decomposition of matrices into 2 involutions abstract we consider the group slnf of all n by n matrices with determinant 1 over a field let res a denote rank a i for any a in slnf a matrix a is called a k involution if a2 i and res a k we prove that every matrix a in slnf is the product of at most res a 1 2 2 2 involutions for n 3 if char f 2 and for n 4 if char f 2

multifractal spectra of multi affine functions abstract self affine functions f x with multiscaling height correlations cq x xqhq are described in terms of the standard multifractal formalism with a modified assumption for the partition the corresponding quantities and expressions are shown to exhibit some characteristic differences from the standard ones according to our calculations the f type spectra are not uniquely determined by the hq spectrum but depend on the particular choice which is made for the dependence of n on x where n is the number of points over which the average is taken our results are expected to be relevant in the analysis of signal type data obtained in experiments on systems with an underlying multiplicative process

estimation in the pearson type 3 distribution although the pearson type 3 p3 is one of the basic models in statistical hydrology its use to model untransformed data has been restrained because of difficulties encountered in fitting this distribution by traditional methods in this paper an adaptive estimation procedure of mixed moments for the p3 family is introduced which is based on several fractional moments of the exponentially transformed data and the mean of the original data the procedure is easy to implement in small samples and is valid over the entire parameter space explicit formulae for the variances and covariances of parameter estimators and of the variance of the t year event are derived in addition two variants of the new procedure are compared with two versions of the method of moments and a version of the method of conditional moments via monte carlo simulation with samples generated from p3 populations it is found that one of the variants of the new procedure is the best overall method in estimating 100 year flood events and the other variant is best in estimating the median and 10 year low flow events the good performance of these two variants is also observed in samples generated from alternatives to p3 distributions a modification of the procedure is also introduced and investigated when a prior assumption of positive skewness is adopted

method for generating long range correlations for large systems we propose a new method to generate a sequence of random numbers with long range power law correlations that overcomes known difficulties associated with large systems the new method presents an improvement on the commonly used methods we apply the algorithm to generate enhanced diffusion isotropic and anisotropic self affine surfaces and isotropic and anisotropic correlated percolation

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

commutators and companion matrices over rings of stable rank 1 abstract we consider the group gl n a of all invertible n by n matrices over a ring a satisfying the first bass stable range condition we prove that every matrix is similar to the product of a lower and upper triangular matrix and that it is also the product of two matrices each similar to a companion matrix we use this to show that when n 3 and a is commutative every matrix in sl n a is the product of two commutators

products of commutators of dilatations abstract we consider the group sl n f of all n n matrices with determinant 1 over a field let res a denote rank a i for any a in gl n f a matrix a gl n f is called a dilatation if a is similar to a matrix i n 1 a a 1 we prove that if f 4 then every matrix a in sl n f is the product of at most res a 2 1 commutators of dilatations for n 2

confidence intervals for expected moments algorithm flood quantile estimates historical and paleoflood information can substantially improve flood frequency estimates if appropriate statistical procedures are properly applied however the federal guidelines for flood frequency analysis set forth in bulletin 17b rely on an inefficient weighting procedure that fails to take advantage of historical and paleoflood information this has led researchers to propose several more efficient alternatives including the expected moments algorithm ema which is attractive because it retains bulletin 17b s statistical structure method of moments with the log pearson type 3 distribution and thus can be easily integrated into flood analyses employing the rest of the bulletin 17b approach the practical utility of ema however has been limited because no closed form method has been available for quantifying the uncertainty of ema based flood quantile estimates this paper addresses that concern by providing analytical expressions for the asymptotic variance of ema flood quantile estimators and confidence intervals for flood quantile estimates monte carlo simulations demonstrate the properties of such confidence intervals for sites where a 25 to 100 year streamgage record is augmented by 50 to 150 years of historical information the experiments show that the confidence intervals though not exact should be acceptable for most purposes

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

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

volatility of linear and nonlinear time series previous studies indicated that nonlinear properties of gaussian distributed time series with long range correlations u i can be detected and quantified by studying the correlations in the magnitude series ensuremath mid u i ensuremath mid the volatility however the origin for this empirical observation still remains unclear and the exact relation between the correlations in u i and the correlations in ensuremath mid u i ensuremath mid is still unknown here we develop analytical relations between the scaling exponent of linear series u i and its magnitude series ensuremath mid u i ensuremath mid moreover we find that nonlinear time series exhibit stronger or the same correlations in the magnitude time series compared with linear time series with the same two point correlations based on these results we propose a simple model that generates multifractal time series by explicitly inserting long range correlations in the magnitude series the nonlinear multifractal time series is generated by multiplying a long range correlated time series that represents the magnitude series with uncorrelated time series that represents the sign series mathrm sgn u i we apply our techniques on daily deep ocean temperature records from the equatorial pacific the region of the el nin o phenomenon and find i long range correlations from several days to several years with 1 f power spectrum ii significant nonlinear behavior as expressed by long range correlations of the volatility series and iii broad multifractal spectrum

flood frequency analysis with systematic and historical or paleoflood data based on the two parameter general extreme value models historical and paleoflood data have become an important source of information for flood frequency analysis a number of studies have been proposed in the literature regarding the value of historical and paleoflood information for estimating flood quantiles these studies have been generally based on computer simulation experiments in this paper the value of using systematic and historical paleoflood data relative to using systematic records alone is examined analytically by comparing the asymptotic variances of flood quantiles assuming a two parameter general extreme value marginal distribution type 1 and type 2 censored data and maximum likelihood estimation method the results of this study indicate that the value of historical and paleoflood data for estimating flood quantiles can be small or large depending on only three factors the relative magnitudes of the length of the systematic record n and the length of the historical period m the return period t of the flood quantile of interest and the return period h of the threshold level of perception for instance for n 50 m 50 and t 500 the statistical gain for type 2 censoring becomes significantly larger than for type 1 censoring as h becomes greater than 100 years in addition computer experiments have shown that the results regarding the statistical gain based on asymptotic considerations are valid for the usual sample sizes

plotting positions for historical floods and their precision plotting positions are needed for situations where in addition to a systematically recorded annual flood series one would have a record of any large floods which occurred during an extended historical period if they occurred many of the published estimators are based on uncensored sampling theory which is not appropriate for such data sets here such historical and systematic flood records are viewed as resulting from a partially censored sampling experiment plotting positions are derived for such experiments using both classical and bayesian viewpoints in general it is impossible to construct highly accurate estimates of the exceedance probabilities of the largest floods using only their rank the number of observed historical floods and the lengths of the historical period and the systematic record for the largest flood the coefficient of variation of exceedance probability estimators is of the order of 1 as it is for complete systematic records examples illustrate the bias and precision of a variety of plotting position formulas the differences among the different plotting positions are generally small in comparison to the sampling variability however plotting positions which are unbiased with uncensored samples are often the most biased when used with a combination of historical and systematic data three appendices consider the effect of misspecification of the length of the historical period the effect of misspecification of the threshold of perception or observation level and plotting positions for situations with several perception thresholds

finite size effect and the components of multifractality in transport economics volatility based on multifractal detrending moving average method abstract analysis of freight rate volatility characteristics attracts more attention after year 2008 due to the effect of credit crunch and slowdown in marine transportation the multifractal detrended fluctuation analysis technique is employed to analyze the time series of baltic dry bulk freight rate index and the market trend of two bulk ship sizes namely capesize and panamax for the period march 1st 1999 february 26th 2015 in this paper the degree of the multifractality with different fluctuation sizes is calculated besides multifractal detrending moving average mf dma counting technique has been developed to quantify the components of multifractal spectrum with the finite size effect taken into consideration numerical results show that both capesize and panamax freight rate index time series are of multifractal nature the origin of multifractality for the bulk freight rate market series is found mostly due to nonlinear correlation

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

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

low flow analysis with a conditional weibull tail model estimates of low flow quantiles such as the 7 day 10 year low flow which are usually obtained by statistical modeling of observed data series are widely used in water quality management this paper presents a conditional modeling approach to low flow analysis that employs only those data values which are less than or equal to a ceiling value modeling in this fashion has been motivated by the observation that annual low flows may derive from mixed processes and by the subjective nature of graphical methods such as those employed by the u s geological survey which are often employed in such cases results of monte carlo experiments demonstrate that the conditional modeling approach yields a low flow quantile estimator whose bias and rmse are comparable to more conventional modeling approaches of fitting a classical textbook probability distribution on the basis of all observed data values even when the underlying population is of a well behaved form since the complex forms of mixed low flow data distributions are not capable of being represented by classical textbook distributions and since the conditional modeling approach performs comparably to those models even when the data derive from well behaved probability distributions these results imply that the conditional modeling approach is worthy of consideration for use by hydrologists the conditional modeling approach also leads rather naturally to a scheme much like that used in index flood methods whereby a regional low flow estimator might be devised an application of the conditional modeling approach to 48 low flow data series in alabama is presented

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

flood frequency analysis with historical and paleoflood information an investigation is made of flood quantile estimators which can employ historical and paleoflood information in flood frequency analyses two categories of historical information are considered censored data where the magnitudes of historical flood peaks are known and binomial data where only threshold exceedance information is available a monte carlo study employing the two parameter lognormal distribution shows that maximum likelihood estimators mles can extract the equivalent of an additional 10 30 years of gage record from a 50 year period of historical observation the mle routines are shown to be substantially better than an adjusted moment estimator similar to the one recommended in bulletin 17b of the united states water resources council hydrology committee 1982 the mle methods performed well even when floods were drawn from other than the assumed lognormal distribution

detecting long range correlations with detrended fluctuation analysis abstract we examine the detrended fluctuation analysis dfa which is a well established method for the detection of long range correlations in time series we show that deviations from scaling which appear at small time scales become stronger in higher orders of dfa and suggest a modified dfa method to remove them the improvement is necessary especially for short records that are affected by non stationarities furthermore we describe how crossovers in the correlation behavior can be detected reliably and determined quantitatively and show how several types of trends in the data affect the different orders of dfa

products of commutators of transvections over local rings abstract let r be a commutative local ring and m the maximal ideal of r we prove that if r m 3 then every matrix in sl n r n 2 is a product of at most n 2 2 commutators of transvections and the length res a 2 2 cannot be reduced for n 2

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

wavelet versus detrended fluctuation analysis of multifractal structures we perform a comparative study of applicability of the multifractal detrended fluctuation analysis mfdfa and the wavelet transform modulus maxima wtmm method in proper detecting of monofractal and multifractal character of data we quantify the performance of both methods by using different sorts of artificial signals generated according to a few well known exactly soluble mathematical models monofractal fractional brownian motion bifractal levy flights and different sorts of multifractal binomial cascades our results show that in the majority of situations in which one does not know a priori the fractal properties of a process choosing mfdfa should be recommended in particular wtmm gives biased outcomes for the fractional brownian motion with different values of hurst exponent indicating spurious multifractality in some cases wtmm can also give different results if one applies different wavelets we do not exclude using wtmm in real data analysis but it occurs that while one may apply mfdfa in a more automatic fashion wtmm must be applied with care in the second part of our work we perform an analogous analysis on empirical data coming from the american and from the german stock market for this data both methods detect rich multifractality in terms of broad f alpha but mfdfa suggests that this multifractality is poorer than in the case of wtmm

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 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

data driven detrending of nonstationary fractal time series with echo state networks abstract in this paper we propose a novel data driven approach for removing trends detrending from nonstationary fractal and multifractal time series we consider real valued time series relative to measurements of an underlying dynamical system that evolves through time we assume that such a dynamical process is predictable to a certain degree by means of a class of recurrent networks called echo state network esn which are capable to model a generic dynamical process in order to isolate the superimposed multi fractal component of interest we define a data driven filter by leveraging on the esn prediction capability to identify the trend component of a given input time series specifically the estimated trend is removed from the original time series and the residual signal is analyzed with the multifractal detrended fluctuation analysis procedure to verify the correctness of the detrending procedure in order to demonstrate the effectiveness of the proposed technique we consider several synthetic time series consisting of different types of trends and fractal noise components with known characteristics we also process a real world dataset the sunspot time series which is well known for its multifractal features and has recently gained attention in the complex systems field results demonstrate the validity and generality of the proposed detrending method based on esns

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

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

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

an algorithm for computing moments based flood quantile estimates when historical flood information is available this paper presents the expected moments algorithm ema a simple and efficient method for incorporating historical and paleoflood information into flood frequency studies ema can utilize three types of at site flood information systematic stream gage record information about the magnitude of historical floods and knowledge of the number of years in the historical period when no large flood occurred ema employs an iterative procedure to compute method of moments parameter estimates initial parameter estimates are calculated from systematic stream gage data these moments are then updated by including the measured historical peaks and the expected moments given the previously estimated parameters of the below threshold floods from the historical period the updated moments result in new parameter estimates and the last two steps are repeated until the algorithm converges monte carlo simulations compare ema bulletin 17b s united states water resources council 1982 historically weighted moments adjustment and maximum likelihood estimators when fitting the three parameters of the log pearson type iii distribution these simulations demonstrate that ema is more efficient than the bulletin 17b method and that it is nearly as efficient as maximum likelihood estimation mle the experiments also suggest that ema has two advantages over mle when dealing with the log pearson type iii distribution it appears that ema estimates always exist and that they are unique although neither result has been proven ema can be used with binomial or interval censored data and with any distributional family amenable to method of moments estimation

multifractal analysis of polyalanines time series abstract multifractal properties of the energy time series of short helix structures specifically from a polyalanine family are investigated through the mf dfa technique multifractal detrended fluctuation analysis estimates for the generalized hurst exponent h q and its associated multifractal exponents q are obtained for several series generated by numerical simulations of molecular dynamics in different systems from distinct initial conformations all simulations were performed using the gromos force field implemented in the program thor the main results have shown that all series exhibit multifractal behavior depending on the number of residues and temperature moreover the multifractal spectra reveal important aspects of the time evolution of the system and suggest that the nucleation process of the secondary structures during the visits on the energy hyper surface is an essential feature of the folding process

generalized hurst exponent and multifractal function of original and translated texts mapped into frequency and length time series a nonlinear dynamics approach can be used in order to quantify complexity in written texts as a first step a one dimensional system is examined two written texts by one author lewis carroll are considered together with one translation into an artificial language i e esperanto are mapped into time series their corresponding shuffled versions are used for obtaining a baseline two different one dimensional time series are used here one based on word lengths lts the other on word frequencies fts it is shown that the generalized hurst exponent h q and the derived f curves of the original and translated texts show marked differences the original texts are far from giving a parabolic f function in contrast to the shuffled texts moreover the esperanto text has more extreme values this suggests cascade model like with multiscale time asymmetric features as finally written texts a discussion of the difference and complementarity of mapping into a lts or fts is presented the fts f curves are more opened than the lts ones

the effects of observational correlated noises on multifractal detrended fluctuation analysis abstract we have numerically investigated the effects that observational correlated noises have on the generalized hurst exponents h q estimated by using the multifractal generalization of detrended fluctuation analysis mf dfa more precisely artificially generated stochastic binomial multifractals with increased amount of colored noises were analyzed via mf dfa it has been recently shown that for moderate additions of white noise the generalized hurst exponents are significantly underestimated for q 2 and they are nearly unchanged for q 2 j ludescher m i bogachev j w kantelhardt a y schumann a bunde on spurious and corrupted multifractality the effects of additive noise short term memory and periodic trends physica a 390 2011 2480 2490 in this paper we have found that h q with q 2 are also affected when correlated noises are considered this is due to the fact that the spurious correlations influence the scaling behaviors associated to large fluctuations the results obtained are significant for practical situations where noises with different correlations are inherently present