a unified method for evaluating the error correction radius of reliability based soft decision algorithms for linear block codes this paper presents a unified method for evaluating the error correction radii of many reliability based soft decision decoding algorithms for binary linear block codes based on this unified method these decoding algorithms as well as their potential improvements can be compared directly the error correction radius for each of these decoding algorithms is determined by finding the closest point on the boundary of the decision region of the soft decision decoder to the transmitted signal sequence it is shown that this problem can be formulated as a constrained optimization problem although no general closed form expression is possible a simple algorithm that always converges to the optimum solution of this optimization problem is presented based on these results the error correction radii of some well known reliability based soft decision decoding algorithms are revisited and compared

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

reliability based soft decision decoding with iterative information set reduction the reliability based decoding approach using the reprocessing of the most reliable information set only is extended into the iterative reprocessing of several information sets at the end of each information set reprocessing some information bits are delivered by the decoder consequently information sets with decreasing cardinality values are considered at each iteration a tight upper bound on the error performance achieved by this new method is derived compared to previously proposed competitive approaches this new method reduces the number of candidate codewords needed to achieve practically optimum decoding importantly it also preserves the very simple structured implementation of the order statistic decoding

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

multifractal detrended cross correlations between the csi 300 index futures and the spot markets based on high frequency data abstract the cross correlation between the china securities index 300 csi 300 index futures and the spot markets based on high frequency data is discussed in this paper we empirically analyze the cross correlation by using the multifractal detrended cross correlation analysis mf dcca and investigate further the characteristics of asymmetry frequency difference and transmission direction of the cross correlation the results indicate that the cross correlation between the two markets is significant and multifractal meanwhile weak asymmetries exist in the cross correlation and higher data frequency results in a lower multifractality degree of the cross correlation the causal relationship between the two markets is bidirectional but the csi 300 index futures market has greater impact on the spot market

a new correlation coefficient for bivariate time series data abstract the correlation in time series has received considerable attention in the literature its use has attained an important role in the social sciences and finance for example pair trading in finance is concerned with the correlation between stock prices returns etc in general pearson s correlation coefficient is employed in these areas although it has many underlying assumptions which restrict its use here we introduce a new correlation coefficient which takes into account the lag difference of data points we investigate the properties of this new correlation coefficient we demonstrate that it is more appropriate for showing the direction of the covariation of the two variables over time we also compare the performance of the new correlation coefficient with pearson s correlation coefficient and detrended cross correlation analysis dcca via simulated examples

measuring correlations between non stationary series with dcca coefficient abstract in this short report we investigate the ability of the dcca coefficient to measure correlation level between non stationary series based on a wide monte carlo simulation study we show that the dcca coefficient can estimate the correlation coefficient accurately regardless the strength of non stationarity measured by the fractional differencing parameter d for a comparison we also report the results for the standard pearson correlation coefficient the dcca coefficient dominates the pearson coefficient for non stationary series

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

multifractal analysis of stock exchange crashes abstract we analyze the complexity of rare events of the djia index we reveal that the returns of the time series exhibit strong multifractal properties meaning that temporal correlations play a substantial role the effect of major stock market crashes can be best illustrated by the comparison of the multifractal spectra of the time series before and after the crash aftershock periods compared to foreshock periods exhibit richer and more complex dynamics compared to an average crash calculated by taking into account the larger 5 crashes of the djia index the 1929 event exhibits significantly more increase in multifractality than the 1987 crisis

sinc interpolation of nonuniform samples it is well known that a bandlimited signal can be uniquely recovered from nonuniformly spaced samples under certain conditions on the nonuniform grid and provided that the average sampling rate meets or exceeds the nyquist rate however reconstruction of the continuous time signal from nonuniform samples is typically more difficult to implement than from uniform samples motivated by the fact that sinc interpolation results in perfect reconstruction for uniform sampling we develop a class of approximate reconstruction methods from nonuniform samples based on the use of time invariant lowpass filtering i e sinc interpolation the methods discussed consist of four cases incorporated in a single framework the case of sub nyquist sampling is also discussed and nonuniform sampling is shown as a possible approach to mitigating the impact of aliasing

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

fractionally integrated process with power law correlations in variables and magnitudes we propose a new stochastic process de ned by only two parameters 1 and 2 which generates power law correlations or anticorrelations in the variable increments and power law correlations in their magnitudes to account for empirical observations in a range of physical systems to demonstrate the utility of our process we consider the case with power law anticorrelations in the variable increments and power law correlations in their magnitudes to model scaling properties in heartbeat data the parameters 1 and 2 control separately the correlations in the increments and their magnitudes and we nd linear relations between each parameter and the corresponding correlation exponent

reliability based code search algorithms for maximum likelihood decoding of block codes efficient code search maximum likelihood decoding algorithms based on reliability information are presented for binary linear block codes the codewords examined are obtained via encoding the information set utilized for encoding comprises the positions of those columns of a generator matrix g of the code which for a given received sequence constitute the most reliable basis for the column space of g substantially reduced computational complexity of decoding is achieved by exploiting the ordering of the positions within this information set the search procedures do not require memory the codeword to be examined is constructed from the previously examined codeword according to a fixed rule consequently the search algorithms are applicable to codes of relatively large size they are also conveniently modifiable to achieve efficient nearly optimum decoding of particularly large codes

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

a monte carlo simulation to the performance of the r s and v s methods statistical revisit and real world application abstract a correct or precise estimation of the hurst exponent is one of the fundamentally important problems in the financial economics literature there are three widely used tools to estimate the hurst exponent the canonical rescaled range r s the variance rescaled statistic v s and the modified rescaled range modified r s to clarify their performance we compare them by monte carlo simulations we generate many time series of a fractal brownian motion of a weierstrass mandelbrot cosine fractal function and of a fractionally integrated process whose theoretical hurst exponents are known to compare the hurst exponents estimated by the three methods to better understand their pragmatic performance we further apply all of these methods empirically in real world applications our results imply it is not appropriate to conclude simply which method is better as v s performs better when the analyzed market is anti persistent while r s seems to be a reliable tool used in persistent market

statistical test for δρdcca cross correlation coefficient abstract in this paper we propose a new statistical test for d c c a detrended cross correlation coefficient difference a tool to measure contagion interdependence effect in time series of size n at different time scale n for this proposition we analyzed simulated and real time series the results showed that the statistical significance of d c c a depends on the size n and the time scale n and we can define a critical value for this dependency in 90 95 and 99 of confidence level as will be shown in this paper

a new approach to quantify power law cross correlation and its application to commodity markets abstract we proposed a new method detrended moving average cross correlation analysis dmca to detect the power law cross correlation between two correlated non stationary time series by combining detrended cross correlation analysis dcca and detrended moving average dma in order to compare the performance of dmca and dcca in the detection of cross correlation and to estimate the influence of periodic trend we generate two cross correlated time series x i and y i by a periodic two component fractionally autoregressive integrated moving average arfima process then we apply both methods to quantify the cross correlations of the generated series whose theoretical values are already known to us by comparing the results we obtained we find that the performance of this new approach is comparable to dcca with less calculating amounts our method can also reduce the impact of trends furthermore dmca for background and forward moving average case outperforms dcca in more accurate estimation when the analyzed times series are short in length to provide an example we also apply this new method to the time series of the real world data from brent and wti crude oil spot markets to investigate the complex cross market correlation between these commodity markets in all our method is another practical choice to detect the cross correlation between two short period non stationary time series and has potential application to real world problems

soft decision decoding of linear block codes using preprocessing and diversification order w reprocessing is a suboptimal soft decision decoding approach for binary linear block codes in which up to w bits are systematically flipped on the so called most reliable information basis mrb this correspondence first incorporates two preprocessing rules into order w reprocessing and shows that with appropriate choice of parameters the proposed order w reprocessing with preprocessing requires comparable complexity to order w reprocessing but achieves asymptotically the performance of order w 2 reprocessing to complement the mrb a second basis is employed for practical snrs and this approach is systematically extended to a multibasis order w reprocessing scheme for high signal to noise ratios snrs it is shown that the proposed multibasis scheme significantly enlarges the error correction radius a commonly used measure of performance at high snrs over the original single basis order w reprocessing as a by product this approach also precisely characterizes the asymptotic performance of the well known chase and generalized minimum distance gmd decoding algorithms the proposed algorithm successfully decodes the 192 96 reed solomon concatenated code and the 256 147 extended bch code in near optimal manner within 0 01 db at a block error rate of 10 5 with affordable computational cost

minimum spanning tree filtering of correlations for varying time scales and size of fluctuations based on a recently proposed q dependent detrended cross correlation coefficient ensuremath rho q j kwapie ifmmode acute n else n fi p o ifmmode acute s else s fi wi ifmmode mbox k e else k e fi cimka and s dro ifmmode dot z else z fi d ifmmode dot z else z fi phys rev e 92 052815 2015 we generalize the concept of the minimum spanning tree mst by introducing a family of q dependent minimum spanning trees q mathrm mst mathrm s that are selective to cross correlations between different fluctuation amplitudes and different time scales of multivariate data they inherit this ability directly from the coefficients ensuremath rho q which are processed here to construct a distance matrix being the input to the mst constructing kruskal s algorithm the conventional mst with detrending corresponds in this context to q 2 in order to illustrate their performance we apply the q mathrm msts to sample empirical data from the american stock market and discuss the results we show that the q mathrm mst graphs can complement ensuremath rho q in disentangling hidden correlations that cannot be observed in the mst graphs based on ensuremath rho mathrm dcca and therefore they can be useful in many areas where the multivariate cross correlations are of interest as an example we apply this method to empirical data from the stock market and show that by constructing the q mathrm msts for a spectrum of q values we obtain more information about the correlation structure of the data than by using q 2 only more specifically we show that two sets of signals that differ from each other statistically can give comparable trees for q 2 while only by using the trees for q ensuremath ne 2 do we become able to distinguish between these sets we also show that a family of q mathrm msts for a range of q expresses the diversity of correlations in a manner resembling the multifractal analysis where one computes a spectrum of the generalized fractal dimensions the generalized hurst exponents or the multifractal singularity spectra the more diverse the correlations are the more variable the tree topology is for different q s as regards the correlation structure of the stock market our analysis exhibits that the stocks belonging to the same or similar industrial sectors are correlated via the fluctuations of moderate amplitudes while the largest fluctuations often happen to synchronize in those stocks that do not necessarily belong to the same industry

asymptotic optimality of the gmd and chase decoding algorithms the generalized minimum distance gmd and chase 1972 decoding algorithms are some of the most important suboptimum bounded distance decoding algorithms for binary linear block codes over an additive white gaussian noise awgn channel we compute the limitation of the ratio between the probability of decoding error for the gmd or any one of the chase decoding algorithms and that of the maximum likelihood ml decoding when the signal to noise ratio snr approaches infinity if the minimum hamming distance of the code is greater than 2 the limitation is shown to be equal to 1 and thus the gmd and chase decoding algorithms are asymptotically optimum

comparative analysis of grey detrended fluctuation analysis methods based on empirical research on china s interest rate market abstract this study empirically compares the development of china s interest rate market in the past decade the yield of shibor market from 2006 to 2016 showed anti persistence and the later five year trend was stronger than that in the previous half period indicating a significantly growing trend of china s interest rate market we perform a comparative analysis of detrended fluctuation analysis dfa detrending moving average dma algorithm and the maximum overlap wavelet transform dfa modwt using grey and original sequences the autoregressive integrated moving average model is adopted to generate set point h sequences results illustrated that 1 for original sequences both the dfa modwt and dma 0 5 shows outstanding performances when the set hurst exponents are 0 6 and 0 7 and 0 8 and 0 9 respectively 2 for grey sequences g dfa performs best among the three methods followed by g dma and g dfa modwt 3 the long range correlation of the original sequences is slightly lower than the set values on the contrary the long range correlation of grey sequences is much higher than the set values thus the grey sequence exerts a strong aggregation effect as it can accumulate the trend of the sequence our results show that the grey sequence can determine the regular pattern from the messy sequence however grey sequences tend to be overly analyzed and misleading when large volumes of data are involved empirical studies confirm that china s interest rate market remains an inefficient market

reliability based soft decision decoding with multiple biases in this paper a new reliability based soft decision decoding algorithm is presented this algorithm repeatedly uses biased reliability values to construct the most reliable basis mrb as a result this new method makes use of multiple information sets in a stochastic way compared to previously proposed competitive approaches this new method produces a more efficient mrb reprocessing type algorithm to achieve near maximum likelihood decoding mld performance with a proper choice of the bias value it can be combined with any mrb reprocessing type algorithm and in each case a tight performance analysis can be derived

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

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

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

on the reliability order based decoding algorithms for binary linear block codes in this correspondence we consider the decoding of binary block codes over the additive white gaussian noise awgn channel with binary phase shift keying bpsk signaling by a reliability order based decoding algorithm robda we mean a soft decision decoding algorithm which decodes to the best most likely codeword of the form that is the sum of the hard decision tuple and an error pattern in a set determined only by the order of the reliabilities of the hard decisions examples of robdas include many well known decoding algorithms such as the generalized minimum distance gmd decoding algorithm chase decoding algorithms and the reliability based decoding algorithms proposed by fossorier and lin it is known that the squared error correction radii of robdas can be computed from the minimal squared euclidean distances mseds between the all one sequence and the polyhedra corresponding to the error patterns for the computation of such mseds we give a new method which is more compact than the one proposed by fossorier and lin these results are further used to show that any bounded distance robda is asymptotically optimal the ratio between the probability of decoding error of a bounded distance robda and that of the maximum likelihood ml decoding approaches 1 when the signal to noise ratio snr approaches infinity provided that the minimum hamming distance of the code is greater than 2

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

a dfa approach for assessing asymmetric correlations abstract here we propose a method based on detrended fluctuation analysis to investigate asymmetric correlations in nonstationary time series the aim is to show that for a certain range of time scales different scaling properties are found if signal trending is either positive and negative we illustrate the method by selected examples from physics and finance

iterative soft input soft output decoding of reed solomon codes by adapting the parity check matrix an iterative algorithm is presented for soft input soft output siso decoding of reed solomon rs codes the proposed iterative algorithm uses the sum product algorithm spa in conjunction with a binary parity check matrix of the rs code the novelty is in reducing a submatrix of the binary parity check matrix that corresponds to less reliable bits to a sparse nature before the spa is applied at each iteration the proposed algorithm can be geometrically interpreted as a two stage gradient descent with an adaptive potential function this adaptive procedure is crucial to the convergence behavior of the gradient descent algorithm and therefore significantly improves the performance simulation results show that the proposed decoding algorithm and its variations provide significant gain over hard decision decoding hdd and compare favorably with other popular soft decision decoding methods

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

detrending moving average cross correlation coefficient measuring cross correlations between non stationary series abstract in the paper we introduce a new measure of correlation between possibly non stationary series as the measure is based on the detrending moving average cross correlation analysis dmca we label it as the dmca coefficient d m c a with a moving average window length we analytically show that the coefficient ranges between 1 and 1 as a standard correlation does in the simulation study we show that the values of d m c a very well correspond to the true correlation between the analyzed series regardless the non stationarity level dependence of the newly proposed measure on other parameters correlation level moving average window length and time series length is discussed as well

dcca cross correlation analysis in time series with removed parts abstract in this paper we analyze the effect of removing pieces in time series with long range memory by dfa method and detrended cross correlation coefficient to achieve this purpose initially simulated time series are produced by arfima process long time dependence from these simulated time series cuts and removals are produced the results show that for up to 50 of removed parts compared to the original time series there is no change in the final results for detrended auto and cross correlations therefore with this paper we show that the dfa method and the detrended cross correlation coefficient are robust for time series analysis even for time series with removed parts this result ensures that these methods can be applied to real time series which in many cases lacks measurement for a variety of reasons and causes

on a ast algorithms for decoding short linear block codes the a ast algorithm for decoding linear block codes is an efficient tree search method for decoding short linear block codes the information contained in the parity bits are potentially useful for reducing the edges needed in the tree search we propose to extract the information embedded in the parity bits by considering sums of parity bits which can be decided by part of the message bits analysis for the number of required message bits for obtaining sums of parity bits is provided the information contained in the parity bits can help to reduce the number of search tree edges

cross correlation between crude oil and refined product prices abstract in this paper we investigate cross correlations between crude oil and refined product prices based on the well known detrended cross correlation analysis dcca our findings indicate that the cross correlations are significant and strong furthermore the multifractality in cross correlations is also revealed the cross correlation coefficients are as high as 0 9 for larger time scales and are greater than those for smaller time scales two popular models vector error correction model and bivariate bekk volatility model are found to have very limited power in capturing long range cross correlations suggesting the drawbacks of these conventional models in actual applications long term cross correlations are stronger in recent ten years than those in the past decades

detrended multiple cross correlation coefficient abstract based on the detrended cross correlation coefficient x a x b we propose in this paper to establish a detrended multiple cross correlation coefficient d m c x 2 to be applied in order to quantify the relations between non stationary signals on different time scales this detrended multiple cross correlation coefficient will be the measure of the total association between the dependent variable y with the others i independent variables x it will be the generalization of x a x b for more than two independent variables to validate d m c x 2 we set up a cross correlation table ranging from 0 to 1 and we determined the detrended multiple cross correlation coefficient into simulated and real time series the results of this analysis show that the detrended multiple cross correlation coefficient may be suitable and useful to measure multiple cross correlations as we will see in this paper

backcasting and forecasting time series using detrended cross correlation analysis abstract in this paper we addressed the problem of backcasting and forecasting non stationary time series given that traditional backcasting are based on the classical cross correlation function assuming two stationary time series assumptions based on two non stationary time series need a new approach thus detrended cross correlation analysis dcca provides a fanned estimator for a correlation between two non stationary time series providing then the stationary time series therefore we developed a backcaster estimator and a predictor for the obtained stationary time series the practical example of a chilean cement production time series 1991 2015 illustrates our results

dcca cross correlation coefficient differentiation theoretical and practical approaches abstract we propose in this paper to establish a well defined relationship between d f a the long range auto correlation exponent and d c c a the long range cross correlation exponent respectively described by the dfa and dcca methods this relationship will be accomplished theoretically by differentiating the dcca cross correlation coefficient d c c a n also for some specific times series we apply this theory in order to establish its validity