can one make any crash prediction in finance using the local hurst exponent idea abstract we apply the hurst exponent idea for investigation of djia index time series data the behavior of the local hurst exponent prior to drastic changes in financial series signal is analyzed the optimal length of the time window over which this exponent can be calculated in order to make some meaningful predictions is discussed our prediction hypothesis is verified with examples of 1929 and 1987 crashes as well as with more recent phenomena in stock market from the period 1995 to 2003 some interesting agreements are found

cross correlations between baltic dry index and crude oil prices this paper examines the cross correlation properties of baltic dry index bdi and crude oil prices using cross correlation statistics test and multifractal detrended cross correlation analysis mf dcca the empirical results show that the cross correlations between bdi and crude oil prices are significantly multifractal by introducing the concept of a crossover we find that the cross correlations are strongly persistent in the short term and weakly anti persistent in the long term moreover cross correlations of all kinds of fluctuations are persistent in the short time while cross correlations of small fluctuations are persistent and those of large fluctuations are anti persistent in the long term we have also verified that the multifractality of the cross correlations of bdi and crude oil prices is both attributable to the persistence of fluctuations of time series and fat tailed distributions

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

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

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

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

an optimization based domain decomposition method for partial differential equations abstract an optimization based domain decomposition method for the solution of partial differential equations is presented the crux of the method is a constrained minimization problem for which the objective functional measures the jump in the dependent variables across the common boundaries between subdomains the constraints are the partial differential equations the existence of optimal solutions for the optimization problem is shown as is the convergence to the exact solution of the given problem we then derive an optimality system of partial differential equations from which solutions of the domain decomposition problem may be determined finite element approximations to solutions of the optimality system are defined and analyzed as well as an eminently parallelizable gradient method for solving the optimality system then the results of some numerical experiments and some concluding remarks are given the latter includes the extension of the method to nonlinear problems such as the navier stokes equations

an optimization based domain decomposition method for pdes with random inputs an optimization based domain decomposition method for stochastic elliptic partial differential equations is presented the main idea of the method is a constrained optimization problem for which the minimization of an appropriate functional forces the solutions on the two subdomains to agree on the interface the constraints are the stochastic partial differential equations the existence of optimal solutions for the stochastic optimal control problem is shown as is the convergence to the exact solution of the given problem we prove the existence of a lagrange multiplier and derive an optimality system from which solutions of the domain decomposition problem may be determined finite element approximations to the solutions of the optimality system are defined and analyzed with respect to both spatial and random parameter spaces then the results of some numerical experiments are given to confirm theoretical error estimate results

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

sad and stock returns revisited nonlinear analysis based on mf dcca and granger test abstract using both multifractal detrended fluctuation analysis mf dfa and multifractal detrended cross correlation analysis mf dcca methods this paper examines the effects of seasonal affective disorder sad on stock returns in the chinese stock market we first separate stocks into small and large cap stocks according to market value and find that sad and these two stock return series are multifractal based on mf dfa moreover we employ mf dcca and show that the cross correlation between sad and stock returns is anti persistent and the cross correlation between sad and return of small cap stock is stronger than that between sad and return of large cap stock furthermore we find that long range correlation is the main source of multifractality in the cross correlations between sad and small cap stock while both long range correlation and fat tails contribute to the multifractality between sad and large cap stock finally utilizing nonlinear granger causality test we find that sad is the granger cause of stock returns not vice versa

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

a domain decomposition method for optimization problems for partial differential equations abstract a nonoverlapping domain decomposition method for optimization problems for partial differential equations is presented the domain decomposition is effected through an auxiliary optimization problem this results in an multiobjective optimization problem involving the given functional and the auxiliary functional the existence of an optimal solution to the multiobjective optimization problem is proved as are convergence estimates as the parameters used to regularize the problem penalty parameters and to combine the two objective functionals tend to zero an optimality system for the optimal solution is derived and used to define a gradient method convergence results are obtained for the gradient method and the results of some numerical experiments are obtained then unregularized problems having vanishing penalty parameters are discussed

finite element approximation of soluble surfactant spreading on a thin film we consider a fully practical finite element approximation of the following system of nonlinear degenerate parabolic equations begin align frac partial u partial t frac12 nabla cdot u 2 nabla sigma v frac13 nabla cdot u 3 nabla w 0 w c delta u delta u nu a u 3 hspace 0 1cm frac partial v partial t nabla cdot u v nabla sigma v frac12 nabla cdot u 2 v nabla w rho s delta v k left psi v right 0 frac partial psi partial t frac12 u nabla sigma v cdot nabla psi frac13 u 2 nabla w cdot nabla psi rho b u 1 nabla cdot left u nabla psi right beta k u 1 psi v 0 hspace 2cm nonumber end align the above equations model a marangoni driven thin film laden with a soluble surfactant in which the bulk surfactant concentration has been vertically averaged the model accounts for the presence of both attractive a geq 0 and repulsive delta 0 with nu 3 van der waals forces here u is the height of the film v is the concentration of the interfacial surfactant species psi is the concentration of the surfactant species within the bulk phase and sigma v 1 v is the typical surface tension moreover rhos geq 0 rhob 0 and c 0 are the inverses of the surface peclet number the bulk peclet number and the modified capillary number respectively finally beta 0 and k 0 are parameters that characterize the solubility and the rate of interfacial adsorption in addition to showing stability bounds for our approximation we prove convergence and hence existence of a solution to this nonlinear degenerate parabolic system i in one space dimension when rhos 0 and moreover ii in two space dimensions if in addition nu geq 7 furthermore iterative schemes for solving the resulting nonlinear discrete system are discussed finally some numerical experiments are presented

existence of solution for a micro macro model of polymeric fluid the fene model abstract we analyse a non linear micro macro model of polymeric fluids in the case of a shear flow more precisely we consider the fene dumbbell model which models polymers by nonlinear springs accounting for the finite extensibility of the polymer chain we prove the existence of a unique solution to the stochastic differential equation which rules the evolution of a representative polymer in the flow and next deduce a local in time existence and uniqueness result on the system coupling the stochastic differential equation and the momentum equation on the fluid

continuity of velocity gradients in suspensions of rod like molecules we investigate the doi model for suspensions of rod like molecules in the dilute regime for certain parameter values the velocity gradient vs stress relation defined by the stationary and homogeneous flow is not rank one monotone we then consider the evolution of possibly large perturbations of stationary flows we prove that even in the absence of a microscopic cut off discontinuities in the velocity gradient cannot occur in finite time the proof relies on a novel type of estimate for the smoluchowski equation

an optimization based domain decomposition method for the navier stokes equations an optimization based nonoverlapping domain decomposition method for the solution of the navier stokes equations is presented the crux of the method is a constrained minimization problem for which the objective functional measures the jump in the dependent variables across the common boundaries between subdomains the constraints are the navier stokes equations in the subdomains with suitably chosen boundary conditions along the interfaces we show that solutions of the minimization problem exist and derive an optimality system from which these solutions may be determined finite element approximations of the solutions of the optimality system are examined the domain decomposition method is also reformulated as a nonlinear least squares problem and the results of some numerical experiments are given

an optimization based domain decomposition method for parabolic equations an optimization based non overlapping domain decomposition method for the solution of the heat equation is presented the crux of the method is a constrained minimization problem for which the objective functional measures the jump in the dependent variables across the common boundaries between subdomains the existence of an optimal solution is proved as is convergence of optimal solutions an optimality system for the optimal solution is derived and used to define a gradient method convergence results are obtained for the gradient method and the results of some numerical experiments are obtained

dynamic relationship between chinese rmb exchange rate index and market anxiety a new perspective based on mf dcca abstract this paper employs multifractal detrended cross correlation analysis mf dcca to study the cross correlations between the chinese rmb exchange rate index and market anxiety using data from june 21 2010 to december 28 2018 cross correlation statistics and coefficients verify the existence of cross correlations and the mf dcca method quantitatively confirms the presence of multifractality between the chinese rmb index and market anxiety for both the long and short term the results of the rolling window analysis reveal that cross correlation scaling exponents of the chinese rmb index and market anxiety are sensitive to external shocks

cross correlations between price and volume in chinese gold markets abstract we apply the multifractal detrended cross correlation analysis mf dcca method to investigate the cross correlation behaviors between price and volume in chinese gold spot and futures markets qualitatively we find that the price and volume series are significantly cross correlated using the cross correlation test statistics q c c m and the d c c a coefficients quantitatively by employing the mf dcca analysis we find that there is a power law cross correlation and significant multifractal features between price and volume in gold spot and futures markets furthermore by comparing the multifractality of the original series to the shuffled and surrogated series we find that for the gold spot market the main contribution of multifractality is fat tail distribution for the gold futures market both long range correlations and fat tail distributions play important roles in the contribution of multifractality finally by employing the method of rolling windows we undertake further investigation into the time varying features of the cross correlations between price and volume we find that for both spot and futures markets the cross correlations are anti persistent in general in the short term the cross correlation shows obvious fluctuations due to exogenous shocks while in the long term the relationship tends to be at a metastable level due to the dynamic mechanism

existence of global weak solutions to finitely extensible nonlinear bead spring chain models for dilute polymers with variable density and viscosity abstract we prove the existence of global in time weak solutions to a general class of coupled bead spring chain models that arise from the kinetic theory of dilute solutions of nonhomogeneous polymeric liquids with noninteracting polymer chains with finitely extensible nonlinear elastic fene spring potentials the class of models under consideration involves the unsteady incompressible navier stokes equations with variable density and density dependent dynamic viscosity in a bounded domain in r d d 2 or 3 for the density the velocity and the pressure of the fluid with an elastic extra stress tensor appearing on the right hand side in the momentum equation the extra stress tensor stems from the random movement of the polymer chains and is defined by the kramers expression through the associated probability density function that satisfies a fokker planck type parabolic equation a crucial feature of which is the presence of a centre of mass diffusion term and a nonlinear density dependent drag coefficient we require no structural assumptions on the drag term in the fokker planck equation in particular the drag term need not be corotational with initial density 0 min max for the continuity equation where min 0 a square integrable and divergence free initial velocity datum u 0 for the navier stokes equation and a nonnegative initial probability density function 0 for the fokker planck equation which has finite relative entropy with respect to the maxwellian m associated with the spring potential in the model we prove via a limiting procedure on certain regularization parameters the existence of a global in time weak solution t t u t t to the coupled navier stokes fokker planck system satisfying the initial condition 0 u 0 0 0 u 0 0 such that t t min max t u t belongs to the classical leray space and t t has bounded relative entropy with respect to m and t t m has integrable fisher information w r t the gibbs measure d m q d q d x over any time interval 0 t t 0