improved finite sample hurst exponent estimates using rescaled range analysis 1 rescaled range analysis is one of the classical methods used for detecting and quantifying long term dependence in time series however rescaled range analysis has been shown in several studies to give biased estimates of the hurst exponent in finite samples a new estimator based on a modified expression of the expected value of the rescaled range is proposed a comparison of the modified estimator with other alternatives shows that the modified estimator offers a great improvement over the classical rescaled range estimator in terms of bias and root mean square error which makes it comparable to some of the leading estimators the application of the proposed modified rescaled range estimator to a group of temperature rainfall river flow and tree ring time series in the midwest usa demonstrates the extent to which classical rescaled range analysis can give misleading results based on a statistical test of significance the number of time series exhibiting the hurst effect is reduced from 36 to only 11 out of 56 temperature series and from 23 to 7 out of 60 rainfall series on the other hand the number of time series exhibiting the hurst effect marginally increased from 8 to 9 out of 49 river flow series and from 49 to 54 out of 88 tree ring series

on maximum likelihood estimation of the differencing parameter of fractionally integrated noise with unknown mean abstract there are two approaches to maximum likelihood ml estimation of the parameter of fractionally integrated noise approximate frequency domain ml fox and taqqu 1986 and exact time domain ml sowell 1992b if the mean of the process is known then a clear finite sample mean squared error ranking of the estimators emerges the exact time domain estimator is superior we show in this paper however that the finite sample efficiency of approximate frequency domain ml relative to exact time domain ml rises dramatically when the mean is unknown and so must be estimated the intuition for our result is straightforward the frequency domain ml estimator is invariant to the true but unknown mean of the process while the time domain ml estimator is not feasible time domain estimation must therefore be based upon de meaned data but the long memory associated with fractional integration makes precise estimation of the mean difficult we conclude that the frequency domain estimator is an attractive and efficient alternative for situations in which large sample sizes render time domain estimation impractical

the weierstrass mandelbrot process revisited we derive a functional central limit theorem for quasi gaussian processes in particular we prove that the limit of the mandelbrot weierstrass process is a complex fractional brownian motion

a generalized fast marching method on unstructured triangular meshes in this paper we extend the generalized fast marching method gfmm presented in e carlini et al siam j numer anal 46 2008 pp 2920 2952 to unstructured meshes the gfmm generalizes the classical fast marching method in the sense that it can be applied to propagate interfaces with time dependent and changing sign velocity the main motivation for this extension is that in many areas such as in fluid dynamics the method for tracking the motion of an interface in time has to be coupled with other solvers based on finite elements or finite volumes typically constructed on triangular grids and on domains with complex geometries we prove an abstract convergence result for the two dimensional 2d case which requires only some properties of the mesh and of the local solvers used to compute the solution on a narrow band in particular this result applies to a class of monotone schemes for 2d problems on triangular grids with acute angles finally some numerical tests in two dimensions illu

on estimation of a regression model with long memory stationary errors we consider estimation of a regression model with long memory stationary errors first we estimate the regression parameters by the least squares estimator lse and next those describing the correlation structure of the error terms by using the residuals obtained from the lse certain regularity conditions introduced to develop the asymptotic theory no longer hold in this model in this situation we derive asymptotic properties of the preceding estimation procedure

scaling and long range dependence in option pricing iii a fractional version of the merton model with transaction costs abstract a model for option pricing of fractional version of the merton model with hurst exponent h being in 1 2 1 is established with transaction costs in particular for h 1 2 1 the minimal price c min t s t of an option under transaction costs is obtained which displays that the timestep t and the hurst exponent h play an important role in option pricing with transaction costs

asymptotic properties of the lse in a regression model with long memory stationary errors we consider asymptotic properties of the least squares estimator lse in a regression model with long memory stationary errors first we derive a necessary and sufficient condition that the lse be asymptotically efficient relative to the best linear unbiased estimator blue then we derive the asymptotic distribution of the lse under a condition on the higher order cumulants of the white noise process of the errors

global solution for a non local eikonal equation modelling dislocation dynamics abstract in this paper we study a non local eikonal equation that arises from the theory of dislocation dynamics for this equation the global existence and uniqueness are available only for lipschitz continuous viscosity solutions in some particular cases based on a new gradient entropy estimate we prove the global existence of a continuous viscosity solution of this equation considering non signed velocity

a test of location for data with slowly decaying serial correlations summary slowly decaying serial correlations have if ignored disastrous effects on classical tests and confidence intervals we propose a modified t test for the location parameter which takes into account such correlations an approximate distribution function of the test statistic is given under the assumption of fractional gaussian noise the results are generalized to prediction intervals for a future average an example is given to illustrate the methods

infinitesimal robustness for autoregressive processes we define the influence function and construct optimal robust estimators for autoregressive processes we show that the asymptotic bias caused by small contaminations of the marginals can be written as the integral of a certain function with respect to the contamination this function is called the influence function it is unique only up to an equivalence relation but there is a natural unique version which describes the limiting influence of an additional observation given the previous observations moreover with this version the asymptotic variance at the true model can be expressed in a simple form optimal robust estimators minimize this asymptotic variance under a constraint on the influence function as in the i i d case they are found by truncating a multiple of the influence function of the maximum likelihood estimator

another look at velocity extensions in the level set method the level set method s osher and j a sethian j comput phys 79 1988 pp 12 49 has become a widely used numerical method for moving interfaces e g see the many examples in j sethian level set methods evolving interfaces in geometry fluid mechanics computer vision and material science cambridge university press london 1996 s osher and r fedkiw level set methods and dynamic implicit surfaces springer verlag heidelberg 2002 for many applications the velocity of the interface is known only on the interface while the level set method requires information about the interface speed at least in a neighborhood of grid points near the interface to address this issue velocity extensions are used to map the velocity information on the interface into the rest of the computational domain d adalsteinsson and j sethian j comput phys 118 1995 pp 269 277 this allows the level set method to proceed the velocity extension method presented in d adalsteinsson and j sethian j comput phys 118 1995 pp 269 277 uses the fast marching method j sethian proc natl acad sci 93 1996 pp 1591 1595 j sethian siam rev 41 1999 pp 199 235 and is only a first order approximation for the velocity field near the interface furthermore it can lead to unexpected behavior in some cases this is primarily due to the strictly local solution for the characteristics of the flow near the interface in this paper we look more closely at the characteristics near the interface and then present a modified velocity extension method also based on the fast marching method which handles the characteristcs more accurately in turn this new method will lead to some interesting new possibilities for the fast marching method

fuzzy multiresolution signal representation we present a multiresolution signal representation technique which uses fuzzy rules a fuzzy tree is used to connect different levels of resolution we apply our representation to several random processes and demonstrate some useful properties of our representation when applied to fractals

a posteriori error estimates for the effective hamiltonian of dislocation dynamics we study an implicit and discontinuous scheme for a non local hamilton jacobi equation modelling dislocation dynamics for the evolution problem we prove an a posteriori estimate of crandall lions type for the error between continuous and discrete solutions we deduce an a posteriori error estimate for the effective hamiltonian associated to a stationary cell problem in dimension one and under suitable assumptions we also give improved a posteriori estimates numerical simulations are provided

two approximations of solutions of hamilton jacobi equations abstract equations of hamilton jacobi type arise in many areas of application including the calculus of variations control theory and differential games the associated initial value problems almost never have global time classical solutions and one must deal with suitable generalized solutions the correct class of generalized solutions has only recently been established by the authors this article establishes the convergence of a class of difference approximations to these solutions by obtaining explicit error estimates analogous results are proved by similar means for the method of vanishing viscosity author

the law of the iterated logarithm for the rescaled rs statistics without the second moment abstract in the paper we show a law of the iterated logarithm for rescaled r s statistics without second moment

estimating the differencing parameter via the partial autocorrelation function this paper provides an explanation for the puzzling phenomenon in tieslau et al 1996 journal of econometrics 71 249 264 that a substantial e ciency loss occurs if low order autocorrelations are omitted when estimating the di erencing parameter d this is because for all n strictly bigger than 1 the nth order autocorrelation function does not depend uniquely on the di erencing parameter we construct a new estimator for the di erencing parameter based on the partial autocorrelation function comparisons of the asymptotic and nite sample variance of our estimator and those of tsb are made a substantial e ciency gain is achieved by our estimator as compared to tsb s 2000 elsevier science s a all rights reserved jel classixcation c22

china s soybean crush spread nonlinear analysis based on mf dcca abstract in this paper we investigate cross correlations among the soybean soymeal and soyoil futures return series at china s dalian commodity exchange using both multifractal detrended fluctuation analysis mf dfa and multifractal detrended cross correlation analysis mf dcca methods we find that there exists multifractality in the soybean soymeal and soyoil futures return series using mf dfa method moreover results of mf dcca demonstrate that there exists a power law cross correlation and significant multifractal features among soybean soymeal and soyoil futures returns furthermore by comparing the multifractality of the original series to the shuffled and surrogated series we find that both the long range correlations and fat tailed distribution contribute to the multifractality in cross correlation among soybean soymeal and soyoil futures return series in dalian commodity exchanges furthermore we use nonlinear granger causality test and show that anyone of the three products returns is the granger cause of the other two products returns

stability and lack of memory of the returns of the hang seng index abstract in this paper we show that the logarithmic returns of the hang seng index from january 2 1987 to november 14 2005 statistically resemble a sequence of independent identically distributed levy stable random variables this is in stark contrast to xiu and jin 2007 39 where long memory farima processes with gaussian noise were suggested as well fitted to the data the lack of memory is checked by using lo s modified r s statistic and a new method of estimation of the memory parameter d which applies the notion of empirical mean squared displacement in order to test stability of the data we employ several statistical tests based on the empirical distribution function finally we also show that the returns possess no conditional heteroscedasticity property thus excluding the arch garch family of processes as possible underlying models

comparison principle for a generalized fast marching method in carlini falcone forcadel and monneau siam j numer anal 46 2008 pp 2920 2952 the authors have proposed a generalization of the classical fast marching method of sethian for the eikonal equation in the case where the normal velocity depends on space and time and can change sign the goal of this paper is to propose a modified version of the generalized fast marching method proposed in carlini falcone forcadel and monneau siam j numer anal 46 2008 pp 2920 2952 for which we state a general comparison principle we also prove the convergence of the new algorithm

fractionally integrated generalized autoregressive conditional heteroskedasticity abstract the new class of fractionally integrated generalized autoregressive conditionally heteroskedastic figarch processes is introduced the conditional variance of the process implies a slow hyperbolic rate of decay for the influence of lagged squared innovations unlike i d processes for the mean maximum likelihood estimates mle of the figarch parameters are argued to be t 1 2 consistent the small sample behavior of an approximate mle procedure is assessed through a simulation study which also documents how the estimation of a standard garch model tends to produce integrated or igarch like estimates an empirical example with daily deutschmark u s dollar exchange rates illustrates the practical relevance of the new figarch specification

arbitrage with fractional gaussian processes abstract while the arbitrage opportunity in the black scholes model driven by fractional brownian motion has a long history the arbitrage strategy in the black scholes model driven by general fractional gaussian processes is in its infancy the development of stochastic calculus with respect to fractional gaussian processes allowed us to study such models in this paper following the idea of shiryaev 1998 an arbitrage strategy is constructed for the black scholes model driven by fractional gaussian processes when the stochastic integral is interpreted in the riemann stieltjes sense arbitrage opportunities in some fractional gaussian processes including fractional brownian motion sub fractional brownian motion bi fractional brownian motion weighted fractional brownian motion and tempered fractional brownian motion are also investigated

long term memory in stock market prices a test for long term memory that is robust to short range dependence is developed it is a modification of the r s statistic and the relevant asymptotic sampling theory is derived via functional central limit theory contrary to previous findings when applied to daily and monthly stock returns indexes over several time periods this test yields no evidence of long range dependence once short range dependence is accounted for monte carlo experiments show that the modified r s test has power against at least two specific models of long term memory suggesting that models with short range dependence may adequately capture the behavior of historical stock returns copyright 1991 by the econometric society

analytical pricing of geometric asian power options on an underlying driven by a mixed fractional brownian motion abstract in this paper we study the pricing problem of the continuously monitored fixed and floating strike geometric asian power options in a mixed fractional brownian motion environment first we derive both closed form solutions and mixed fractional partial differential equations for fixed and floating strike geometric asian power options based on delta hedging strategy and partial differential equation method second we present the lower and upper bounds of the prices of fixed and floating strike geometric asian power options under the assumption that both risk free interest rate and volatility are interval numbers finally numerical studies are performed to illustrate the performance of our proposed pricing model

regular article a pde based fast local level set method we develop a fast method to localize the level set method of osher and sethian 1988 j comput phys 79 12 and address two important issues that are intrinsic to the level set method a how to extend a quantity that is given only on the interface to a neighborhood of the interface b how to reset the level set function to be a signed distance function to the interface efficiently without appreciably moving the interface this fast local level set method reduces the computational effort by one order of magnitude works in as much generality as the original one and is conceptually simple and easy to implement our approach differs from previous related works in that we extract all the information needed from the level set function or functions in multiphase flow and do not need to find explicitly the location of the interface in the space domain the complexity of our method to do tasks such as extension and distance reinitialization is o n where n is the number of points in space not o n log n as in works by sethian 1996 proc nat acad sci 93 1591 and helmsen and co workers 1996 spie microlithography ix p 253 this complexity estimation is also valid for quite general geometrically based front motion for our localized method

volatility behavior of visibility graph emd financial time series from ising interacting system abstract a financial market dynamics model is developed and investigated by stochastic ising system where the ising model is the most popular ferromagnetic model in statistical physics systems applying two graph based analysis and multiscale entropy method we investigate and compare the statistical volatility behavior of return time series and the corresponding imf series derived from the empirical mode decomposition emd method and the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model further we find that the degree distribution of visibility graph for the simulation series has the power law tails and the assortative network exhibits the mixing pattern property all these features are in agreement with the real market data the research confirms that the financial model established by the ising system is reasonable

m estimators of location for gaussian and related processes with slowly decaying serial correlations abstract we investigate the behavior of m estimators of the location parameter for stochastic processes with long range dependence the processes considered are gaussian or one dimensional transformations of gaussian processes it turns out that up to a constant all m estimators are asymptotically equivalent to the arithmetic mean for gaussian processes this constant is always equal to one independently of the function in view of the case of iid observations the results are surprising they are related to earlier work by gastwirth and rubin some simulations illustrate the results

complexity and multifractal behaviors of multiscale continuum percolation financial system for chinese stock markets abstract a new financial agent based time series model is developed and investigated by multiscale continuum percolation system which can be viewed as an extended version of continuum percolation system in this financial model for different parameters of proportion and density two poisson point processes where the radii of points represent the ability of receiving or transmitting information among investors are applied to model a random stock price process in an attempt to investigate the fluctuation dynamics of the financial market to validate its effectiveness and rationality we compare the statistical behaviors and the multifractal behaviors of the simulated data derived from the proposed model with those of the real stock markets further the multiscale sample entropy analysis is employed to study the complexity of the returns and the cross sample entropy analysis is applied to measure the degree of asynchrony of return autocorrelation time series the empirical results indicate that the proposed financial model can simulate and reproduce some significant characteristics of the real stock markets to a certain extent

dislocation dynamics short time existence and uniqueness of the solution we study a mathematical model describing dislocation dynamics in crystals we consider a single dislocation line moving in its slip plane the normal velocity is given by the peach koehler force created by the dislocation line itself the mathematical model is an eikonal equation with a velocity which is a non local quantity depending on the whole shape of the dislocation line we study the special case where the dislocation line is assumed to be a graph or a closed loop in the framework of discontinuous viscosity solutions for hamilton jacobi equations we prove the existence and uniqueness of a solution for small time we also give physical explanations and a formal derivation of the mathematical model finally we present numerical results based on a level sets formulation of the problem these results illustrate in particular the fact that there is no general inclusion principle for this model

fractional brownian motion time changed by gamma and inverse gamma process abstract many real time series exhibit behavior adequate to long range dependent data additionally very often these time series have constant time periods and also have characteristics similar to gaussian processes although they are not gaussian therefore there is need to consider new classes of systems to model these kinds of empirical behavior motivated by this fact in this paper we analyze two processes which exhibit long range dependence property and have additional interesting characteristics which may be observed in real phenomena both of them are constructed as the superposition of fractional brownian motion fbm and other process in the first case the internal process which plays role of the time is the gamma process while in the second case the internal process is its inverse we present in detail their main properties paying main attention to the long range dependence property moreover we show how to simulate these processes and estimate their parameters we propose to use a novel method based on rescaled modified cumulative distribution function for estimation of parameters of the second considered process this method is very useful in description of rounded data like waiting times of subordinated processes delayed by inverse subordinators by using the monte carlo method we show the effectiveness of proposed estimation procedures finally we present the applications of proposed models to real time series

the fractional and mixed fractional cev model abstract the continuous observation of the financial markets has identified some stylized facts which challenge the conventional assumptions promoting the born of new approaches on the one hand the long range dependence has been faced replacing the traditional gauss wiener process brownian motion characterized by stationary independent increments by a fractional version on the other hand the cev model addresses the leverage effect and smile skew phenomena efficiently in this paper these two insights are merging and both the fractional and mixed fractional extensions for the cev model are developed using the fractional versions of both the ito s calculus and the fokker planck equation the transition probability density function of the asset price is obtained as the solution of a non stationary feller process with time varying coefficients getting an analytical valuation formula for a european call option besides the greeks are computed and compared with the standard case

a bayesian monte carlo markov chain method for parameter estimation of fractional differenced gaussian processes we present a bayesian monte carlo markov chain method to simultaneously estimate the spectral index and power amplitude of a fractional differenced gaussian process at low frequency in presence of white noise and a linear trend and periodic signals this method provides a sample of the likelihood function and thereby using monte carlo integration all parameters and their uncertainties are estimated simultaneously we test this method with simulated and real global positioning system height time series and propose it as an alternative to optimization methods currently in use furthermore without any mathematical proof the results from the simulations suggest that this method is unaffected by the stationary regime and hence can be used to check whether or not a time series is stationary

time evolution of stochastic processes with correlations in the variance stability in power law tails of distributions abstract we model the time series of the s p500 index by a combined process the ar garch process where ar denotes the autoregressive process which we use to account for the short range correlations in the index changes and garch denotes the generalized autoregressive conditional heteroskedastic process which takes into account the long range correlations in the variance we study the ar garch process with an initial distribution of truncated levy form we find that this process generates a new probability distribution with a crossover from a levy stable power law to a power law with an exponent outside the levy range beyond the truncation cutoff we analyze the sum of n variables of the ar garch process and find that due to the correlations the ar garch process generates a probability distribution which exhibits stable behavior in the tails for a broad range of values n a feature which is observed in the probability distribution of the s p500 index we find that this power law stability depends on the characteristic scale in the correlations we also find that inclusion of short range correlations through the ar process is needed to obtain convergence to a limiting gaussian distribution for large n as observed in the data

auto correlated behavior of wti crude oil volatilities a multiscale perspective abstract in this paper we investigate the long range auto correlated behavior of wti crude oil volatility series employing multifractal detrended fluctuation analysis our findings show that the for small time scales the auto correlations of volatilities were multifractal while for large time scales the auto correlations were nearly monofractal based on multiscale analysis we also investigate the dynamics of auto correlations for different intervals of time scales and find that several shocks could make significant effects on the auto correlated behaviors for small time scales analyzing the dynamics of multifractality degrees of auto correlations for small time scales we find that the stronger auto correlations were always related to the lower degrees of multifractality at last we have discussions on the determination factors of price behavior the predictive implications of scaling behavior in volatilities for oil markets and the reasons why long range auto correlations of volatility were always strong for both small time scales and large time scales our results are very important theoretically and practically

autocorrelation type timescale and statistical property in financial time series abstract earlier studies have documented that three types of autocorrelations exist in financial time series sign volatility and return autocorrelation in this paper we examine how each type of the above autocorrelations affects the statistical properties of financial time series and its role in maintaining such statistical properties using three different shuffling series that correspondingly destroy each type of autocorrelation upon different timescales we find that 1 the statistical properties of the shuffling series significantly vary from the original ones 2 volatility and return autocorrelations show greater impacts than sign autocorrelation 3 the effects on the statistical properties are intensified as time scale expands 4 the nonlinear component of autocorrelation is the major drive of the effect

on a class of estimation and test for long memory this paper advances a new analysis technology path of estimation and test for long memory time series i propose the definitions of time scale series strong variance scale exponent and weak variance scale exponent and prove the strict mathematical equations that strong and weak variance scale exponent can accurately identify the time series of white noise short memory and long memory especially derive the equation relationships between weak variance scale exponent and long memory parameters i also construct two statistics which slmemory statistic tests for long memory properties the paper further displays monte carlo performance for mse of weak variance scale exponent estimator and the empirical size and power of slmemory statistic giving practical recommendations of finite sample and also provides brief empirical examples of logarithmic return rate series data for sino us stock markets

efficient algorithms for globally optimal trajectories we present serial and parallel algorithms for solving a system of equations that arises from the discretization of the hamilton jacobi equation associated to a trajectory optimization problem of the following type a vehicle starts at a prespecified point x sub o and follows a unit speed trajectory x t inside a region in spl rscr sup m until an unspecified time t that the region is exited a trajectory minimizing a cost function of the form spl int sub 0 sup t r x t dt q x t is sought the discretized hamilton jacobi equation corresponding to this problem is usually solved using iterative methods nevertheless assuming that the function r is positive we are able to exploit the problem structure and develop one pass algorithms for the discretized problem the first algorithm resembles dijkstra s shortest path algorithm and runs in time o n log n where n is the number of grid points the second algorithm uses a somewhat different discretization and borrows some ideas from a variation of dial s shortest path algorithm 1969 that we develop here it runs in time o n which is the best possible under some fairly mild assumptions finally we show that the latter algorithm can be efficiently parallelized for two dimensional problems and with p processors its running time becomes o n p provided that p o spl radic n log n

intermittency stochastic growth and phase transition in a simple deterministic partial differential equation with a singular term we show by numerical integration that the discretized version of simple deterministic partial differential equations with singular terms proposed by zhang 1992 exhibit rich spatio temporal behaviour representing a mixture of stochastic and deterministic regimes varying the relative weight b of the singular term we have been able to detect transitions in the global behaviour of the solutions by determining their total width w t in particular we have found intermittent solutions as well as a power law dependence of w w t to infinity on b

efficiency and multifractality analysis of csi 300 based on multifractal detrending moving average algorithm abstract we apply the multifractal detrending moving average mfdma to investigate and compare the efficiency and multifractality of 5 min high frequency china securities index 300 csi 300 the results show that the csi 300 market becomes closer to weak form efficiency after the introduction of csi 300 future we find that the csi 300 is featured by multifractality and there are less complexity and risk after the csi 300 index future was introduced with the shuffling surrogating and removing extreme values procedures we unveil that extreme events and fat distribution are the main origin of multifractality besides we discuss the knotting phenomena in multifractality and find that the scaling range and the irregular fluctuations for large scales in the f q s vs s plot can cause a knot

deciding between i 1 and i 0 abstract a class of procedures that consistently classify the stochastic component of a time series as being integrated either of order zero i 1 or one i 1 are proposed for general i 0 or i 1 processes and polynomial or piecewise linear detrending large sample bayesian inference is free of nuisance parameters describing short run dynamics and requires specifying priors only on the point hypotheses i 1 and i 1 thereby avoiding problematic choices of parametric priors over roots and nuisance parameters applied to the nelson plosser 1982 data with linear detrending these procedures largely support nelson and plosser s original inferences with piecewise linear detrending these data are typically uninformative producing bayes ratios close to one

statistical volatility duration and complexity of financial dynamics on sierpinski gasket lattice percolation abstract a novel agent based financial dynamics is established based on the percolation system on sierpinski gasket lattice to reproduce the statistical characteristics of financial markets sierpinski gasket lattice is a fractal like graph which corresponds to the fractal well known sierpinski gasket modeling a financial dynamics on sierpinski gasket lattice is a new approach in financial micro mechanism construction in an attempt to investigate the statistical properties of returns and prove the feasibility of the proposed model two new nonlinear statistics maximum and average monotonous volatility duration are introduced in this work for the first time which describe the trend of volatility of return time series in financial markets furthermore a new method cmcid is proposed to measure the synchronization and similarity behaviors of return volatility duration in multiscale the results show that the pairs of real data and simulated data have synchronization and the synchronization becomes stronger when the scale increases and the power law distribution is employed to investigate the corresponding statistical properties which shows that the proposed model shares a common power law distribution with regard to monotonous volatility duration the empirical results show that the simulated series from the financial model and the historical data share common statistical properties which indicate that the proposed model is reasonable in terms of volatility behavior

a delay financial model with stochastic volatility martingale method abstract in this paper we extend a delayed geometric brownian model by adding a stochastic volatility term which is driven by a hidden process of fast mean reverting diffusion to the delayed model combining a martingale approach and an asymptotic method we develop a theory for option pricing under this hybrid model the core result obtained by our work is a proof that a discounted approximate option price can be decomposed as a martingale part plus a small term subsequently a correction effect on the european option price is demonstrated both theoretically and numerically for a good agreement with practical results

the cauchy problem for ut δu u q with q a positive real number the nonlinear partial differential equation in the title of the paper arises in the study of the growth of surfaces in that context it is known as the generalized deterministic kpz equation the paper is concerned with the initial value problem for the equation under the assumption that the initial data function is bounded and continuous results on the existence uniqueness and regularity of solutions are obtained

a generalized fast marching method for dislocation dynamics in this paper we consider a generalized fast marching method gfmm as a numerical method to compute dislocation dynamics the dynamics of a dislocation hypersurface in mathbb r n with n 2 for physical applications is given by its normal velocity which is a nonlocal function of the whole shape of the hypersurface itself for this dynamics we show a convergence result of the gfmm as the mesh size goes to zero we also provide some numerical simulations in dimension n 2

the origin of fat tailed distributions in financial time series abstract a classic problem in physics is the origin of fat tailed distributions generated by complex systems we study the distributions of stock returns measured over different time lags we find that destroying all correlations without changing the 1 d distribution by shuffling the order of the daily returns causes the fat tails to almost vanish for 1 d we argue that the fat tails are caused by the well known long range volatility correlations that have already been systematically studied previously indeed destroying only sign correlations by shuffling the order of only the signs but not the absolute values of the daily returns allows the fat tails to persist for 1 d

testing for the source of multifractality in water level records abstract the multifractality in hydrologic data has been studied in many literatures but few literatures focus on its source which is helpful for understanding the underlying mechanisms that generate hydrologic data we propose a hypothesis testing procedure for the source of multifractality in water level records based on the empirical distributions of generalized hurst exponent estimated from a set of shuffled or surrogate series the proposed hypothesis testing procedure can show more details about the source of multifractality than previous methods with some statistics especially about the effects of large and small fluctuations on multifractality the generalized hurst exponents are estimated via multifractal detrended fluctuation analysis the data set contains about two million high frequency water level records of a northern china river at its 10 observation stations the testing results show that the multifractality in water levels is mainly caused by nonlinear correlations in small fluctuations and linear correlations in small and large fluctuations and is also related to the probability distribution of small fluctuations this conclusion is validated via some constructed semi surrogate series and values of statistics for source testing

periodic seasonal reg arfima garch models for daily electricity spot prices novel periodic extensions of dynamic long memory regression models with autoregressive conditional heteroscedastic errors are considered for the analysis of daily electricity spot prices the parameters of the model with mean and variance specifications are estimated simultaneously by the method of approximate maximum likelihood the methods are implemented for time series of 1 200 4 400 daily price observations in four european power markets apart from persistence heteroscedasticity and extreme observations in prices a novel empirical finding is the importance of day of the week periodicity in the autocovariance function of electricity spot prices in particular the very persistent daily log prices from the nord pool power exchange of norway are effectively modeled by our framework which is also extended with explanatory variables to capture supply and demand effects the daily log prices of the other three electricity markets eex in germany powernext in france and apx in the netherlands are less

on a class of m estimators for gaussian long memory models summary we consider estimation for parametric stationary gaussian models with long memory the spectral density f x 0 is assumed to be characterised by a vector 0 01 022 03 om such that 02 he 1 1 and f x 0 is proportional to xl 2h as x tends to zero an approximate maximum likelihood estimator based on the autoregressive representation of the process is proposed its asymptotic distribution is derived more generally the approach leads to a class of m estimators for which a central limit theorem holds by choosing an appropriate t function robustness against additive outliers can be achieved while keeping high efficiency under the ideal model this is illustrated by a small simulation study a simple algorithm and an explicit formula for the efficiency and thus for choosing an appropriate tuning parameter are given for hampel s redescending function

convergence of a generalized fast marching method for an eikonal equation with a velocity changing sign we present a new fast marching algorithm for an eikonal equation with a velocity changing sign this first order equation models a front propagation in the normal direction the algorithm is an extension of the fast marching method in two respects the first is that the new scheme can deal with a time dependent velocity and the second is that there is no restriction on its change in sign we analyze the properties of the algorithm and we prove its convergence in the class of discontinuous viscosity solutions finally we present some numerical simulations of fronts propagating in mathbb r 2

complex spatiotemporal patterns in two lattice models with instability abstract in this paper we consider two lattice models i the discretized version of a simple nonlinear partial differential equation pde with a singular term and ii a coupled map lattice cml with unstable coupling both systems are defined by simple iteration rules involving the nearest neighbour grid points of the corresponding one dimensional lattice we show numerically that these models result in an apparently stochastic spatiotemporal behaviour and exhibit interesting regimes as the function of the parameters of the models in particular we find that by varying the relative weight b of the singular term in the pde the total width of the solution scales with b the cml leads to an intermittent behaviour between structured and turbulent regimes

statistical properties and economic implications of jump diffusion processes with shot noise effects abstract the shot noise jump diffusion snjd model aims to reflect how economic variables respond to the arrival of sudden information this paper analyzes the snjd model providing its statistical distribution and closed form expressions for the characteristic function and moments we also analyze the dynamics of the model concluding that the degree of serial autocorrelation is related to the occurrence and magnitude of abnormal information in addition we provide some useful approximations in a particular case that considers exponential type decay empirically we propose a gmm approach to estimate the parameters of the model and present an empirical application for the stocks included in the dow jones averaged index our findings seem to confirm the presence of shot noise effects in 73 of the stocks and a strong relationship between the shot noise process and the autocorrelation pattern embedded in data

convergence of a generalized fast marching method for a non convex eikonal equation we present a new fast marching algorithm for a non convex eikonal equation modeling front evolutions in the normal direction the algorithm is an extension of the fast marching method since the new scheme can deal with a emph time dependent velocity without emph any restriction on its sign we analyze the properties of the algorithm and we prove its convergence in the class of discontinuous viscosity solutions finally we present some numerical simulations of fronts propagating in r 2

fitting long memory models by generalized linear regression summary there is an increasing awareness of the importance of long memory models in statistical applications if long memory is present it has to be taken into account in order to obtain reliable tests and confidence intervals one obstacle to using models with long memory in routine statistical analysis has been the lack of easily available and sufficiently versatile statistical software here we propose a simple but flexible class of parametric models which can be used to model such behaviour we demonstrate that these models can be fitted by generalized linear regression standard statistical software packages can be used a data example is discussed

deterministic and stochastic surface growth with generalized nonlinearity the scaling behavior of the interface width for the generalized kardar parisi zhang kpz equation ensuremath partial h ensuremath partial t ensuremath nu mathrm ensuremath nabla 2 h ensuremath lambda ensuremath vert ensuremath nabla h mathrm ensuremath vert mathrm ensuremath mu ensuremath eta x t is studied in two dimensions as a function of ensuremath mu with and without the additive noise term ensuremath eta in the case of additive noise the scaling of the surface width is found for all ensuremath mu to be the same as for the ordinary kpz equation ensuremath mu 2 in contrast to a previous conjecture this appears to be due to the combined action of the nonlinearity ensuremath vert ensuremath nabla h mathrm ensuremath vert mathrm ensuremath mu and the noise under renormalization which together induce a ensuremath vert ensuremath nabla h mathrm ensuremath vert 2 term for the deterministic case corresponding to the smoothing of an initially rough interface with roughness exponent ensuremath alpha good agreement with the scaling relation z min 2 ensuremath alpha 1 ensuremath mu ensuremath mu is obtained for ensuremath mu ensuremath ge 1 however for ensuremath mu 1 an instability is observed which leads to a fluctuating grooved surface for an asymptotically large system the roughness exponent is 1 and the growth exponent is approximately equal to 1 2 the evolution of two slightly different surfaces is studied in order to determine a lyapunov exponent characterizing this instability

towards the evaluation of the relevant degrees of freedom in nonlinear partial differential equations we investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations the proposed renormalization group approach is formulated as an analytical method providing the fundamental concepts of a numerical algorithm applicable to various dynamical systems we examine dynamical scaling characteristics in the short time and the long time evolution regime providing only a reduced number of degrees of freedom to the evolution process