inversion of circulant matrices over z m in this paper we consider the problem of inverting an n n circulant matrix with entries over zm we show that the algorithm for inverting circulants based on the reduction to diagonal form by means of fft has some drawbacks when working over zm we present three different algorithms which do not use this approach our algorithms require different degrees of knowledge of m and n and their costs range roughly from n log n log log n to n log2 n log log n log m operations over zm we also present an algorithm for the inversion of finitely generated bi infinite toeplitz matrices the problems considered in this paper have applications to the theory of linear cellular automata

on a family of circulant matrices for quasi cyclic low density generator matrix codes we present a new class of sparse and easily invertible circulant matrices that can have a sparse inverse though not being permutation matrices their study is useful in the design of quasi cyclic low density generator matrix codes that are able to join the inner structure of quasi cyclic codes with sparse generator matrices so limiting the number of elementary operations needed for encoding circulant matrices of the proposed class permit to hit both targets without resorting to identity or permutation matrices that may penalize the code minimum distance and often cause significant error floors

on the complexity of multiplication in finite fields abstract in this paper we study the bilinear complexity of multiplying two arbitrary elements from an nth degree extension of a finite field f and the related problem of multiplying over f two polynomials of degree n 1 with indeterminate coefficients we derive a new linear lower bound and we describe an algorithm leading to a quasi linear upper bound

dcca cross correlation coefficient quantifying level of cross correlation abstract in this paper a new coefficient is proposed with the objective of quantifying the level of cross correlation between nonstationary time series this cross correlation coefficient is defined in terms of the dfa method and the dcca method the implementation of this cross correlation coefficient will be illustrated with selected time series

inference for imputation estimators we derive an estimator of the asymptotic variance of both single and multiple imputation estimators we assume a parametric imputation model but allow for non and semiparametric analysis models our variance estimator in contrast to the estimator proposed by rubin 1987 is consistent even when the imputation and analysis models are misspecified and incompatible with one another

a solution to certain polynomial equations with applications to nonlinear fitting we present a combinatorial method for solving a certain system of polynomial equations of vandermonde type in 2n variables by reducing it to the problem of solving two special linear systems of size n and rooting a single univariate polynomial of degree n over c all solutions can be found with fixed precision using up to polylogarithmic factors o n 2 bitwise operations in the worst case furthermore if the data is well conditioned then this can be reduced to o n bit operations up to polylogarithmic factors as an application we show how this can be used to fit data to a complex exponential sum with n terms in the same nearly optimal time

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

construction and encoding of qc ldpc codes using group rings quasi cyclic qc low density parity check ldpc codes which are known as qc ldpc codes have many applications due to their simple encoding implementation by the means of cyclic shift registers in this paper we construct qc ldpc codes from group rings a group ring is a free module at the same time a ring constructed in a natural way from any given ring and any given group we present a structure based on the elements of a group ring for constructing qc ldpc codes some of the previously addressed methods for constructing qc ldpc codes based on finite fields are special cases of the proposed construction method the constructed qc ldpc codes perform very well over the additive white gaussian noise channel with iterative decoding in terms of bit error probability and block error probability simulation results demonstrate that the proposed codes have competitive performance in comparison with the similar existing ldpc codes finally we propose a new encoding method for the proposed group ring based qc ldpc codes that can be implemented faster than the current encoding methods the encoding complexity of the proposed method is analyzed mathematically and indicates a significate reduction in the required number of operations even when compared to the available efficient encoding methods that have linear time and space complexities

application of robust estimating equations to the analysis of quantitative longitudinal data a model fit by general estimating equations gee has been used extensively for the analysis of longitudinal data in medical studies to some extent gee tries to minimize a quadratic form of the residuals and therefore is not robust in the sense that it like least squares estimates is sensitive to heavy tailed distributions contaminated distributions and extreme values this paper describes the family of truncated robust estimating equations and its properties for the analysis of quantitative longitudinal data like gee the robust estimating equations aim to assess the covariate effects in the generalized linear model in the complete population of observations but in a manner that is more robust to the influence of aberrant observations a simulation study has been conducted to compare the finite sample performance of gee and the robust estimating equations under a variety of error distributions and data structures it shows that the parameter estimates based on gee and the robust estimating equations are approximately unbiased and the type i errors of wald tests do not tend to be inflated gee is slightly more efficient with pure normal data but the efficiency of gee declines much more quickly than the robust estimating equations when the data become contaminated or have heavy tails which makes the robust estimating equations advantageous with non normal data both gee and the robust estimating equations are applied to a longitudinal analysis of renal function in the diabetes control and complications trial dcct for this application gee seems to be sensitive to the working correlation specification in that different working correlation structures may lead to different conclusions about the effect of intensive diabetes treatment on the other hand the robust estimating equations consistently conclude that the treatment effect is highly significant no matter which working correlation structure is used the dcct research group also demonstrated a significant effect using a mixed effects longitudinal model

robust restricted maximum likelihood in mixed linear models summary definitions of robust maximum likelihood robust ml and robust restricted maximum likelihood robust reml are introduced and the definitions are applied to data from biological and chemical experiments a simulation study is undertaken to investigate the asymptotic properties of robust ml and robust reml in small samples and to examine the advantages of using robust methods 1 introduction and definitions linear models with multiple sources of error are widely used in designed experiments across many scientific fields an example of such an experiment is described by patterson and nabugoomu 1992 from patterson and silvey 1980 six varieties of wheat were grown at ten centres that formed a sample of the main types of growing area for wheat in scotland and the yields in tonnes hectare were recorded the experiment is unbalanced because of 60 possible variety centre combinations only 46 were used at seven centres four varieties were grown and at the remaining three centres all six varieties were grown in this paper we fit the simplest mixed linear model proposed for this data by patterson and nabugoomu namely

analysis of longitudinal clinical trials with missing data using multiple imputation in conjunction with robust regression summary in a typical randomized clinical trial a continuous variable of interest e g bone density is measured at baseline and fixed postbaseline time points the resulting longitudinal data often incomplete due to dropouts and other reasons are commonly analyzed using parametric likelihood based methods that assume multivariate normality of the response vector if the normality assumption is deemed untenable then semiparametric methods such as weighted generalized estimating equations are considered we propose an alternate approach in which the missing data problem is tackled using multiple imputation and each imputed dataset is analyzed using robust regression m estimation huber 1973 annals of statistics 1 799 821 to protect against potential non normality outliers in the original or imputed dataset the robust analysis results from each imputed dataset are combined for overall estimation and inference using either the simple rubin 1987 multiple imputation for nonresponse in surveys new york wiley method or the more complex but potentially more accurate robins and wang 2000 biometrika 87 113 124 method we use simulations to show that our proposed approach performs at least as well as the standard methods under normality but is notably better under both elliptically symmetric and asymmetric non normal distributions a clinical trial example is used for illustration

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

crossing of two mobile averages a method for measuring the roughness exponent self affine signals characterized by a defined hurst roughness exponent h can be investigated through mobile averages the density ensuremath rho of crossing points between any two moving averages is a measure of long range power law correlations in the signal the method is compared to the detrended fluctuation analysis we take advantage of our findings in order to propose a practically powerful and accurate technique for determining h and apply it right away to cases with persistent or antipersistent correlations

multifractal properties of price change and volume change of stock market indices abstract we study auto correlations and cross correlations of daily price changes and daily volume changes of thirteen global stock market indices using multifractal detrended fluctuation analysis mf dfa and multifractal detrended cross correlation analysis mf dxa we find rather distinct multifractal behavior of price and volume changes our results indicate that the time series of price changes are more complex than those of volume changes and that large fluctuations dominate multifractal behavior of price changes while small fluctuations dominate multifractal behavior of volume changes we also find that there is an absence of correlations in price changes there are anti persistent long term correlations in volume changes and there are anti persistent long term cross correlations between price and volume changes shuffling the series reveals that multifractality of both price changes and volume changes arises from a broad probability density function

transfer entropy coefficient quantifying level of information flow between financial time series abstract in this paper a new coefficient is proposed with the objective of quantifying the level of information flow between financial time series this transfer entropy coefficient which provides an assessment on the multiscale information flow between measurements is defined in terms of the transfer entropy method and the multiscale method the implementation of this transfer entropy coefficient is illustrated with simulated time series and financial time series examples taken from simulated and financial data demonstrate that the dynamic mechanism of a complex system cannot be detected solely on the basis of transfer entropy of single scale

chaos based nonlinear analysis to study cardiovascular responses to changes in posture abstract cardiovascular responses to changes in posture have been the focus of numerous investigations in the past analysis of ecg and arterial blood pressure abp data for different postures obtained from physionet was done from a new perspective of analyzing nonlinear time series having multifractal features multifractal detrended fluctuation analysis mfdfa and also the cross correlation between ecg and bp with another technique multifractal detrended cross correlation analysis mfdxa reveals ecg and abp time series of different subjects to be multifractal in nature with different degree of complexity different degree of auto and cross correlation for both ecg and abp signals is also observed for all subjects further significant information obtained from the cross correlation parameters obtained from mfdxa analysis is very important and relevant particularly for understanding the dynamics of orthostatic stress

multifractal cross correlation analysis in electricity spot market abstract in this paper we investigate the multiscale cross correlations between electricity price and trading volume in czech market based on a newly developed algorithm called multifractal cross correlation analysis mfcca the new algorithm is a natural multifractal generalization of the detrended cross correlation analysis dcca and is sensitive to cross correlation structure and free from limitations of other algorithms by considering the original sign of the cross covariance it allows us to properly quantify and detect the subtle characteristics of two simultaneous recorded time series first the multifractality and the long range anti persistent auto correlations of price return and trading volume variation are confirmed using multifractal detrended fluctuation analysis mf dfa furthermore we show that there exist long range anti persistent cross correlations between price return and trading volume variation by mfcca and we also identify that the cross correlations disappear on the level of relative small fluctuations in order to obtain deeper insight into the dynamics of the electricity market we analyze the relation between generalized hurst exponent and the multifractal cross correlation scaling exponent q we find that the difference between the generalized hurst exponent and the multifractal cross correlation scaling exponent is significantly different for smaller fluctuation which indicates that the multifractal character of cross correlations resembles more each other for electricity price and trading volume on the level of large fluctuations and weakens for the smaller ones

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

measuring multifractality of stock price fluctuation using multifractal detrended fluctuation analysis abstract analyzing the shanghai stock price index daily returns using mf dfa method it is found that there are two different types of sources for multifractality in time series namely fat tailed probability distributions and non linear temporal correlations based on that a sliding window of 240 frequency data in 5 trading days was used to study stock price index fluctuation it is found that when the stock price index fluctuates sharply a strong variability is clearly characterized by the generalized hurst exponents h q therefore two measures h and based on generalized hurst exponents were proposed to compare financial risks before and after price limits and reform of non tradable shares the empirical results verify the validity of the measures and this has led to a better understanding of complex stock markets

autocorrelation and cross correlation in time series of homicide and attempted homicide abstract we propose in this paper to establish the relationship between homicides and attempted homicides by a non stationary time series analysis this analysis will be carried out by detrended fluctuation analysis dfa detrended cross correlation analysis dcca and dcca cross correlation coefficient d c c a n through this analysis we can identify a positive cross correlation between homicides and attempted homicides at the same time looked at from the point of view of autocorrelation dfa this analysis can be more informative depending on time scale for short scale days we cannot identify auto correlations on the scale of weeks dfa presents anti persistent behavior and for long time scales n 90 days dfa presents a persistent behavior finally the application of this new type of statistical analysis proved to be efficient and in this sense this paper can contribute to a more accurate descriptive statistics of crime

multifractal analysis of shanghai and hong kong stock markets before and after the connect program abstract in this paper we study the multifractal scaling behaviour in shanghai and hong kong stock markets by means of multifractal detrended fluctuation analysis mf dfa and multifractal detrended cross correlation analysis mf dcca the results show that the multifractal degrees of each stock market are larger after the shanghai hong kong stock connect program shscp than before scaling analysis demonstrates that multifractality exists in cross correlations and the cross correlation coefficients after the shscp are larger than those before the shscp moreover an analysis of the origin of multifractality indicates that long range correlation and fat tailed distribution play important roles in the contributions of multifractality finally the results via the sliding window procedure indicate that the multifractal degrees after the shscp are not significantly affected by the stock market turbulence in 2015

exact results for deterministic cellular automata with additive rules deterministic cellular automata ca with additive rules are studied by exploiting the properties of circulant matrices on finite fields complete state transition diagrams for higher order and multidimensional ca on finite lattices are analyzed conditions on the rules which make them reversible are obtained it is shown that all state transition diagrams of the ca have identical trees rooted on cycles general formulae for cycle lengths and multiplicities are given

a complete and efficiently computable topological classification of d dimensional linear cellular automata over z m we study the dynamical behavior of d dimensional linear cellular automata over zm we provide easy to check necessary and sufficient conditions for a d dimensional linear cellular automata over zm to be sensitive to initial conditions positively expansive strongly transitive and equicontinuous as a consequence of our results we have a complete and efficiently computable topological classification of d dimensional linear cellular automata over zm according to the most important dynamical properties studied in the theory of discrete time dynamical systems

multiscale multifractal dcca and complexity behaviors of return intervals for potts price model abstract to investigate the characteristics of extreme events in financial markets and the corresponding return intervals among these events we use a potts dynamic system to construct a random financial time series model of the attitudes of market traders we use multiscale multifractal detrended cross correlation analysis mm dcca and lempel ziv complexity lzc perform numerical research of the return intervals for two significant china s stock market indices and for the proposed model the new mm dcca method is based on the hurst surface and provides more interpretable cross correlations of the dynamic mechanism between different return interval series we scale the lzc method with different exponents to illustrate the complexity of return intervals in different scales empirical studies indicate that the proposed return intervals from the potts system and the real stock market indices hold similar statistical properties

small sample degrees of freedom with multiple imputation an appealing feature of multiple imputation is the simplicity of the rules for combining the multiple complete data inferences into a final inference the repeated imputation inference rubin 1987 this inference is based on a t distribution and is derived from a bayesian paradigm under the assumption that the complete data degrees of freedom com are infinite but the number of imputations m is finite when com is small and there is only a modest proportion of missing data the calculated repeated imputation degrees of freedom m for the t reference distribution can be much larger than com which is clearly inappropriate following the bayesian paradigm we derive an adjusted degrees of freedom m with the following three properties for fixed m and estimated fraction of missing information m monotonically increases in com m is always less than or equal to com and m equals m when com is infinite a small simulation study demonstrates the superior frequentist performance when using m rather than m

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

random matrix theory analysis of cross correlations in the us stock market evidence from pearson s correlation coefficient and detrended cross correlation coefficient abstract in this study we first build two empirical cross correlation matrices in the us stock market by two different methods namely the pearson s correlation coefficient and the detrended cross correlation coefficient dcca coefficient then combining the two matrices with the method of random matrix theory rmt we mainly investigate the statistical properties of cross correlations in the us stock market we choose the daily closing prices of 462 constituent stocks of s p 500 index as the research objects and select the sample data from january 3 2005 to august 31 2012 in the empirical analysis we examine the statistical properties of cross correlation coefficients the distribution of eigenvalues the distribution of eigenvector components and the inverse participation ratio from the two methods we find some new results of the cross correlations in the us stock market in our study which are different from the conclusions reached by previous studies the empirical cross correlation matrices constructed by the dcca coefficient show several interesting properties at different time scales in the us stock market which are useful to the risk management and optimal portfolio selection especially to the diversity of the asset portfolio it will be an interesting and meaningful work to find the theoretical eigenvalue distribution of a completely random matrix r for the dcca coefficient because it does not obey the marcenko pastur distribution

modeling long range cross correlations in two component arfima and fiarch processes we investigate how simultaneously recorded long range power law correlated multivariate signals cross correlate to this end we introduce a two component arfima stochastic process and a two component fiarch process to generate coupled fractal signals with long range power law correlations which are at the same time long range cross correlated we study how the degree of cross correlations between these signals depends on the scaling exponents characterizing the fractal correlations in each signal and on the coupling between the signals our findings have relevance when studying parallel outputs of multiple component of physical physiological and social systems

computations with infinite toeplitz matrices and polynomials we relate polynomial computations with operations involving infinite band toeplitz matrices and show applications to the numerical solution of markov chains of nonlinear matrix equations to spectral factorizations and to the solution of finite toeplitz systems in particular two matrix versions of graeffe s iteration are introduced and their convergence properties are analyzed correlations between graeffe s iteration for matrix polynomials and cyclic reduction for block toeplitz matrices are pointed out the paper contains a systematic treatment of known topics and presentation of new results improvements and extensions

universal and nonuniversal properties of cross correlations in financial time series we use methods of random matrix theory to analyze the cross correlation matrix c of stock price changes of the largest 1000 u s companies for the 2 year period 1994 1995 we find that the statistics of most of the eigenvalues in the spectrum of c agree with the predictions of random matrix theory but there are deviations for a few of the largest eigenvalues we find that c has the universal properties of the gaussian orthogonal ensemble of random matrices furthermore we analyze the eigenvectors of c through their inverse participation ratio and find eigenvectors with large ratios at both edges of the eigenvalue spectrum a situation reminiscent of localization theory results

dynamical mechanism in aero engine gas path system using minimum spanning tree and detrended cross correlation analysis abstract identifying the mutual interaction in aero engine gas path system is a crucial problem that facilitates the understanding of emerging structures in complex system by employing the multiscale multifractal detrended cross correlation analysis method to aero engine gas path system the cross correlation characteristics between gas path system parameters are established further we apply multiscale multifractal detrended cross correlation distance matrix and minimum spanning tree to investigate the mutual interactions of gas path variables the results can infer that the low spool rotor speed n1 and engine pressure ratio epr are main gas path parameters the application of proposed method contributes to promote our understanding of the internal mechanisms and structures of aero engine dynamics

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

fuzzy entropy complexity and multifractal behavior of statistical physics financial dynamics abstract the present paper introduces a novel stochastic statistical physics financial system by combining exclusion system with compound poisson process the financial system is a model concerning with price fluctuations derived from dissemination of trading attitudes of financial agents and random drastic jumps caused by exogenous economic factors respectively multifractal detrended cross correlation analysis and fuzzy entropy of simulation dataset are performed fractional fuzzy entropy based on fuzzy entropy method and fractional calculus is also developed to explore nonlinear complexity of the proposed model in the paper empirical results display that there are significant multifractality and fractal asymmetry in the proposed model and the complexity of return series increases when or increases correspondingly and same analyses for actual stock market dataset are comparatively investigated the conclusions reveal that the novel compound dynamics can reproduce various nonlinear behaviors of actual stock markets to a certain extent

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

the informativeness of options trading activities non linear analysis based on mf dcca and granger test abstract using both put call ratio p c and option to stock volume ratio o s as measures of options trading activities this paper investigates the information content of sse 50 etf options we begin by using detrended fluctuation analysis mf dfa method to examine the multifractal properties of p c ratio change series o s ratio change series and etf returns and find that these time series exhibit strong multifractality moreover employing multifractal detrended cross correlation analysis mf dcca we show that there exists strong anti persistent cross correlation between p c ratios and 50 etf returns but no significant cross correlation between o s ratios and 50 etf returns suggesting that p c ratio is more pronounced detecting the information content of options furthermore we use nonlinear granger causality test and show that the granger causality relationships between p c ratio and 50 etf return series is more significant and stronger than that between o s ratio and 50 etf return series our findings imply that p c ratio can better capture the informativeness of options

long range correlation properties of coding and noncoding dna sequences genbank analysis an open question in computational molecular biology is whether long range correlations are present in both coding and noncoding dna or only in the latter to answer this question we consider all 33301 coding and all 29453 noncoding eukaryotic sequences each of length larger than 512 base pairs bp in the present release of the genbank to dtermine whether there is any statistically significant distinction in their long range correlation properties standard fast fourier transform fft analysis indicates that coding sequences have practically no correlations in the range from 10 bp to 100 bp spectral exponent beta 0 00 0 04 where the uncertainty is two standard deviations in contrast for noncoding sequences the average value of the spectral exponent beta is positive 0 16 0 05 which unambiguously shows the presence of long range correlations we also separately analyze the 874 coding and the 1157 noncoding sequences that have more than 4096 bp and find a larger region of power law behavior we calculate the probability that these two data sets coding and noncoding were drawn from the same distribution and we find that it is less than 10 10 we obtain independent confirmation of these findings using the method of detrended fluctuation analysis dfa which is designed to treat sequences with statistical heterogeneity such as dna s known mosaic structure patchiness arising from the nonstationarity of nucleotide concentration the near perfect agreement between the two independent analysis methods fft and dfa increases the confidence in the reliability of our conclusion

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

statically transformed autoregressive process and surrogate data test for nonlinearity the key feature for the successful implementation of the surrogate data test for nonlinearity on a scalar time series is the generation of surrogate data that represent exactly the null hypothesis statically transformed normal stochastic process i e they possess the sample autocorrelation and amplitude distribution of the given data a conceptual approach and algorithm for the generation of surrogate data is proposed called the statically transformed autoregressive process stap it identifies a normal autoregressive process and a monotonic static transform so that the transformed realizations of this process fulfill exactly both conditions and do not suffer from bias in autocorrelation as the surrogate data generated by other algorithms the appropriateness of stap is demonstrated with simulated and real world data

specification of covariance structure in longitudinal data analysis for randomized clinical trials misspecification of the covariance structure for repeated measurements in longitudinal analysis may lead to biased estimates of the regression parameters and under or overestimation of the corresponding standard errors in the presence of missing data the so called sandwich estimator can correct the variance but it does not reduce the bias in point estimates removing all assumptions from the covariance structure i e using an unstructured un covariance will remove such biases however an excessive amount of missing data may cause convergence problems for iterative algorithms such as the default newton raphson algorithm in the popular sas proc mixed this article examines both through theory and simulations the existence and the magnitude of these biases we recommend the use of un covariance as the default strategy for analyzing longitudinal data from randomized clinical trials with moderate to large number of subjects and small to moderate number of time points we also present an algorithm to assist in the convergence when the un covariance is used

long range correlation and market segmentation in bond market abstract this paper investigates the long range auto correlations and cross correlations in bond market based on detrended moving average dma method empirical results present a clear evidence of long range persistence that exists in one year scale the degree of long range correlation related to maturities has an upward tendency with a peak in short term these findings confirm the expectations of fractal market hypothesis fmh furthermore we have developed a method based on a complex network to study the long range cross correlation structure and applied it to our data and found a clear pattern of market segmentation in the long run we also detected the nature of long range correlation in the sub period 2007 2012 and 2011 2016 the result from our research shows that long range auto correlations are decreasing in the recent years while long range cross correlations are strengthening

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

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

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

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

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

analysis of semiparametric regression models for repeated outcomes in the presence of missing data abstract we propose a class of inverse probability of censoring weighted estimators for the parameters of models for the dependence of the mean of a vector of correlated response variables on a vector of explanatory variables in the presence of missing response data the proposed estimators do not require full specification of the likelihood they can be viewed as an extension of generalized estimating equations estimators that allow for the data to be missing at random but not missing completely at random these estimators can be used to correct for dependent censoring and nonrandom noncompliance in randomized clinical trials studying the effect of a treatment on the evolution over time of the mean of a response variable the likelihood based parametric g computation algorithm estimator may also be used to attempt to correct for dependent censoring and nonrandom noncompliance but because of possible model misspecification the parametric g computation algorithm estimator in contrast with the proposed w

price volume cross correlation analysis of csi300 index futures abstract we investigate the cross correlation between price returns and trading volumes for the china securities index 300 csi300 index futures which are the only stock index futures traded on the china financial futures exchange cffex the basic statistics suggest that distributions of these two time series are not normal but exhibit fat tails based on the detrended cross correlation analysis dcca we obtain that returns and trading volumes are long range cross correlated the existence of multifractality in the cross correlation between returns and trading volumes has been proven with the multifractal detrended cross correlation analysis mfdcca algorithm the multifractal analysis also confirms that returns and trading volumes have different degrees of multifractality we further perform a cross correlation statistic to verify whether the cross correlation significantly exists between returns and trading volumes for csi300 index futures in addition results of the test for lead lag effect demonstrate that contemporaneous cross correlation of return and trading volume series is stronger than cross correlations of leaded or lagged series

algebraic properties of cellular automata cellular automata are discrete dynamical systems of simple construction but complex and varied behaviour algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata the complete structure of state transition diagrams is derived in terms of algebraic and number theoretical quantities the systems are usually irreversible and are found to evolve through transients to attractors consisting of cycles sometimes containing a large number of configurations

multifractal detrended fluctuation analysis on high frequency szse in chinese stock market abstract we use multifractal detrended fluctuation analysis mf dfa method to investigate the multifractal behavior of shenzhen component index szse 5 minute high frequency stock data from 2017 6 15 2018 4 11 we determine generalized hurst exponent and singularity spectrum and find that these fluctuations have multifractal nature in order to maintain the long term memory of the stock all 9696 data are divided into 6 units according to the multifractal spectrum the main parameters of the six units are obtained comparing the mf dfa results for the original szse high frequency time series with those for shuffled series we conclude that the origin of multifractality is due to both the broadness of probability density function and long range correlation the generalized hurst exponent obviously depend on the order of fluctuation function and change with it the curve of scaling function clearly departs from a straight line i e it shows clearly nonlinear property and the multifractal spectrum displays the commonly observed bell shape this will provide an important and theoretical foundation for researching the forecasting of finance markets

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

multifractal detrended cross correlation analysis of gold price and sensex abstract this paper studies the variation of autocorrelation and cross correlation coefficients of gold price and sensex fluctuations with time the paper uses mfdfa and mfdxa methodologies sensex plays a more dominant role in the variation of cross correlations it is observed that the cross correlation coefficients can be linked with the stability of the market the market is most stable when the two series are most correlated

cross correlation analysis between chinese tf contracts and treasury etf based on high frequency data abstract in this paper we investigate the high frequency cross correlation relationship between chinese treasury futures contracts and treasury etf we analyze the logarithmic return of these two price series from which we can conclude that both return series are not normally distributed and the futures markets have greater volatility we find significant cross correlation between these two series we further confirm the relationship using the dcca coefficient and the dmca coefficient we quantify the long range cross correlation with dcca method and we further show that the relationship is multifractal an arbitrage algorithm based on dfa regression with stable return is proposed in the last part

circulants inversion of circulants and some related matrix algebras abstract the spectral theory for circulants over r or c is discussed followed by a discussion of inversion of circulants the algebraic theory of one generator matrix algebras and applications to circulants and some related algebras are presented the theory of symmetric functions plays an important role thus the latter methods apply over arbitrary commutative rings

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

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

improved surrogate data for nonlinearity tests current tests for nonlinearity compare a time series to the null hypothesis of a gaussian linear stochastic process for this restricted null assumption random surrogates can be constructed which are constrained by the linear properties of the data we propose a more general null hypothesis allowing for nonlinear rescalings of a gaussian linear process we show that such rescalings cannot be accounted for by a simple amplitude adjustment of the surrogates which leads to spurious detection of nonlinearity an iterative algorithm is proposed to make appropriate surrogates which have the same autocorrelations as the data and the same probability distribution

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

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

time dependent cross correlations between different stock returns a directed network of influence we study the time dependent cross correlations of stock returns i e we measure the correlation as the function of the time shift between pairs of stock return time series using tick by tick data we find a weak but significant effect showing that in many cases the maximum correlation appears at nonzero time shift indicating directions of influence between the companies due to the weakness of this effect and the shortness of the characteristic time of the order of a few minutes our findings are compatible with market efficiency the interaction of companies defines a directed network of influence

inversion of two level circulant matrices over zp abstract we consider the problem of inverting block circulant with circulant blocks bccb matrices with entries over the field z p this problem arises in the study of of two dimensional linear cellular automata since the standard reduction to diagonal form by means of fft has some drawbacks when working over z p we solve this problem by transforming it into the equivalent problem of inverting a circulant matrix with entries over a suitable ring r we show that a bccb matrix of size mn can be inverted in o mn c m n operations in z p where c is a low degree polynomial in log m and log n