abstracthammerstein systems are composed by the cascading of a static nonlinearity and a linear system in this paper a methodology for identifying such systems using a combination of least squares support vector machines ls svm and best linear approximation bla techniques is proposed to do this a novel method for estimating the intermediate variable is presented allowing a clear separation of the identification steps first an approximation to the linear block is obtained through the bla of the system then an approximation to the intermediate variable is obtained using the inversion of the estimated linear block and the known output afterwards a nonlinear model is calculated through ls svm using the estimated intermediate variable and the known input to do this the regularisation capabilities of ls svm play a crucial role finally a parametric re estimation of the linear block is made the method was tested in three examples two of them with hard nonlinearities and was compared with four

price volume multifractal analysis and its application in chinese stock markets abstract an empirical research on chinese stock markets is conducted using statistical tools first the multifractality of stock price return series r i r i ln p t 1 ln p t and trading volume variation series v i v i ln v t 1 ln v t is confirmed using multifractal detrended fluctuation analysis furthermore a multifractal detrended cross correlation analysis between stock price return and trading volume variation in chinese stock markets is also conducted it is shown that the cross relationship between them is also found to be multifractal second the cross correlation between stock price p i and trading volume v i is empirically studied using cross correlation function and detrended cross correlation analysis it is found that both shanghai stock market and shenzhen stock market show pronounced long range cross correlations between stock price and trading volume third a composite index r based on price and trading volume is introduced compared with stock price return series r i and trading volume variation series v i r variation series not only remain the characteristics of original series but also demonstrate the relative correlation between stock price and trading volume finally we analyze the multifractal characteristics of r variation series before and after three financial events in china namely price limits reform of non tradable shares and financial crisis in 2008 in the whole period of sample to study the changes of stock market fluctuation and financial risk it is found that the empirical results verified the validity of r

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

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

feature of topological properties in an earthquake network abstract earthquake network is investigated by considering the volume resolution and the temporal causality we perform the numerical computations for network metrics from seismic time series data taken in japan for our case we mainly treat the feature of the topological properties via various statistical quantities such as the characteristic path length the average clustering coefficient the small worldness the cost efficiency the global efficiency the modularity and the assortativity the universal and irregular properties of statistical quantities in earthquake network do not find unambiguously but it may be inferred that these topological properties improve by implementing the method and its technique from registered data of earthquake networks

frequency domain identification of hammerstein models discusses hammerstein model identification in the frequency domain using sampled input output data by exploring the fundamental frequency and harmonics generated by the unknown nonlinearity we propose a frequency domain approach and show its convergence for both the linear and nonlinear subsystems in the presence of noise no a priori knowledge of the structure of the nonlinearity is required and the linear part can be nonparametric

testing for the source of multifractality in water level records abstract the multifractality in hydrologic data has been studied in many literatures but few literatures focus on its source which is helpful for understanding the underlying mechanisms that generate hydrologic data we propose a hypothesis testing procedure for the source of multifractality in water level records based on the empirical distributions of generalized hurst exponent estimated from a set of shuffled or surrogate series the proposed hypothesis testing procedure can show more details about the source of multifractality than previous methods with some statistics especially about the effects of large and small fluctuations on multifractality the generalized hurst exponents are estimated via multifractal detrended fluctuation analysis the data set contains about two million high frequency water level records of a northern china river at its 10 observation stations the testing results show that the multifractality in water levels is mainly caused by nonlinear correlations in small fluctuations and linear correlations in small and large fluctuations and is also related to the probability distribution of small fluctuations this conclusion is validated via some constructed semi surrogate series and values of statistics for source testing

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

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

multifractal detrended fluctuation analysis of derivative and spot markets abstract we investigate the multifractal properties of price increments in the cases of derivative and spot markets through the multifractal detrended fluctuation analysis we estimate the generalized hurst and the renyi exponents for price fluctuations by deriving the singularity spectrum from the above exponents we quantify the multifractality of a financial time series and compare the multifractal properties of two different markets the different behavior of each agent group in transactions is also discussed in order to identify the nature of the underlying multifractality we apply the method of surrogate data to both sets of financial data it is shown that multifractality due to a fat tailed distribution is significant

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

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

identification of hammerstein systems without explicit parameterisation of non linearity this article proposes a new approach to identification of hammerstein systems where a non linearity precedes a linear dynamic system driven by piece wise constant inputs the proposed approach does not require an explicit parameterisation of the non linearity moreover the non linearity does not have to be static but could be the one with finite memories like backlash by exploiting input s piecewise constant property the denominator of the linear system described by an arx model is consistently identified from the information of the output only next a subspace direct equalisation method estimates the unmeasurable inner signal based on the resulted denominator estimate and output measurements contrary to the existing blind approaches the numerator of the linear system is not required which leads to a significant improvement of removing an error propagation on the basis of the estimated inner signal the measured input and output the non linearity and linear system are obtained separately the

a reactive lattice gas approach to economic cycles abstract a microscopic approach to macroeconomic features is intended a model for macroeconomic behavior under heterogeneous spatial economic conditions is reviewed a birth death lattice gas model taking into account the influence of an economic environment on the fitness and concentration evolution of economic entities is numerically and analytically examined the reaction diffusion model can also be mapped onto a high order logistic map the role of the selection pressure along various dynamics with entity diffusion on a square symmetry lattice has been studied by monte carlo simulation the model leads to a sort of phase transition for the fitness gap as a function of the selection pressure and to cycles the control parameter is a scalar business plan the business plan s allows for spin offs or merging and enterprise survival evolution law s whence bifurcations cycles and chaotic behavior