incremental stochastic subgradient algorithms for convex optimization this paper studies the effect of stochastic errors on two constrained incremental subgradient algorithms the incremental subgradient algorithms are viewed as decentralized network optimization algorithms as applied to minimize a sum of functions when each component function is known only to a particular agent of a distributed network first the standard cyclic incremental subgradient algorithm is studied in this the agents form a ring structure and pass the iterate in a cycle when there are stochastic errors in the subgradient evaluations sufficient conditions on the moments of the stochastic errors are obtained that guarantee almost sure convergence when a diminishing step size is used in addition almost sure bounds on the algorithm s performance with a constant step size are also obtained next the markov randomized incremental subgradient method is studied this is a noncyclic version of the incremental algorithm where the sequence of computing agents is modeled as a time nonhomogeneous markov chain such a model is appropriate for mobile networks as the network topology changes across time in these networks convergence results and error bounds for the markov randomized method in the presence of stochastic errors for diminishing and constant step sizes are obtained

multifractal property of chinese stock market in the csi 800 index based on mf dfa approach abstract csi 800 index consists of csi 500 index and csi 300 index aiming to reflect the performance of stocks with large mid and small size of china a share market in this paper we analyze the multifractal structure of chinese stock market in the csi 800 index based on the multifractal detrended fluctuation analysis mf dfa method we find that the fluctuation of the closing logarithmic returns have multifractal properties the shape and width of multifractal spectrum are depended on the weighing order q more interestingly we observe a bigger market crash in june august 2015 than the one in 2008 based on the local hurst exponents the result provides important information for further study on dynamic mechanism of return fluctuation and whether it would trigger a new financial crisis

on the estimation of the large deviations spectrum we propose an estimation algorithm for large deviations spectra of measures and functions the algorithm converges for natural examples of multifractals

a second order multi agent network for bound constrained distributed optimization this technical note presents a second order multi agent network for distributed optimization with a sum of convex objective functions subject to bound constraints in the multi agent network the agents connect each others locally as an undirected graph and know only their own objectives and constraints the multi agent network is proved to be able to reach consensus to the optimal solution under mild assumptions moreover the consensus of the multi agent network is converted to the convergence of a dynamical system which is proved using the lyapunov method compared with existing multi agent networks for optimization the second order multi agent network herein is capable of solving more general constrained distributed optimization problems simulation results on two numerical examples are presented to substantiate the performance and characteristics of the multi agent network

multifractal analysis of ssec in chinese stock market a different empirical result from heng seng index abstract in this paper high frequency per 5 min data of shanghai stock exchange composite index ssec from january 1999 to july 2001 is analyzed by multifractal we find that the correlation of the parameters of the multifractal spectra with the variation of daily return z in ssec is noticeably different from that in previous studies of heng seng index in hong kong stock market sun et al phys a 291 2001 553 562 sun et al phys a 301 2001 473 482 so we suppose that there may not be a universal rule for the dependence of the parameters of the multifractal spectra with daily return of a stock index then we construct a new measurement of market risk based on multifractal spectra and test its ability of predicting index fluctuations with a more thorough method than that in sun et al phys a 301 2001 473 482

a collective neurodynamic approach to distributed constrained optimization this paper presents a collective neurodynamic approach with multiple interconnected recurrent neural networks rnns for distributed constrained optimization the objective function of the distributed optimization problems to be solved is a sum of local convex objective functions which may be nonsmooth subject to its local constraints each local objective function is minimized individually by using an rnn with consensus among others in contrast to existing continuous time distributed optimization methods the proposed collective neurodynamic approach is capable of solving more general distributed optimization problems simulation results on three numerical examples are discussed to substantiate the effectiveness and characteristics of the proposed approach in addition an application to the optimal placement problem is delineated to demonstrate the viability of the approach

dynamical model for dna sequences we address the problem of dna sequences developing a dynamical method based on the assumption that the statistical properties of dna paths are determined by the joint action of two processes one deterministic with long range correlations and the other random and ensuremath delta function correlated the generator of the deterministic evolution is a nonlinear map belonging to a class of maps recently tailored to mimic the processes of weak chaos that are responsible for the birth of anomalous diffusion it is assumed that the deterministic process corresponds to unknown biological rules that determine the dna path whereas the noise mimics the influence of an infinite dimensional environment on the biological process under study we prove that the resulting diffusion process if the effect of the random process is neglected is an ensuremath alpha stable l evy process with 12 we also show that if the diffusion process is determined by the joint action of the deterministic and the random process the correlation effects of the deterministic dynamics are cancelled on the short range scale but show up in the long range one we denote our prescription to generate statistical sequences as the copying mistake map cmm we carry out our analysis of several dna sequences and their cmm realizations with a variety of techniques and we especially focus on a method of regression to equilibrium which we call the onsager analysis with these techniques we establish the statistical equivalence of the real dna sequences with their cmm realizations we show that long range correlations are present in exons as well as in introns but are difficult to detect since the exon dynamics is shown to be determined by the entanglement of three distinct and independent cmm s

multifractal detrended fluctuation analysis based on fractal fitting the long range correlation detection method for highway volume data abstract in this paper we investigate the traffic time series for volume data observed on the guangshen highway we introduce a multifractal detrended fluctuation analysis based on fractal fitting mfdfa ff which is one of the most effective methods to detect long range correlations of time series through effective detecting of long range correlations highway volume can be predicted more accurately in order to get a better detrend effect we use fractal fitting to replace polynomial fitting in detrend process the result shows that fractal fitting can get a better detrend effect than polynomial fitting and the mfdfa ff method can achieve a more accurate research result then we introduce the legendre spectrum to detect the multifractal property characterized by the long range correlation and multifractality of guangshen highway volume data

constrained consensus algorithms with fixed step size for distributed convex optimization over multiagent networks in this technical note we are concerned with constrained consensus algorithms for distributed convex optimization with a sum of convex objective functions subject to local bound and equality constraints in multiagent networks each agent has its own data on objective function and constraints all the agents cooperatively find the minimizer while each agent can only communicate with its neighbors the consensus of multiagent networks with time invariant and undirected graphs is proven by the lyapunov method compared with existing consensus algorithms for distributed optimization with diminishing step sizes the proposed algorithms with fixed step size have better convergence rate simulation results on a numerical example are presented to substantiate the performance and characteristics of the proposed algorithms

distributed algorithm for solving convex inequalities in this note a distributed subgradient based algorithm is proposed for continuous time multi agent systems to search a feasible solution to convex inequalities the algorithm involves each agent achieving a state constrained by its own inequalities while exchanging local information with other agents under a time varying directed communication graph with the validity of a mild connectivity condition associated with the communication graph it is shown that all agents will reach agreement asymptotically and the consensus state is in the solution set of the inequalities furthermore the method is also extended to solving the distributed optimization problem of minimizing the sum of local objective functions subject to convex inequalities simulation examples are presented to demonstrate the effectiveness of the theoretical results

effect of nonlinear filters on detrended fluctuation analysis when investigating the dynamical properties of complex multiple component physical and physiological systems it is often the case that the measurable system s output does not directly represent the quantity we want to probe in order to understand the underlying mechanisms instead the output signal is often a linear or nonlinear function of the quantity of interest here we investigate how various linear and nonlinear transformations affect the correlation and scaling properties of a signal using the detrended fluctuation analysis dfa which has been shown to accurately quantify power law correlations in nonstationary signals specifically we study the effect of three types of transforms i linear y i a x i b ii nonlinear polynomial y i a x k i and iii nonlinear logarithmic y i log x i delta filters we compare the correlation and scaling properties of signals before and after the transform we find that linear filters do not change the correlation properties while the effect of nonlinear polynomial and logarithmic filters strongly depends on a the strength of correlations in the original signal b the power k of the polynomial filter and c the offset delta in the logarithmic filter we further apply the dfa method to investigate the apparent scaling of three analytic functions i exponential exp x a ii logarithmic log x a and iii power law x a lambda which are often encountered as trends in physical and biological processes while these three functions have different characteristics we find that there is a broad range of values for parameter a common for all three functions where the slope of the dfa curves is identical we further note that the dfa results obtained for a class of other analytic functions can be reduced to these three typical cases we systematically test the performance of the dfa method when estimating long range power law correlations in the output signals for different parameter values in the three types of filters and the three analytic functions we consider

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

multifractal and singularity analysis of highway volume data abstract recent work has shown that the mathematics of multifractal can be used to provide a quantitative signature in many fields in this paper we investigate the traffic time series for volume data observed on guangshen highway firstly we find there exists a multifractal behavior in the traffic data and the data on both work days and rest days have similar multifractality then we study the singularity of these data a singularity exponent method based on multifractal theory is proposed to extract or classify singular data which is more precise and clear than the holder exponent method

assessing market uncertainty by means of a time varying intermittency parameter for asset price fluctuations abstract maximum likelihood estimation techniques for multifractal processes are applied to high frequency data in order to quantify intermittency in the fluctuations of asset prices from time records as short as one month these methods permit extraction of a meaningful intermittency parameter characterising the degree of volatility clustering we can therefore study the time evolution of volatility clustering and test the statistical significance of this variability by analysing data from the oslo stock exchange and comparing the results with the investment grade spread we find that the estimates of are lower at times of high market uncertainty

distributed continuous time approximate projection protocols for shortest distance optimization problems in this paper we investigate a distributed shortest distance optimization problem for a multi agent network to cooperatively minimize the sum of the quadratic distances from some convex sets where each set is only associated with one agent to deal with this optimization problem with projection uncertainties we propose a distributed continuous time dynamical protocol where each agent can only obtain an approximate projection and communicate with its neighbors over a time varying communication graph first we show that no matter how large the approximate angle is system states are always bounded for any initial condition and uniformly bounded with respect to all initial conditions if the inferior limit of the stepsize is greater than zero then in both cases of nonempty and empty intersection of convex sets we provide stepsize and approximate angle conditions to ensure the optimal convergence respectively moreover we also give some characterizations about the optimal solutions for the empty intersection case

network flows that solve linear equations we study distributed network flows as solvers in continuous time for the linear algebraic equation mathbf z mathbf h mathbf y each node i has access to a row mathbf h i mathrm t of the matrix mathbf h and the corresponding entry z i in the vector mathbf z the first consensus projection flow under investigation consists of two terms one from standard consensus dynamics and the other contributing to projection onto each affine subspace specified by the mathbf h i and z i the second projection consensus flow on the other hand simply replaces the relative state feedback in consensus dynamics with projected relative state feedback without dwell time assumption on switching graphs we prove that all node states converge to a common solution of the linear algebraic equation if there is any the convergence is global for the consensus projection flow while local for the projection consensus flow in the sense that the initial values must lie on the affine subspaces if the linear equation has no exact solutions we show that the node states can converge to a ball around the least squares solution whose radius can be made arbitrarily small through selecting a sufficiently large gain for the consensus projection flow for a fixed bidirectional graph semi global convergence to approximate least squares solutions is also demonstrated for switching balanced directed graphs under suitable conditions it is also shown that the projection consensus flow drives the average of the node states to the least squares solution with a complete graph numerical examples are provided as illustrations of the established results

scale invariant distribution and multifractality of volatility multipliers in stock markets abstract the statistical properties of the multipliers of the absolute returns are investigated using 1 min high frequency data of financial time series the multiplier distribution is found to be independent of the box size s when s is larger than some crossover scale providing direct evidence of the existence of scale invariance in financial data the multipliers with base a 2 are well approximated by a normal distribution and the most probable multiplier scales as a power law with respect to the base a we unravel that the volatility multipliers possess multifractal nature which is independent of construction of the multipliers that is the values of s and a

scaling characteristics in the taiwan stock market some statistical tools including histogram spectral analysis and fractal theory were used on the daily taiwan stock price index tspi from 1987 to 2002 to examine the possible scale invariant behavior and the clustering characteristics in taiwan stock market it was found that the tspi data exhibited the characteristic of right skewed frequency distribution the long term memory and the possibility of scale invariance were roughly identified through the analysis of autocorrelation and power spectrum respectively the monofractal analysis was then performed by the box counting method scale invariance was clearly found in the time series and the box dimension was shown to be a decreasing function of the threshold index level implying multifractal characteristics i e the low and high regions scale differently to test this hypothesis the time series were transferred into a useful compact form through the multifractal formalism namely the q q and f plots the analysis confirmed the existence of multifractal characteristics in the investigated time series the origin of multifractal phenomena in taiwan stock market might be interpreted in terms of the multiplicative cascade process of stock market information

scaling range and cutoffs in empirical fractals fractal structures appear in a vast range of physical systems a literature survey including all experimental papers on fractals which appeared in the six physical review journals a char21 e and letters during the 1990s shows that experimental reports of fractal behavior are typically based on a scaling range ensuremath delta that spans only 0 5 char21 2 decades this range is limited by upper and lower cutoffs either because further data are not accessible or due to crossover bends focusing on spatial fractals a classification is proposed into a aggregation b porous media c surfaces and fronts d fracture and e critical phenomena most of these systems except for class e involve processes far from thermal equilibrium the fact that for self similar fractals in contrast to the self affine fractals of class c there are hardly any exceptions to the finding of ensuremath delta l 2 decades raises the possibility that the cutoffs are due to intrinsic properties of the measured systems rather than the specific experimental conditions and apparatus to examine the origin of the limited range we focus on a class of aggregation systems in these systems a molecular beam is deposited on a surface giving rise to nucleation and growth of diffusion limited aggregation like clusters scaling arguments are used to show that the required duration of the deposition experiment increases exponentially with ensuremath delta furthermore using realistic parameters for surfaces such as al 111 it is shown that these considerations limit the range of fractal behavior to less than two decades in agreement with the experimental findings it is conjectured that related kinetic mechanisms that limit the scaling range are common in other nonequilibrium processes that generate spatial fractals

perturbation theorems for estimating magnitudes of roots of polynomials two additional new theorems are posed and proven to estimate the magnitudes of roots of polynomials perturbation theory and the order of magnitude of terms are employed to develop the theorems the theorems may be useful to estimate the order of magnitudes of the roots of a polynomial a priori before solving the equation the theorems are developed for two special classes of polynomials of arbitrary order with their coefficients satisfying certain conditions numerical applications of the theorems are presented as examples it is shown that the theorems produce good estimates for the magnitudes of roots

a simple analytics framework for evaluating mean escape time in different term structures with stochastic volatility abstract the aim of this paper is to propose a simple framework for analyzing the mean escape time of interest rate product in different term structures with stochastic volatility in the modeling perspective we utilize the one factor hull white model to design the dynamics of interest rate returns whose stochastic volatility term is assumed to follow the cox ingersoll ross process furthermore we apply the nelson siegel function to simulate various scenarios of term structure based on the us treasury bill and european bond then we analyze the mean escape time surfaces of different term structures for theoretical flat yield curves and two empirical s shaped yield curves whose term structures of short mid and long term maturities are shifted by the modified parameters of the nelson siegel function we observe that the survival probability begins with one and reduces to zero with different rate of decay for different interest rates and volatilities furthermore the results of empirical term structures imply that the adjustment in the yield of long term maturity changes the structure of met surface more significantly than that of short and long term maturities lastly we detect the noise enhanced stability phenomenon from the mean escape time for all cases of flat yield treasury bill and european bond

predictability of multifractal analysis of hang seng stock index in hong kong in this paper the daily hang seng index in hong kong stock market is studied by multifractal analysis the main parameter of multifractal spectra used is f which can be used to characterize the ratio of number of highest index moments to that of lowest ones the dependence of today s gain probability g and the day s index increase probability n with f of the previous 3 days are studied it is found that g and n can reach 70 80 at the large positive f region and can be very close to 20 at the big negative f region the predictability decreases with the increasing number of the previous days

distributed continuous time optimization nonuniform gradient gains finite time convergence and convex constraint set in this paper a distributed optimization problem with general differentiable convex objective functions is studied for continuous time multi agent systems with single integrator dynamics the objective is for multiple agents to cooperatively optimize a team objective function formed by a sum of local objective functions with only local interaction and information while explicitly taking into account nonuniform gradient gains finite time convergence and a common convex constraint set first a distributed nonsmooth algorithm is introduced for a special class of convex objective functions that have a quadratic like form it is shown that all agents reach a consensus in finite time while minimizing the team objective function asymptotically second a distributed algorithm is presented for general differentiable convex objective functions in which the interaction gains of each agent can be self adjusted based on local states a corresponding condition is then given to guarantee that all agents reach a consensus in finite time while minimizing the team objective function asymptotically third a distributed optimization algorithm with state dependent gradient gains is given for general differentiable convex objective functions it is shown that the distributed continuous time optimization problem can be solved even though the gradient gains are not identical fourth a distributed tracking algorithm combined with a distributed estimation algorithm is given for general differentiable convex objective functions it is shown that all agents reach a consensus while minimizing the team objective function in finite time fifth as an extension of the previous results a distributed constrained optimization algorithm with nonuniform gradient gains and a distributed constrained finite time optimization algorithm are given it is shown that both algorithms can be used to solve a distributed continuous time optimization problem with a common convex constraint set numerical examples are included to illustrate the obtained theoretical results

stochastic gradient push for strongly convex functions on time varying directed graphs we investigate the convergence rate of the recently proposed subgradient push method for distributed optimization over time varying directed graphs the subgradient push method can be implemented in a distributed way without requiring knowledge of either the number of agents or the graph sequence each node is only required to know its out degree at each time our main result is a convergence rate of o ln t t for strongly convex functions with lipschitz gradients even if only stochastic gradient samples are available this is asymptotically faster than the o ln t sqrt t rate previously known for general convex functions

multifractal analysis of hang seng index in hong kong stock market abstract in this paper the daily hang seng index in hong kong stock market is analyzed by multifractal the correlation of the parameters of the multifractal spectra with the variation of close return z is studied statistically it is found that the amount of the variation of return is correlated with the amount of of that day the increase or decrease of the return is related to the positive or negative value of f the gain probability and the increasing day s probability can be higher than 70 at the larger f region and be lower than 20 at the more negative region

forecasting volatility in shanghai and shenzhen markets based on multifractal analysis abstract this paper analyzes the multifractality in shanghai and shenzhen stock markets using multifractal spectrum analysis and multifractal detrended fluctuation analysis we find that the main source of multifractality is long range correlations of large and small fluctuations then we introduce a multifractal volatility measure mv and find that by taking mv as daily conditional volatility the simulated series displayed similar stylized facts to the original daily return series by capturing the dynamics of mv using the arfima model we find that the out of sample forecasting performance of the arfima mv model is better than some garch class models and the arfima rv model under some criteria of loss function

measuring daily value at risk of ssec index a new approach based on multifractal analysis and extreme value theory abstract recent studies in the econophysics literature reveal that price variability has fractal and multifractal characteristics not only in developed financial markets but also in emerging markets taking high frequency intraday quotes of the shanghai stock exchange component ssec index as example this paper proposes a new method to measure daily value at risk var by combining the newly introduced multifractal volatility mfv model and the extreme value theory evt method two var backtesting techniques are then employed to compare the performance of the model with that of a group of linear and nonlinear generalized autoregressive conditional heteroskedasticity garch models the empirical results show the multifractal nature of price volatility in chinese stock market var measures based on the multifractal volatility model and evt method outperform many garch type models at high risk levels

distributed convex optimization via continuous time coordination algorithms with discrete time communication this paper proposes a novel class of distributed continuous time coordination algorithms to solve network optimization problems whose cost function is a sum of local cost functions associated to the individual agents we establish the exponential convergence of the proposed algorithm under i strongly connected and weight balanced digraph topologies when the local costs are strongly convex with globally lipschitz gradients and ii connected graph topologies when the local costs are strongly convex with locally lipschitz gradients when the local cost functions are convex and the global cost function is strictly convex we establish asymptotic convergence under connected graph topologies we also characterize the algorithm s correctness under time varying interaction topologies and study its privacy preservation properties motivated by practical considerations we analyze the algorithm implementation with discrete time communication we provide an upper bound on the stepsize that guarantees exponential convergence over connected graphs for implementations with periodic communication building on this result we design a provably correct centralized event triggered communication scheme that is free of zeno behavior finally we develop a distributed asynchronous event triggered communication scheme that is also free of zeno with asymptotic convergence guarantees several simulations illustrate our results

multifractality in stock indexes fact or fiction abstract multifractal analysis and extensive statistical tests are performed upon intraday minutely data within individual trading days for four stock market indexes including hsi szsc s p 500 and nasdaq to check whether the indexes instead of the returns possess multifractality we find that the mass exponent q is linear and the singularity q is close to 1 for all trading days and all indexes furthermore we find strong evidence showing that the scaling behaviors of the original data sets cannot be distinguished from those of shuffled time series hence the so called multifractality in the intraday stock market indexes is merely an illusion

a convergent incremental gradient method with a constant step size an incremental aggregated gradient method for minimizing a sum of continuously differentiable functions is presented the method requires a single gradient evaluation per iteration and uses a constant step size for the case that the gradient is bounded and lipschitz continuous we show that the method visits infinitely often regions in which the gradient is small under certain unimodality assumptions global convergence is established in the quadratic case a global linear rate of convergence is shown the method is applied to distributed optimization problems arising in wireless sensor networks and numerical experiments compare the new method with other incremental gradient methods

gossip algorithms for convex consensus optimization over networks in many applications nodes in a network desire not only a consensus but an optimal one to date a family of subgradient algorithms have been proposed to solve this problem under general convexity assumptions this technical note shows that for the scalar case and by assuming a bit more novel non gradient based algorithms with appealing features can be constructed specifically we develop pairwise equalizing pe and pairwise bisectioning pb two gossip algorithms that solve unconstrained separable convex consensus optimization problems over undirected networks with time varying topologies where each local function is strictly convex continuously differentiable and has a minimizer we show that pe and pb are easy to implement bypass limitations of the subgradient algorithms and produce switched nonlinear networked dynamical systems that admit a common lyapunov function and asymptotically converge moreover pe generalizes the well known pairwise averaging and randomized gossip algorithm while pb relaxes a requirement of pe allowing nodes to never share their local functions

a multi agent system with a proportional integral protocol for distributed constrained optimization this technical note presents a continuous time multi agent system for distributed optimization with an additive objective function composed of individual objective functions subject to bound equality and inequality constraints each individual objective function is assumed to be convex in the region defined by its local bound constraints only without the need to be globally convex all agents in the system communicate using a proportional integral protocol with their output information instead of state information to reduce communication bandwidth it is proved that all agents with any initial state can reach output consensus at an optimal solution to the given constrained optimization problem provided that the graph describing the communication links among agents is undirected and connected it is further proved that the system with only integral protocol is also convergent to the unique optimal solution if each individual objective function is strictly convex simulation results are presented to substantiate the theoretical results

enlightenment from various conditional probabilities about hang seng index in hong kong stock market abstract the daily hang seng index in the hong kong stock market has been analyzed in this paper two kinds of sign sequences as given conditions have been used to predict the future price movements one is the parameter of multifractal spectrum f based on the indexes recorded in every minute and the other is the variation of the close index i results show that correlation between large fluctuations of the close price and the condition in these two methods is strong and some sign sequences of the parameter f can be used to predict the probability of the near future price movements

forecasting volatility of ssec in chinese stock market using multifractal analysis abstract in this paper taking about 7 years high frequency data of the shanghai stock exchange composite index ssec as an example we propose a daily volatility measure based on the multifractal spectrum of the high frequency price variability within a trading day an arfima model is used to depict the dynamics of this multifractal volatility mfv measures the one day ahead volatility forecasting performances of the mfv model and some other existing volatility models such as the realized volatility model stochastic volatility model and garch are evaluated by the superior prediction ability spa test the empirical results show that under several loss functions the mfv model obtains the best forecasting accuracy

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

which is the better forecasting model a comparison between har rv and multifractality volatility abstract in this paper by taking the 5 min high frequency data of the shanghai composite index as example we compare the forecasting performance of har rv and multifractal volatility realized volatility realized bipower variation and their corresponding short memory model with rolling windows forecasting method and the model confidence set which is proved superior to spa test the empirical results show that for six loss functions har rv outperforms other models moreover to make the conclusions more precise and robust we use the mcs test to compare the performance of their logarithms form models and find that the har log rv has a better performance in predicting future volatility furthermore by comparing the two models of har rv and har log rv we conclude that in terms of performance forecasting the har log rv model is the best model among models we have discussed in this paper

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

multifractal description of stock price index fluctuation using a quadratic function fitting abstract in order to obtain a quantitative multifractal characterization of the stock price index the multifractal spectrum of shanghai stock price index time series in 2005 was investigated and the multifractal spectrum was fitted using a quadratic function a sliding window of 240 frequency data in 5 trading days was used to investigate the stock price index fluctuation the multifractal parameters and coefficients in each window were obtained by fitting the local multifractal spectrum using a quadratic function it is found that when the stock price index fluctuates sharply a strong variability is clearly characterized by the multifractal parameters and the quadratic function coefficients this has led to a better understanding of complex stock markets

distributed adaptive convex optimization on directed graphs via continuous time algorithms this note considers the distributed optimization problem on directed graphs with nonconvex local objective functions and the unknown network connectivity a new adaptive algorithm is proposed to minimize a differentiable global objective function by introducing dynamic coupling gains and updating the coupling gains using relative information of system states the nonconvexity of local objective functions unknown network connectivity and the uncertain dynamics caused by locally lipschitz gradients are tackled concurrently consequently the global asymptotic convergence is established when the global objective function is strongly convex and the gradients of local objective functions are only locally lipschitz when the communication graph is strongly connected and weight balanced the algorithm is independent of any global information then the algorithm is naturally extended to unbalanced directed graphs by using the left eigenvector of the laplacian matrix associated with the zero eigenvalue several numerical simulations are presented to verify the results

zero gradient sum algorithms for distributed convex optimization the continuous time case this technical note presents a set of continuous time distributed algorithms that solve unconstrained separable convex optimization problems over undirected networks with fixed topologies the algorithms are developed using a lyapunov function candidate that exploits convexity and are called zero gradient sum zgs algorithms as they yield nonlinear networked dynamical systems that evolve invariantly on a zero gradient sum manifold and converge asymptotically to the unknown optimizer we also describe a systematic way to construct zgs algorithms show that a subset of them actually converge exponentially and obtain lower and upper bounds on their convergence rates in terms of the network topologies problem characteristics and algorithm parameters including the algebraic connectivity laplacian spectral radius and function curvatures the findings of this technical note may be regarded as a natural generalization of several well known algorithms and results for distributed consensus to distributed convex optimization

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

approximate periodic solutions for the helmholtz duffing equation approximate periodic solutions for the helmholtz duffing oscillator are obtained in this paper he s energy balance method hebm and he s frequency amplitude formulation hfaf are adopted as the solution methods oscillation natural frequencies are analytically analyzed error analysis is carried out and accuracy of the solution methods is evaluated

asymmetric market efficiency using the index based asymmetric mfdfa abstract we explore the asymmetric market efficiency for various countries stock indices using the index based asymmetric mfdfa we divide market based on its trend within certain sub period then we test whether the overall up and down trend markets are efficient via the asymmetric generalized hurst exponent at first we provide the criteria for testing the asymmetric market efficiency based on the monte carlo simulation using the brownian motion secondly we analyze the asymmetric market efficiency of 34 countries for different sub periods by comparing the hurst exponents of original and shuffled time series we discover that the sources of inefficiency are different with respect to time periods by presenting the groups of countries based on the asymmetric market inefficiency lastly we discuss a time varying feature of market efficiency where the wider gap between the up and down trend efficiency and the stronger correlation between stock index and the asymmetric hurst exponent are discovered during the financial crisis

randomness and degrees of irregularity the fundamental question are sequential data random arises in myriad contexts often with severe data length constraints furthermore there is frequently a critical need to delineate nonrandom sequences in terms of closeness to randomness e g to evaluate the efficacy of therapy in medicine we address both these issues from a computable framework via a quantification of regularity apen approximate entropy defining maximal randomness for sequences of arbitrary length indicating the applicability to sequences as short as n 5 points an infinite sequence formulation of randomness is introduced that retains the operational and computable features of the finite case in the infinite sequence setting we indicate how the foundational definition of independence in probability theory and the definition of normality in number theory reduce to limit theorems without rates of convergence from which we utilize apen to address rates of convergence of a deficit from maximal randomness refining the aforementioned concepts in a computationally essential manner representative applications among many are indicated to assess i random number generation output ii well shuffled arrangements and iii the quality of bootstrap replicates

multifractal properties of chinese stock market in shanghai abstract in this article we apply three methods of multifractal analysis partition function method singular spectrum method and multifractal detrended fluctuation analysis method to analyze the closing index fluctuations of shanghai stock market during the past seven years we have found that shanghai stock market has weak multifractal features and there are long range power law correlations between index series the shapes of singular spectrums do not change with time scales and their strengths weaken when the scales shorten but when the orders of partition function increase the strengths of multifractal increase the singular spectrums become rougher and the general hurst exponents decrease these results provide solid and important values for further study on the dynamic mechanism of stock market price fluctuation

a new perturbation technique in solution of nonlinear differential equations by using variable transformation a perturbation algorithm using a new variable transformation is introduced this transformation enables control of the independent variable of the problem the problems are solved with new transformation classical duffing equation with cubic nonlinear term and a singular perturbation problem results of multiple scales lindstedt poincare method new method and numerical solutions are contrasted

distributed optimal in network resource allocation algorithm design via a control theoretic approach abstract in this paper we consider an in network optimal resource allocation problem with multiple demand equations we propose a novel distributed continuous time algorithm that solves the problem over strongly connected and weight balanced digraph network topologies when the local cost functions are strongly convex we also discuss the extension of our convergence guarantees to dynamically changing topologies finally we show that if the network is an undirected connected graph we can guarantee stability and convergence of our algorithm for problems involving local convex functions this convergence guarantee is to a point in the set of minimizers of our optimal resource allocation problem the design and analysis of our algorithm are carried out using a control theoretic approach we demonstrate our results through a numerical example

on linstedt poincare techniques for the quintic duffing equation abstract an artificial parameter method for the quintic duffing equation is presented the method is based on the introduction of a linear stiffness term and a new dependent variable both of which are proportional to the unknown frequency of oscillation the introduction of an artificial parameter and the expansion of both the solution and the unknown frequency of oscillation in series of the artificial parameter and results in linear ordinary differential equations at each order in the parameter by imposing the nonsecularity condition at each order in the expansion the method provides different approximations to both the solution and the frequency of oscillation the method does not require that a small parameter be present in the governing equation and its results are compared with those of linstedt poincare modified linstedt poincare harmonic balance and galerkin techniques it is shown that these four techniques predict the same first order approximation to the frequency of oscillation as the artificial parameter method presented in this paper and the latter introduces higher order corrections at second order whereas similar corrections are introduced by the linstedt poincare and modified linstedt poincare methods at orders equal to and higher than three

random cascade model in the limit of infinite integral scale as the exponential of a nonstationary 1 f noise application to volatility fluctuations in stock markets in this paper we propose a new model for volatility fluctuations in financial time series this model relies on a nonstationary gaussian process that exhibits aging behavior it turns out that its properties over any finite time interval are very close to continuous cascade models these latter models are indeed well known to reproduce faithfully the main stylized facts of financial time series however it involves a large scale parameter the so called integral scale where the cascade is initiated that is hard to interpret in finance moreover the empirical value of the integral scale is in general deeply correlated to the overall length of the sample this feature is precisely predicted by our model which as illustrated by various examples from daily stock index data quantitatively reproduces the empirical observations