detrended fluctuation analysis made flexible to detect range of cross correlated fluctuations the detrended cross correlation coefficient dcca has recently been proposed to quantify the strength of cross correlations on different temporal scales in bivariate nonstationary time series it is based on the detrended cross correlation and detrended fluctuation analyses dcca and dfa respectively and can be viewed as an analog of the pearson coefficient in the case of the fluctuation analysis the coefficient dcca works well in many practical situations but by construction its applicability is limited to detection of whether two signals are generally cross correlated without the possibility to obtain information on the amplitude of fluctuations that are responsible for those cross correlations in order to introduce some related flexibility here we propose an extension of dcca that exploits the multifractal versions of dfa and dcca multifractal detrended fluctuation analysis and multifractal detrended cross correlation analysis respectively the resulting new coefficient q not only is able to quantify the strength of correlations but also allows one to identify the range of detrended fluctuation amplitudes that are correlated in two signals under study we show how the coefficient q works in practical situations by applying it to stochastic time series representing processes with long memory autoregressive and multiplicative ones such processes are often used to model signals recorded from complex systems and complex physical phenomena like turbulence so we are convinced that this new measure can successfully be applied in time series analysis in particular we present an example of such application to highly complex empirical data from financial markets the present formulation can straightforwardly be extended to multivariate data in terms of the q dependent counterpart of the correlation matrices and then to the network representation

calculation of cfie impedance matrix elements with rwg and n spl times rwg functions the method of moments mom solution of combined field integral equation cfie for electromagnetic scattering problems requires calculation of singular double surface integrals when galerkin s method with triangular vector basis functions rao wilton glisson functions and the cfie are applied to solve electromagnetic scattering by a dielectric object both rwg and n spl times rwg functions n is normal unit vector should be considered as testing functions robust and accurate methods based on the singularity extraction technique are presented to evaluate the impedance matrix elements of the cfie with these basis and test functions in computing the impedance matrix elements including the gradient of the green s function we can avoid the logarithmic singularity on the outer testing integral by modifying the integrand in the developed method all singularities are extracted and calculated in closed form and numerical integration is applied only for regular functions in addition we present compact iterative formulas for computing the extracted terms in closed form by these formulas we can extract any number of terms from the singular kernels of cfie formulations with rwg and n spl times rwg functions

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

a new spatial interpolation algorithm to reduce the matrix fill time in the method of moments analysis of planar microstrip structures a new spatial interpolation scheme is proposed to reduce the matrix fill time in the method of moments implementation of planar microstrip structures the approach is based on the division of the distance between the basis and the testing functions into three namely near intermediate and far regions the matrix entries in the near region are computed directly the entries corresponding to both intermediate and far regions are evaluated in two steps 1 choosing an adequate number of sampling points in these regions and computing the associated entries directly and 2 interpolating the remaining entries by using cubic spline or bicubic spline algorithms to demonstrate the efficiency and accuracy the technique is applied to a planar microstrip low pass filter and a microstrip line fed patch antenna problems it is shown that the interpolation scheme can result in significant savings with high accuracy

fast periodic interpolation method for periodic unit cell problems a fast periodic interpolation method fpim is presented for rapidly computing fields in a unit cell of an infinitely periodic array for low and moderate frequencies for unit cells smaller than or on the order of the wavelength the fpim has the computational cost of o n and it requires only o 1 periodic green s function pgf evaluations for n sources and observers for higher mixed frequencies the computational cost scales as o d 3 log d n where d is the domain size within the unit cell and is the wavelength fpim is based on splitting the field into the near field from the sources around the unit cell and the far field from the remaining sources the near field component can be evaluated rapidly using any available fast method the far field component is computed by tabulating the pgf at sparse source and observer grids using this table to calculate the field at the observation grid and interpolating from the observation grid to the actual observers the fpim is kernel independent and allows using any method for evaluating the pgf including simple floquet expansions the computational times can be comparable to those of conventional non periodic n body electromagnetic problems the presented method can be used to accelerate integral equations for periodic unit cell problems with many applications in microwave engineering and optics

efficient calculation of the green s function for multilayered planar periodic structures an efficient calculation scheme is presented for the periodic green s function in planar multilayered structures the proposed method is based on the static complex image conversion and the ewald sum technique and it converts the slowly convergent green s function into the sum of two rapidly convergent series

efficient computation of 1 d periodic layered mixed potentials for the analysis of leaky wave antennas with vertical elements an efficient mixed potential integral equation formulation is proposed for the analysis of one dimensional 1 d periodic leaky wave antennas lwas based on planar stratified configurations with inclusions of arbitrarily oriented metallic or dielectric perturbations both the transverse and vertical components of the mixed potential green s functions due to a 1 d phased array of dipoles in a layered medium are accelerated using suitable homogeneous medium asymptotic extractions from the standard spectral series of floquet harmonics a novel acceleration procedure is applied for the computation of the vertical potentials whose extracted terms can be expressed as potentials from a 1 d phased array of half line sources in a homogeneous medium their numerical calculation requires a suitable modification of the ewald method thus resulting in new modified spectral and spatial series having gaussian convergence even in the case of complex modes and improper harmonics numerical comparisons for the 1 d periodic potentials both in the case of bounded and unbounded e g leaky harmonics validate the efficiency and accuracy of the proposed acceleration technique the method is illustrated and verified by determining the dispersion behavior of both bound and leaky modes for several lwa test cases

multifractal detrended cross correlation analysis for two nonstationary signals we propose a method called multifractal detrended cross correlation analysis to investigate the multifractal behaviors in the power law cross correlations between two time series or higher dimensional quantities recorded simultaneously which can be applied to diverse complex systems such as turbulence finance ecology physiology geophysics and so on the method is validated with cross correlated one and two dimensional binomial measures and multifractal random walks as an example we illustrate the method by analyzing two financial time series

efficient computation of the 2 d green s function for 1 d periodic structures using the ewald method the ewald method is applied to accelerate the evaluation of the green s function of an infinite periodic phased array of line sources the ewald representation for a cylindrical wave is obtained from the known representation for the spherical wave and a systematic general procedure is applied to extend previous results only a few terms are needed to evaluate ewald sums which are cast in terms of error functions and exponential integrals to high accuracy singularities and convergence rates are analyzed and a recipe for selecting the ewald splitting parameter spl epsiv is given to handle both low and high frequency ranges indeed it is shown analytically that the choice of the standard optimal splitting parameter spl epsiv sub 0 will cause overflow errors at high frequencies numerical examples illustrate the results and the sensitivity of the ewald representation to the splitting parameter spl epsiv

efficient computation of the 3d green s function for the helmholtz operator for a linear array of point sources using the ewald method the ewald method is applied to accelerate the evaluation of the green s function gf of an infinite equispaced linear array of point sources with linear phasing only a few terms are needed to evaluate ewald sums which are cast in terms of error functions and exponential integrals to high accuracy it is shown analytically that the choice of the standard optimal ewald splitting parameter e0 causes overflow errors at high frequencies period large compared to the wavelength and convergence rates are analyzed a recipe for selecting the ewald splitting parameter is provided

accelerated macro basis functions analysis of finite printed antenna arrays through 2d and 3d multipole expansions an efficient technique is presented for the analysis of finite printed antenna arrays made of identical elements it is based on a closed form expression for the spatial domain green s function gf given as a finite sum of cylindrical waves obtained through rational function fitting plus one spherical wave from there a multipole expansion can be obtained for planar layered medium gfs the macro basis function mbf technique is applied to the method of moments mom solution of a mixed potential integral equation this reduces the size of the mom impedance matrix and allows for a direct solution however the evaluation of the entries of this reduced matrix becomes the dominant contribution to the total computation time the aforementioned multipole expansion is exploited to provide a fast construction of the reduced mom matrix whose elements are the reaction integrals between the mbfs considered to characterize the currents on the array element the complexity of evaluating the interactions between mbfs is found to be dominated by the calculations related to the spherical wave term thus taking into account the layered medium does not increase the order of the complexity with respect to a multipole accelerated computation of reaction integrals in a homogeneous medium

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

detrended cross correlation analysis consistently extended to multifractality we propose an algorithm multifractal cross correlation analysis mfcca which constitutes a consistent extension of the detrended cross correlation analysis and is able to properly identify and quantify subtle characteristics of multifractal cross correlations between two time series our motivation for introducing this algorithm is that the already existing methods like multifractal extension have at best serious limitations for most of the signals describing complex natural processes and often indicate multifractal cross correlations when there are none the principal component of the present extension is proper incorporation of the sign of fluctuations to their generalized moments furthermore we present a broad analysis of the model fractal stochastic processes as well as of the real world signals and show that mfcca is a robust and selective tool at the same time and therefore allows for a reliable quantification of the cross correlative structure of analyzed processes in particular it allows one to identify the boundaries of the multifractal scaling and to analyze a relation between the generalized hurst exponent and the multifractal scaling parameter ensuremath lambda q this relation provides information about the character of potential multifractality in cross correlations and thus enables a deeper insight into dynamics of the analyzed processes than allowed by any other related method available so far by using examples of time series from the stock market we show that financial fluctuations typically cross correlate multifractally only for relatively large fluctuations whereas small fluctuations remain mutually independent even at maximum of such cross correlations finally we indicate possible utility of mfcca to study effects of the time lagged cross correlations

semantics of dyadic and mixed potential field representation for 3 d current distributions in planar stratified media the full spectral electric dyadic green s function for three dimensional current distributions in planar stratified media can be obtained straight from maxwell s equations by following a physical reasoning analogous with the free space case but using general derivative relations for multilayered green s functions we derive a basic mixed potential form with a simple vector potential kernel but multiple scalar potential kernels and also obtain the well established single scalar potential formulations with a dyadic vector potential kernel mixed potential forms are thus arrived at without the a priori introduction of scalar and vector potential or choice of gauge condition the nonuniqueness of the scalar potential kernel and the dyadic nature of the scalar and or vector potentials are believed to be clarified by the proposed approach a discussion of the different formulations focuses on physical meaning and numerical consequences for the solution of integral equations

nonlinearity estimation in hammerstein systems based on ordered observations the nonlinear subsystem of a hammerstein system is identified i e its characteristic is recovered from input output ohservations of the whole system the input and disturbance are white stochastic processes the identified characteristic satisfies a piecewise lipschitz condition only algorithms presented in the paper are calculated from ordered input output observations i e from pairs of observations arranged in a sequence in which input measurements increase in value the mean integrated square error converges to zero as the number of observations tends to infinity convergence rates are insensitive to the shape of the probability density of the input signal results of numerical simulation are also shown

self affine fractals embedded in spectra of complex networks the scaling properties of spectra of real world complex networks are studied by using the wavelet transform it is found that the spectra of networks are multifractal according to the values of the long range correlation exponent the hust exponent h the networks can be classified into three types namely h 0 5 h 0 5 and h 0 5 all real world networks considered belong to the class of h 0 5 which may be explained by the hierarchical properties

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

accelerating the convergence of series representing the free space periodic green s function a method for improving the convergence of the series representing the doubly periodic free space green s function is presented the method consists of successively applying three different transformations to the green s function spectral representation kummer s transformation is first applied to convert the slowly converging spectral representation into the sum of a rapidly converging series and a slowly converging series the latter series is recognized as the spectral representation of the original periodic source distribution radiating in a medium with an imaginary wavenumber application of the poisson transformation to this series renders it exponentially convergent since it effectively represents propagation of point source contributions through a medium with imaginary wavenumber finally shanks transform is plotted versus the number of terms taken in the series numerical results confirm that an improvement in the convergence rate of the series is achieved for a particular convergence criterion

efficient computation of the 2d periodic green s function using the ewald method an efficient computation of the periodic helmholtz green s function for a 2d array of point sources using the ewald method is presented limitations on the numerical accuracy when using the optimum e parameter which gives optimum asymptotic convergence at high frequency are discussed a best e parameter is then derived to overcome these limitations which allows for the fastest convergence while maintaining a specific level of accuracy loss of significant figures in the final result the actual loss of significant figures has been verified through numerical simulations formulas for the number of terms needed for convergence have also been derived for both the spectral and the spatial series that appear in the ewald method and are found to be accurate in almost all cases

acceleration of mixed potentials from vertical currents in layered media for 2 d structures with 1 d periodicity an original acceleration procedure is proposed for the efficient calculation of the vertical components of the dyadic and scalar mixed potential layered media periodic green s functions the extraction of suitable asymptotic terms i e quasi static images is performed in order to speed up the convergence of the relevant spectral series this procedure well known for planar green s functions is here generalized to treat the off diagonal dyadic components and the corrective scalar potential arising from the vertical currents the extracted terms are homogeneous medium green s functions due to a periodic phased array of half plane currents computed through a modified ewald method leading to a pair of gaussian convergent series the highly improved convergence rate of the relevant series is shown and the reduction of the computation time is numerically tested and discussed the algorithm is implemented in eiger an open source code based on the method of moments several periodic structures are analyzed and fully validated through numerical comparisons the proposed formulation has been proven very efficient accurate and stable

interpolation of ewald accelerated periodic green s function representations for homogeneous or layered media a method is explored and developed for significantly accelerating the computation of the ewald series representation for periodic homogeneous media green s functions the method involves extracting corner singularity terms from the corners of the unit cell resulting in a smooth regularized green s function that is amenable to interpolation the approach can be used to accelerate layered media problems where application of kummer s method splits the spectral floquet modal series representation into a rapidly converging difference series that is regular plus a residual series that contains any spatial singularities present the residual series corresponds to a homogeneous medium and can thus be treated with the method proposed here

quasi 3 d mixed potential integral equation formulation for periodic structures this paper introduces the use of the quasi 3 d mixed potential integral equation formulation for structures with a periodicity in two dimensions the quasi 3 d formulation allows to use both horizontal and vertical conductors and dielectric inclusions the key innovation is the use of an effective algorithm to calculate periodic green s functions pgfs for vertical currents in the planar multilayered background medium this algorithm retains the same scheme as for a single source green s function gf in both cases the gfs are calculated via an inverse fourier transform of the gfs in the spectral domain which are known in closed form in order to remedy the poor convergence for small source observation distances an asymptotic extraction is used yielding a very compact algorithm and acceleration techniques are applied simple guidelines are proposed to construct asymptotes having the required leading terms and a good convergence it is shown that many acceleration algorithms widely used in literature are actually able to perform well only in specific circumstances as far as the authors can see there is still no general and robust technique yielding highly accurate results under all circumstances several examples illustrate the efficiency of the technique

stochastic dynamical model for stock stock correlations we propose a model of coupled random walks for stock stock correlations the walks in the model are coupled via a mechanism that the displacement price change of each walk stock is activated by the price gradients over some underlying network we assume that the network has two underlying structures describing the correlations among the stocks of the whole market and among those within individual groups respectively each with a coupling parameter controlling the degree of correlation the model provides the interpretation of the features displayed in the distribution of the eigenvalues for the correlation matrix of real market on the level of time sequences we verify that such modeling indeed gives good fitting for the market data of us stocks

multilayered media green s functions in integral equation formulations a compact representation is given of the electric and magnetic type dyadic green s functions for plane stratified multilayered uniaxial media based on the transmission line network analog along the aids normal to the stratification furthermore mixed potential integral equations are derived within the framework of this transmission line formalism for arbitrarily shaped conducting or penetrable objects embedded in the multilayered medium the development emphasizes laterally unbounded environments but an extension to the case of a medium enclosed by a rectangular shield is also included

fast and accurate mom analysis of periodic arrays of multilayered stacked rectangular patches with application to the design of reflectarray antennas the scattering of plane waves by periodic arrays of stacked rectangular patches in multilayered substrates is a problem that has to be solved many times when designing reflectarray antennas made of those patches under the local periodicity assumption the solution to the periodic multilayered problem has been traditionally carried out by means of the galerkin s version of the method of moments mom in the spectral domain this approach involves the computation of double infinite summations and whereas some of these summations converge very fast some other converge very slowly in this paper the slowly convergent summations are computed by making use of an enhanced mixed potential integral equation mpie formulation of the mom in the spatial domain this enhanced formulation is based on the interpolation of the multilayered periodic green s functions and on the efficient computation of the four dimensional 4 d integrals leading to the mom matrix entries both the novel hybrid spectral spatial mom code and the standard spectral domain mom code have been used for the design of a contoured beam reflectarray antenna it has been verified that the spectral spatial mom code requires cpu times that are typically 30 times smaller than those required by the pure spectral domain mom code

complexity and multifractal behaviors of multiscale continuum percolation financial system for chinese stock markets abstract a new financial agent based time series model is developed and investigated by multiscale continuum percolation system which can be viewed as an extended version of continuum percolation system in this financial model for different parameters of proportion and density two poisson point processes where the radii of points represent the ability of receiving or transmitting information among investors are applied to model a random stock price process in an attempt to investigate the fluctuation dynamics of the financial market to validate its effectiveness and rationality we compare the statistical behaviors and the multifractal behaviors of the simulated data derived from the proposed model with those of the real stock markets further the multiscale sample entropy analysis is employed to study the complexity of the returns and the cross sample entropy analysis is applied to measure the degree of asynchrony of return autocorrelation time series the empirical results indicate that the proposed financial model can simulate and reproduce some significant characteristics of the real stock markets to a certain extent

scattering and radiation from by 1 d periodic metallizations residing in layered media an efficient technique is proposed to compute the scattering or radiation from by 1 d periodic structures residing in a layered background medium the technique is based on a mixed potential integral equation mpie combined with the method of moments mom solving for the unknown current density flowing within a unit cell of the periodic structure the formalism requires the knowledge of the pertinent layered medium green s functions with 1 d periodicity here these green s functions are derived in closed form by invoking the perfectly matched layer pml paradigm the stationary phase method is applied to determine the far field of the infinite periodic structure leading to a series of floquet modes in addition approximating this series leads to an efficient technique to estimate the scattering or radiation from by large but finite periodic structures with a 1 d periodic character the theory is illustrated and validated by means of various examples stemming from scattering and radiation applications from by antenna arrays residing on microstrip substrates the efficiency of the method is also demonstrated

enhanced mom analysis of the scattering by periodic strip gratings in multilayered substrates the method of moments mom is applied to the analysis of the scattering of a multilayered periodic strip grating by a plane wave with oblique incidence and arbitrary polarization although this problem has been traditionally solved by means of the mom in the spectral domain this is an approach which leads to the computation of slowly convergent infinite summations in this paper the problem is solved by means of the mixed potential integral equation mpie formulation of the mom in the spatial domain while applying the mom in the spatial domain two improvements are introduced which lead to important cpu time savings first the multilayered periodic green s functions are accurately interpolated in terms of chebyshev polynomials second half the integrals involved in the computation of the mom matrix entries are obtained in closed form as a consequence of these two improvements the spatial domain version of the mom presented in this paper turns out to be between one and two orders of magnitude faster than the conventional spectral domain version when basis functions that account for edge singularities are used in the modeling of the current density on the metallizations

multifractal detrending moving average cross correlation analysis there are a number of situations in which several signals are simultaneously recorded in complex systems which exhibit long term power law cross correlations the multifractal detrended cross correlation analysis mfdcca approaches can be used to quantify such cross correlations such as the mfdcca based on the detrended fluctuation analysis mfxdfa method we develop in this work a class of mfdcca algorithms based on the detrending moving average analysis called mfxdma the performances of the proposed mfxdma algorithms are compared with the mfxdfa method by extensive numerical experiments on pairs of time series generated from bivariate fractional brownian motions two component autoregressive fractionally integrated moving average processes and binomial measures which have theoretical expressions of the multifractal nature in all cases the scaling exponents h xy extracted from the mfxdma and mfxdfa algorithms are very close to the theoretical values for bivariate fractional brownian motions the scaling exponent of the cross correlation is independent of the cross correlation coefficient between two time series and the mfxdfa and centered mfxdma algorithms have comparative performances which outperform the forward and backward mfxdma algorithms for two component autoregressive fractionally integrated moving average processes we also find that the mfxdfa and centered mfxdma algorithms have comparative performances while the forward and backward mfxdma algorithms perform slightly worse for binomial measures the forward mfxdma algorithm exhibits the best performance the centered mfxdma algorithms performs worst and the backward mfxdma algorithm outperforms the mfxdfa algorithm when the moment order q 0 we apply these algorithms to the return time series of two stock market indexes and to their volatilities for the returns the centered mfxdma algorithm gives the best estimates of h xy q since its h xy 2 is closest to 0 5 as expected and the mfxdfa algorithm has the second best performance for the volatilities the forward and backward mfxdma algorithms give similar results while the centered mfxdma and the mfxdfa algorithms fail to extract rational multifractal nature

comparative analysis of acceleration techniques for 2 d and 3 d green s functions in periodic structures along one and two directions the problem of accelerating the calculation of the periodic green s function is addressed here for both 3 d and 2 d free space configurations in the 3 d case periodicity is considered both along one axis and along two generally skew axes a comprehensive review of the existing methods is first presented and some extensions are developed the possibility of treating the case of complex phase shifts between unit cells necessary for the study of complex modes in periodic structures is also investigated comparisons among the various acceleration methods are performed thus providing fundamental information on their actual efficiency in typical problems

cross correlations between volume change and price change in finance one usually deals not with prices but with growth rates r defined as the difference in logarithm between two consecutive prices here we consider not the trading volume but rather the volume growth rate r the difference in logarithm between two consecutive values of trading volume to this end we use several methods to analyze the properties of volume changes r and their relationship to price changes r we analyze 14 981 daily recordings of the standard and poor s s p 500 index over the 59 year period 1950 2009 and find power law cross correlations between r and r by using detrended cross correlation analysis dcca we introduce a joint stochastic process that models these cross correlations motivated by the relationship between r and r we estimate the tail exponent of the probability density function p r r 1 for both the s p 500 index as well as the collection of 1819 constituents of the new york stock exchange composite index on 17 july 2009 as a new method to estimate we calculate the time intervals q between events where r q we demonstrate that q the average of q obeys q q we find 3 furthermore by aggregating all q values of 28 global financial indices we also observe an approximate inverse cubic law

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

1 f behavior in cross correlations between absolute returns in a us market abstract employing detrended fluctuation analysis dfa and detrended cross correlations analysis dcca we analyze auto correlations in the absolute returns for each of 30 dow jones industrial average djia constituents s i and cross correlations in the absolute returns between the djia and each s i we find that each djia member follows the djia in absolute returns since the dcca curve for each pair s i djia i exhibits strong cross correlations with average dcca exponent 1 03 0 04 this value for implies that the power law cross correlations are of the 1 f functional form for the financial firms comprising the djia we also find that the dfa and dcca exponents controlling the duration of firm risk are somewhat larger than the corresponding values for the rest of the us financial industry

efficient computation of the off diagonal elements of the vector potential multilayered periodic dyadic green s function the authors focus on the efficient computation of the slowly convergent infinite series that lead to the off diagonal elements of the vector potential multilayered periodic dyadic green s function two different approaches based on kummer s transformation are applied to the evaluation of these series the well known approach that makes use of the generalized pencil of functions gpof and ewald s method is the fastest approach but it does not provide accurate results when the distance between the field point and any of the source points is close to zero to avoid this problem we present a novel approach based on the gpof and the spectral kummer poisson s method with higher order asymptotic extraction this latter approach is slightly slower than the former one but it is accurate in the whole range of distances between the field point and the sources

contour fft based spectral domain mbf analysis of large printed antenna arrays a fast spectral domain method is proposed to evaluate the reaction terms between the macro basis functions in regular and non regular arrays made of identical printed antennas the presented technique first exploits the filtering capabilities of the macro basis functions in the spectral domain the method is then strongly accelerated with the help of a newly formulated fast fourier transform fft based technique which is applicable to a contour integration in the complex plane we name the method as contour fft c fft besides an effective homogeneous medium term treated with multipoles a computational complexity of order n log2 n is achieved for the tabulation of substrate related reaction terms for any possible relative positions the complexity of the proposed method is independent from the complexity of the elements numerical results obtained with the proposed method are compared with those from a pre validated reference solution based on the traditional macro basis functions technique an excellent agreement is observed

regularization of mixed potential layered media green s functions for efficient interpolation procedures in planar periodic structures the problem of improving the computational efficiency in the numerical analysis of planar periodic structures is investigated here using the mixed potential integral equation mpie approach a new regularization of the periodic green s functions pgfs that are involved in the analysis of multilayered structures is introduced based on the effective medium concept this regularization involves extracting the singularities of the pgfs up to second order terms the resulting regularized pgf is very smooth and amenable to interpolation thus optimized interpolation procedures for the pgfs can be applied resulting in a considerable reduction of computation time without any significant effect on the accuracy another benefit of the regularization is that it significantly enhances the convergence of the series for both the vector and scalar potential pgfs the theoretical formulation is fully validated with various numerical results for both two dimensional 2 d and one dimensional 1 d layered media periodic structures

coupling detrended fluctuation analysis of asian stock markets abstract this paper uses the coupling detrended fluctuation analysis cdfa method to investigate the multifractal characteristics of four asian stock markets using three stock indices stock price returns trading volumes and the composite index the results show that coupled correlations exist among the four stock markets and the coupled correlations have multifractal characteristics we then use the chi square 2 test to identify the sources of multifractality for the different stock indices the contributions of a single series to multifractality are different in other words the contributions of each country to coupled correlations are different the comparative analysis shows that the research on the combine effect of stock price returns and trading volumes may be more comprehensive than on an individual index by comparing the strength of multifractality for original data with the residual errors of the vector autoregression var model we find that the var model could not be used to describe the dynamics of the coupled correlations among four financial time series

detrended partial cross correlation analysis of two nonstationary time series influenced by common external forces when common factors strongly influence two power law cross correlated time series recorded in complex natural or social systems using detrended cross correlation analysis dcca without considering these common factors will bias the results we use detrended partial cross correlation analysis dpxa to uncover the intrinsic power law cross correlations between two simultaneously recorded time series in the presence of nonstationarity after removing the effects of other time series acting as common forces the dpxa method is a generalization of the detrended cross correlation analysis that takes into account partial correlation analysis we demonstrate the method by using bivariate fractional brownian motions contaminated with a fractional brownian motion we find that the dpxa is able to recover the analytical cross hurst indices and thus the multiscale dpxa coefficients are a viable alternative to the conventional cross correlation coefficient we demonstrate the advantage of the dpxa coefficients over the dcca coefficients by analyzing contaminated bivariate fractional brownian motions we calculate the dpxa coefficients and use them to extract the intrinsic cross correlation between crude oil and gold futures by taking into consideration the impact of the u s dollar index we develop the multifractal dpxa mf dpxa method in order to generalize the dpxa method and investigate multifractal time series we analyze multifractal binomial measures masked with strong white noises and find that the mf dpxa method quantifies the hidden multifractal nature while the multifractal dcca method fails

nonparametric estimation of a regression function consider the regression model yi g xi ei i 1 2 n where xi s denote unordered design variables and g is an unknown function defined on the interval 0 1 assume ei are iid random variables with zero mean and finite variance priestley and chao 1972 and clark 1977 proposed estimators g2nand g3n respectively for g in this paper the asymptotic behavior of g2nand g3nis studied utilizing the properties of the new estimator g1n it is shown that g1n g2n g3nare asymptotically equivalent in various senses moreover consistency results are established and rates of uniform convergence obtained for example if e e 3 if g is lipschitz of order 1 and if n is any sequence of constants tending to as n then for all 0 a leqq b 1 n 1 mathord left vphantom 1 3 right kern nulldelimiterspace 3 mathord left vphantom n 1 mathord left vphantom 1 3 right kern nulldelimiterspace 3 beta n log n mathop sup limits a leqq x leqq b g 1n x g x xrightarrow w p 1 0 right kern nulldelimiterspace beta n log n mathop sup limits a leqq x leqq b g 1n x g x xrightarrow w p 1 0 as n finally when g is monotone a strong consistent isotonic estimator gn is considered

multifractal analysis of the wti crude oil market us stock market and epu abstract this paper adopts multifractal methods to analyze the nonlinear correlations among economic policy uncertainty epu the crude oil market and the stock market first using multifractal detrended fluctuation analysis mf dfa we find that each of the three series shows multifractality and the sources of multifractality are all from long range correlations and fat tailed distributions however for the stock and oil price series the long range correlation has a greater impact while the fat tailed distribution contributes more to epu multifractality furthermore we apply multifractal detrended cross correlation analysis mf dcca to analyze the cross correlation multifractal features among the three series the generalized hurst exponents of any two series are significantly greater than 0 5 and the stock and oil price series have the strongest cross correlation values coupling detrended fluctuation cdfa analysis of the three series shows that the coupling correlation among the three sequences is also multifractal the chi squared statistic reveals that the contribution of the stock market to the multifractality of the coupling correlation is greater than that of other series and epu has the smallest influence on the coupling correlation finally we employ multiscale multifractal analysis mma to visualize the dynamic behaviors of the correlations among the series the results show that the cross correlation of stock with the oil price has some symmetry at small and large scale fluctuations additionally the influence of epu on the overall coupling features is mainly reflected under small scale fluctuations and at large scales the coupling correlation of the three series remains similar to the hurst surface of stock with the oil price these results are useful for building predictive models

extrapolation methods for sommerfeld integral tails a review is presented of the extrapolation methods for accelerating the convergence of sommerfeld type integrals i e semi infinite range integrals with bessel function kernels which arise in problems involving antennas or scatterers embedded in planar multilayered media attention is limited to partition extrapolation procedures in which the sommerfeld integral is evaluated as a sum of a series of partial integrals over finite subintervals and is accelerated by an extrapolation method applied over the real axis tail segment spl alpha spl infin of the integration path where spl alpha 0 is selected to ensure that the integrand is well behaved an analytical form of the asymptotic truncation error or the remainder which characterizes the convergence properties of the sequence of partial sums and serves as a basis for some of the most efficient extrapolation methods is derived several extrapolation algorithms deemed to be the most suitable for the sommerfeld integrals are described and their performance is compared it is demonstrated that the performance of these methods is strongly affected by the horizontal displacement of the source and field points spl rho and by the choice of the subinterval break points furthermore it is found that some well known extrapolation techniques may fail for a number of values of spl rho and ways to remedy this are suggested finally the most effective extrapolation methods for accelerating sommerfeld integral tails are recommended

on the numerical integration of the linear shape functions times the 3 d green s function or its gradient on a plane triangle formulas for the static and dynamic potentials due to linearly varying source distributions defined on a planar triangle are presented the general linear variation of the source is represented in terms of three linear basis functions each one associated with a different vertex of the triangular domain the singular kernels considered are given by the 3 d green s function and its gradient both for the static and dynamic case in the static case the evaluation of potentials is performed analytically and compact form results are given in the dynamic case the results are given in a form suited for numerical integration

efficient evaluation of half line source potentials and their derivatives four different methods are examined to evaluate the potential due to a half line source in a homogeneous space the derivatives of the potential which are needed to calculate the fields are also treated all four methods are compared in terms of accuracy and computational cost in order to determine the most efficient among them for each region of space the gradient of the potential is also examined