assessing the order of dependence for partially exchangeable binary data abstract the problem we consider is how to assess the order of serial dependence within partially exchangeable binary sequences we obtain exact conditional tests comparing any two orders by finding the conditional distribution of data given certain transition counts these tests are facilitated with a new monte carlo scheme asymptotic tests are also discussed in particular we show that the likelihood ratio tests have an asymptotic chi squared distribution thus generalizing the results of billingsley for the particular case of markov chains we apply these methods to several datasets and perform a simulation to study their properties

integral criteria for a classification of solutions of linear differential equations are positive continuous function on the interval 0 co by solution we always mean a continuously differentiable function such that r t x t has a continuous derivative satisfying e when the func tion r is continuous but does not have a continuous derivative e can be interpreted as the first order system for the vector x y x rx 381

nonoscillation results for third order nonlinear differential equations abstract criteria are obtained in order that all nontrivial solutions of the third order nonlinear eqs a y q t y sgn y 0 and b y q t y sgn y 0 are nonoscillatory where 0 and q t is positive and continuous on 0 these results extend and complement previous results of kura and also may be considered as third order analogues of results for the second order nonlinear equations

stochastic resonance of drawdown risk in energy market prices abstract we investigate the stochastic resonance dynamic behavior characteristics of price drawdown time series driven by internal and external periodic information and discuss the influence of information resonance on price drawdown risk based on price drawdown periodic heston model and signal power amplification a theoretical model of the periodic price drawdown time series is proposed to describe the energy price drawdown time series with the periodic heston model then the signal power amplification spa is employed to measure the stochastic resonance phenomenon in the internal and external periodic information environment of complex energy dynamics system combined with the real data of wti spot price of nymex the least square method of drawdown time series distribution is used to estimate the parameters of the model the probability density functions of drawdown between the theoretical model and the real data are compared and a good agreement can be found between both the simulated data from the proposed model and the real data after the stochastic simulation of signal power amplification under internal and external periodic information respectively the results show that i in the functions of spa versus price volatility parameters noise correlation strength or periodic information strength inverse resonance phenomenon can be observed that is to say there is the best system price volatility parameter noise correlation strength and information strength corresponding to the least risk of the price drawdown ii in the spa versus amplitude of volatility fluctuations the correlation induce multiple inverse stochastic resonance phenomenon can be observed iii the increase of growth rate strengthens spa and weakens drawdown risk of energy market prices

tests of the random walk hypothesis for financial data abstract we propose a method from the viewpoint of deterministic dynamical systems to investigate whether observed data follow a random walk rw and apply the method to several financial data our method is based on the previously proposed small shuffle surrogate method hence our method does not depend on the specific data distribution although previously proposed methods depend on properties of the data distribution the data we use are stock market standard poor s 500 in us market and nikkei225 in japanese market exchange rate british pound us dollar and japanese yen us dollar and commodity market gold price and crude oil price we found that these financial data are rw whose first differences are independently distributed random variables or time varying random variables

on kneser solutions of nonlinear third order differential equations sufficient conditions are given under which the third order differential equation with the middle term y q t y r t f y 0 q positive has a kneser solution y the derivatives of which change their signs

oscillation of third order trinomial delay differential equations the purpose of this paper is to study oscillation and asymptotic behavior of solutions to a third order linear delay differential equation y t p t y t q t y tau t 0 new comparison th

exponential distribution of financial returns at mesoscopic time lags a new stylized fact we study the probability distribution of stock returns at mesoscopic time lags return horizons ranging from about an hour to about a month while at shorter microscopic time lags the distribution has power law tails for mesoscopic times the bulk of the distribution more than 99 of the probability follows an exponential law the slope of the exponential function is determined by the variance of returns which increases proportionally to the time lag at longer times the exponential law continuously evolves into gaussian distribution the exponential to gaussian crossover is well described by the analytical solution of the heston model with stochastic volatility r 2004 elsevier b v all rights reserved

microscopic origin of non gaussian distributions of financial returns abstract in this paper we study the possible microscopic origin of heavy tailed probability density distributions for the price variation of financial instruments we extend the standard log normal process to include another random component in the so called stochastic volatility models we study these models under an assumption akin to the born oppenheimer approximation in which the volatility has already relaxed to its equilibrium distribution and acts as a background to the evolution of the price process in this approximation we show that all models of stochastic volatility should exhibit a scaling relation in the time lag of zero drift modified log returns we verify that the dow jones industrial average index indeed follows this scaling we then focus on two popular stochastic volatility models the heston and hull white models in particular we show that in the hull white model the resulting probability distribution of log returns in this approximation corresponds to the tsallis t student distribution the tsallis parameters are given in terms of the microscopic stochastic volatility model finally we show that the log returns for 30 years dow jones index data is well fitted by a tsallis distribution obtaining the relevant parameters

characteristics of the volatility in the korea composite stock price index abstract we empirically analyze the time series of the korea composite stock price index kospi from march of 1992 to february of 2007 using methods from the hydrodynamic turbulence to this end we focus on characteristics of the return and volatility which are respectively the price change and a measure of the financial market fluctuation over a time interval with these we show that the non gaussian probability distribution of the return can be modeled by the convolution of the conditional probability distribution of the return given the volatility and the distribution of the volatility per se from this model we suggest that the non gaussian characteristic of the return results from the fluctuation of the volatility that is a large return is partly if not entirely due to the market fluctuation in a long time scale influencing the fluctuation in a short time scale via net information flow we further show that the volatility has a multi fractal property which resembles the multifractality of the energy dissipation in the turbulence

stochastic volatility of financial markets as the fluctuating rate of trading an empirical study we present an empirical study of the subordination hypothesis for a stochastic time series of a stock price the fluctuating rate of trading is identified with the stochastic variance of the stock price as in the continuous time random walk ctrw framework the probability distribution of the stock price changes log returns for a given number of trades n is found to be approximately gaussian the probability distribution of n for a given time interval dt is nonpoissonian and has an exponential tail for large n and a sharp cutoff for small n combining these two distributions produces a non trivial distribution of log returns for a given time interval dt which has exponential tails and a gaussian central part in agreement with empirical observations r 2007 elsevier b v all rights reserved

noise intensity fluctuation in langevin model and its higher order fokker planck equation abstract in this paper we investigate a langevin model subjected to stochastic intensity noise sin which incorporates temporal fluctuations in noise intensity we derive a higher order fokker planck equation hfpe of the system taking into account the effect of sin by the adiabatic elimination technique stationary distributions of the hfpe are calculated by using the perturbation expansion we investigate the effect of sin in three cases a parabolic and quartic bistable potentials with additive noise b a quartic potential with multiplicative noise and c a stochastic gene expression model we find that the existence of noise intensity fluctuations induces an intriguing phenomenon of a bimodal to trimodal transition in probability distributions these results are validated with monte carlo simulations

a novel fixed point iteration method for the solution of third order boundary value problems in this work a new alternative uniformly convergent iterative scheme is presented and applied for the solution of an extended class of linear and nonlinear third order boundary value problems that arise in physical applications the method is based on embedding green s functions into well known fixed point iterations including picard s and krasnoselskii mann s schemes convergence of the numerical method is proved by manipulating the contraction principle the effectiveness of the proposed approach is established by implementing it on several numerical examples including linear and nonlinear third order boundary value problems the results show highly accurate approximations when compared to exact and existing numerical solutions

the roles of mean residence time on herd behavior in a financial market abstract we investigate the herd behavior of stock prices in a finance system with the heston model based on parameter estimation of the heston model obtained by minimizing the mean square deviation between the theoretical and empirical return distributions we simulate mean residence time of positive return mrtpr plots of mrtpr against the amplitude or mean reversion of volatility demonstrate a phenomenon of herd behavior for a positive cross correlation between noise sources of the heston model also for a negative cross correlation a phenomenon of herd behavior is observed in plots of mrtpr against the long run variance by increasing amplitude or mean reversion of volatility

misspecification tests in econometrics based on ranks abstract this paper introduces a class of rank statistics for use in testing econometric models for misspecification these statistics are ideally suited to survey data since endogenous and exogenous variables in econometric models may therefore be considered exchangeable thus residuals from a wide class of models e g linear regression non linear regression simultaneous equations etc are also exchangeable since rank statistics are distribution free when based on exchangeable data it follows the rank statistics based on these residuals are also distribution free simulation studies in the linear regression case suggest that they have good power characteristics and are distributionally robust in comparison to the usual classical procedures

multiple time scales and the empirical models for stochastic volatility abstract the most common stochastic volatility models such as the ornstein uhlenbeck ou the heston the exponential ou expou and hull white models define volatility as a markovian process in this work we check the applicability of the markovian approximation at separate times scales and will try to answer the question which of the stochastic volatility models indicated above is the most realistic to this end we consider the volatility at both short a few days and long a few months time scales as a markovian process and estimate for it the coefficients of the kramers moyal expansion using the data for dow jones index it has been found that the empirical data allow to take only the first two coefficients of expansion to be non zero that define form of the volatility stochastic differential equation of ito it proved to be that for the long time scale the empirical data support the expou model at the short time scale the empirical model coincides with expou model for the small volatility quantities only

roles of capital flow on the stability of a market system abstract the roles of capital flow in an ensemble composed of sub markets are investigated a modified heston model and recycled noises are employed to describe the dynamics of stock price and capital flow in the ensemble respectively the mean escape times of two sub markets with a cubic nonlinearity are calculated by using numerical simulation the results evidence that i there is a worst delay time or rate of capital inflow concerning the minimal stability of stock price and an optimal delay time or rate of capital outflow concerning the maximal stability of stock price when 0 denotes strength of correlation between two wiener processes of the stock price and the volatility ii when 0 the stability of stock price is maximally enhanced by an optimal delay time or rate of capital inflow and reduced by a worst rate of capital outflow but monotonously strengthened by delay time of capital outflow

application of heston model and its solution to german dax data abstract we compare two well known examples of stochastic volatility models the heston model and the hull white model we derive the stationary probability density distribution of the variance in addition we apply this stationary solution to the probability density distribution of the logarithmic returns by using the conditional probability density distribution furthermore we compare the received solutions of the logarithmic returns with empirical high frequency data of dax and its stocks

on third order differential equations with property a and b we present some new results concerning relationships between oscillation and property a oscillation and property b the obtained results have necessary and sufficient character they are applied to the nonlinear third order differential equations too

oscillation results for emden fowler type differential equations abstract the third order nonlinear differential equation x a t x b t f x 0 is considered we present oscillation and nonoscillation criteria which extend and improve previous results existing in the literature in particular some results recently stated by m gregus and m gregus jr j math anal appl 181 1994 575 585 in addition contributions to the classification of solutions are given the techniques used are based on a transformation which reduces to a suitable disconjugate form to this aim auxiliary results on the asymptotic behavior of solutions of a second order linear differential equation associated to are stated they are presented in an independent form because they may be applied also to simplify and improve other qualitative problems concerning differential equations with quasiderivatives

critical phenomena in sequence matching we give a generalization of the result of erdos and renyi on the length r n of the longest head run in the first n tosses of a coin consider two independent sequences x 1 x 2 cdots x m and y 1y 2 cdots y n suppose that x 1 x 2 cdots are i i d mu and y 1 y 2 cdots are i i d nu where mu and nu are possibly different distributions on a common finite alphabet s let p equiv p x 1 y 1 in 0 1 the length of the longest matching consecutive subsequence is m m n equiv max k x i r y j r for r 1 to k for some 0 leq i leq m k 0 leq j leq n k for m and n rightarrow infty with log m log mn rightarrow lambda in 0 1 our result is that there is a constant k equiv k mu nu lambda in 0 1 rbrack such that p lim m m n log 1 p mn k 1 the proof uses large deviation methods the constant k is determined from a variational formula involving the kullback liebler distance or relative entropy a simple necessary and sufficient condition for k 1 is given for the case m n lambda 1 2 and mu nu k 1 the set of mu nu lambda for which k 1 has nonempty interior the boundary of this set is the location of a phase transition the results generalize to more than two sequences and to markov chains a strong law of large numbers is given for the proportion of letters within the longest matching word the limiting proportion exhibits critical behavior similar to that of k