long memory continuous time models this paper presents a new family of long memory models the continuous time moving average fractional process the continuous time framework allows to reconcile two competitive types of modelling fractional integration of arma processes and fractional brownian motion a comparison with usual discrete time arfima models is lead some well known empirical evidence on macroeconomic and financial time series such as variability of forward rates aggregation of responses across heterogeneous agents are well captured by this continuous time modelling moreover the usual statistical tools for long memory series and for stochastic differential equations can be jointly applied in this setting

emden fowler equations involving critical exponents on considere le probleme y t k y 2 y 2k 3 0 t 0 pour t 2 0 0 soit t inf t 0 y 0 sur t alors t 0 0 on etudie comment la position t du premier zero de y t varie avec

modelling dependence within joint tail regions standard approaches for modelling dependence within joint tail regions are based on extreme value methods which assume max stability a particular form of joint tail dependence we develop joint tail models based on a broader class of dependence structure which provides a natural link between max stable models and weaker forms of dependence including independence and negative association this approach overcomes many of the problems that are encountered with standard methods and is the basis for a poisson process representation that generalizes existing bivariate results we apply the new techniques to simulated and environmental data and demonstrate the marked advantage that the new approach offers for joint tail extrapolation

on contingent claim valuation in continuous time for volatility models of ornstein uhlenbeck type the paper addresses the valuation of contingent claims in stochastic volatility models of ornstein uhlenbeck type stressing the situation when volatility is driven by purely discontinuous levy processes a reduction series methodology is developed for this purpose which also provides a way for the numerical study of the value functionals the methodology is illustrated in the options case and in models based on gig distributions numerical examples are provided these examples show how the series enable computation accuracies of some three decimal places with just a single digit number of terms

bayesian semiparametric wiener system identification we present a novel method for wiener system identication the method relies on a semiparametric i e a mixed parametric nonparametric model of a wiener system we use a state space model for the linear dynamical system and a nonparametric gaussian process model for the static nonlinearity we avoid making strong assumptions such as monotonicity on the nonlinear mapping stochastic disturbances entering both as measurement noise and as process noise are handled in a systematic manner the nonparametric nature of the gaussian process allows us to handle a wide range of nonlinearities without making problem specic parameterizations we also consider sparsity promoting priors based on generalized hyperbolic distributions to automatically infer the order of the underlying dynamical system we derive an inference algorithm based on an ecient particle markov chain monte carlo method referred to as particle gibbs with ancestor sampling the method is proled on two challenging identication problems with good results blind wiener system identication is handled as a special case

simulated moments estimation of markov models of asset prices this paper provides a simulated moments estimator sme of the parameters of dynamic models in which the state vector follows a time homogeneous markov process conditions are provided for both weak and strong consistency as well as asymptotic normality various tradeoffs among the regularity conditions underlying the large sample properties of the sme are discussed in the context of an asset pricing model this paper provides conditions for the consistency and asymptotic normality of a simulated moments estimator sme of the parameters of asset pricing models with time homogeneous markov representations of the stochastic forc ing process sme s for economic models have been proposed by mcfadden 1989 and pakes and pollard 1989 for i i d environments and by lee and ingram 1991 for a time series environment the sme for time series models examined in this paper is as follows the state vector yt that determines asset prices is assumed to follow a time homogeneous markov process whose transi tion function depends on an unknown parameter vector 3 0 asset prices and possibly other relevant data are observed as f yt 0 for some given function f of the underlying state and parameter vector in parallel a simulated state process y is generated analytically or numerically from the economic model and corresponding simulated observations f yj3 13 are taken for a given parameter choice f3 the parameter is chosen so as to match moments that is to minimize the distance between sample moments of the data f y 8030 and those of the simulated series f yt f3 in a sense to be made precise the proposed sme extends the generalized method of moments gmm estimator hansen 1982 to a large class of asset pricing models for which the moment restrictions of interest do not have analytic representations in terms of observable variables and the unknown parameter vector we provide conditions on the transition function of yt and the observation function f under which the sme of 030 is consistent and characterize the normalized asymptotic distribu tion of the estimator for two reasons neither the regularity conditions underly ing hansen s 1982 analysis of gmm estimators for time series models without

a generalized goodwin business cycle model in random environment abstract this work develops a generalization of the goodwin lotka volterra models the traditional model describes the evolution of the employment rate and the labor share motivated by recent developments on business cycles and goodwin type models we consider a generalized goodwin business cycle model with noise we aim at investigating the impact of telegraph noise and white noise on the evolution of trajectories and the energy on trajectories of the model it is proved that with the presence of the noises all trajectories exit any compact subset of the open unit square d 0 1 0 1 and the energy along trajectories can be arbitrarily large moreover under certain additional conditions the boundary of d is the stable limit cycle of the perturbed model by white noise noise impact on the period of business cycles is also discussed numerical examples are provided to demonstrate our findings

stochastic differential equations applied to the study of geophysical and financial time series abstract this work is devoted to the study of modeling geophysical and financial time series we propose a stochastic differential equation arising from the superposition of independent ornstein uhlenbeck processes driven by a a b process superposition of independent a b ornstein uhlenbeck processes offers analytic flexibility and provides a class of continuous time processes capable of exhibiting long memory behavior the stochastic differential equation is applied to geophysics and finance by fitting the superposed a b ornstein uhlenbeck model to typical geophysical and financial time series

likelihood analysis of non gaussian measurement time series summary in this paper we provide methods for estimating non gaussian time series models these techniques rely on markov chain monte carlo to carry out simulation smoothing and bayesian posterior analysis of parameters and on importance sampling to estimate the likelihood function for classical inference the time series structure of the models is used to ensure that our simulation algorithms are efficient

a monte carlo approach to nonnormal and nonlinear state space modeling abstract a solution to multivariate state space modeling forecasting and smoothing is discussed we allow for the possibilities of nonnormal errors and nonlinear functionals in the state equation the observational equation or both an adaptive monte carlo integration technique known as the gibbs sampler is proposed as a mechanism for implementing a conceptually and computationally simple solution in such a framework the methodology is a general strategy for obtaining marginal posterior densities of coefficients in the model or of any of the unknown elements of the state space missing data problems including the k step ahead prediction problem also are easily incorporated into this framework we illustrate the broad applicability of our approach with two examples a problem involving nonnormal error distributions in a linear model setting and a one step ahead prediction problem in a situation where both the state and observational equations are nonlinear and involve unknown parameters

a novel pricing method for european options based on fourier cosine series expansions here we develop an option pricing method for european options based on the fourier cosine series and call it the cos method the key insight is in the close relation of the characteristic function with the series coefficients of the fourier cosine expansion of the density function in most cases the convergence rate of the cos method is exponential and the computational complexity is linear its range of application covers underlying asset processes for which the characteristic function is known and various types of option contracts we will present the method and its applications in two separate parts the first one is this paper where we deal with european options in particular in a follow up paper we will present its application to options with early exercise features

temporal aggregation of garch processes the authors derive low frequency say weekly models implied by high frequency say daily arma models with symmetric garch errors they show that low frequency models exhibit conditional heteroskedasticity of the garch form as well the parameters in the conditional variance equation of the low frequency model depend upon mean variance and kurtosis parameters of the corresponding high frequency model moreover strongly consistent estimators of the parameters in the high frequency model can be derived from low frequency data the common assumption in applications that rescaled innovations are independent is disputable since it depends upon the available data frequency copyright 1993 by the econometric society

modeling price dynamics in ebay auctions using differential equations empirical research of online auctions has grown dramatically in recent years studies using publicly available bid data from such websites as ebay com have found many divergences of bidding behavior and auction outcomes compared with ordinary offline auctions and auction theory among the main differences between online and offline auctions are the former s longer duration anonymity of bidders and sellers and low barriers of entry all of these factors lead to dynamics in the bid arrival and price process that change throughout the auction in this work we examine the price process in a large and diverse set of ebay auctions for both low and high valued items in terms of item auction bidder and seller characteristics we propose a family of differential equation models that captures online auction dynamics in particular we show that a second order linear differential equation well approximates the dynamics that occur in our diverse set of auctions we also introduce a multiple comparisons test fo

efficient method of moments estimation of a stochastic volatility model a monte carlo study abstract we perform an extensive monte carlo study of efficient method of moments emm estimation of a stochastic volatility model emm uses the expectation under the structural model of the score from an auxiliary model as moment conditions we examine the sensitivity to the choice of auxiliary model using arch garch and egarch models for the score as well as nonparametric extensions emm efficiency approaches that of maximum likelihood for larger sample sizes inference is sensitive to the choice of auxiliary model in small samples but robust in larger samples specification tests and t tests show little size distortion

a reduced form framework for modeling volatility of speculative prices based on realized variation measures abstract building on realized variance and bipower variation measures constructed from high frequency financial prices we propose a simple reduced form framework for effectively incorporating intraday data into the modeling of daily return volatility we decompose the total daily return variability into the continuous sample path variance the variation arising from discontinuous jumps that occur during the trading day as well as the overnight return variance our empirical results based on long samples of high frequency equity and bond futures returns suggest that the dynamic dependencies in the daily continuous sample path variability are well described by an approximate long memory har garch model while the overnight returns may be modeled by an augmented garch type structure the dynamic dependencies in the non parametrically identified significant jumps appear to be well described by the combination of an ach model for the time varying jump intensities coupled with a relatively simple log linear structure for the jump sizes finally we discuss how the resulting reduced form model structure for each of the three components may be used in the construction of out of sample forecasts for the total return volatility

updating schemes correlation structure blocking and parameterization for the gibbs sampler in this paper many convergence issues concerning the implementation of the gibbs sampler are investigated exact computable rates of convergence for gaussian target distributions are obtained different random and non random updating strategies and blocking combinations are compared using the rates the effect of dimensionality and correlation structure on the convergence rates are studied some examples are considered to demonstrate the results for a gaussian image analysis problem several updating strategies are described and compared for problems in bayesian linear models several possible parameterizations are analysed in terms of their convergence rates characterizing the optimal choice

infinitely divisible distributions in turbulence the imbedding of the scale similarity of random fields into the theory of infinitely divisible probability distributions is considered the general probability distribution for the breakdown coefficients of turbulent energy dissipation is obtained along with corresponding similarity exponents related issues of self similarity and asymptotic behavior of statistical characteristics are also considered

marginalization and contemporaneous aggregation in multivariate garch processes abstract we first of all show that contemporaneous aggregation of independent univariate garch processes yields a weak garch process as introduced by drost and nijman 1993 subsequently we analyze the dependence of the parameters in the aggregate on the parameters in the underlying models and show that the variance parameters after aggregation depend on the underlying variance and kurtosis parameters then we generalize the results by showing that a linear combination of variables generated by a multivariate garch process will also be weak garch finally we derive the marginal weak garch processes implied by several multivariate garch processes

particle markov chain monte carlo methods summary markov chain monte carlo and sequential monte carlo methods have emerged as the two main tools to sample from high dimensional probability distributions although asymptotic convergence of markov chain monte carlo algorithms is ensured under weak assumptions the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and or if highly correlated variables are updated independently we show here how it is possible to build efficient high dimensional proposal distributions by using sequential monte carlo methods this allows us not only to improve over standard markov chain monte carlo schemes but also to make bayesian inference feasible for a large class of statistical models where this was not previously so we demonstrate these algorithms on a non linear state space model and a levy driven stochastic volatility model

recent advances in the numerical analysis of volterra functional differential equations with variable delays the numerical analysis of volterra functional integro differential equations with vanishing delays has to overcome a number of challenges that are not encountered when solving classical delay differential equations with non vanishing delays in this paper i shall describe recent results in the analysis of optimal global and local superconvergence orders in collocation methods for such evolutionary problems following a brief survey of results for equations containing volterra integral operators with non vanishing delays the discussion will focus on pantograph type volterra integro differential equations with linear and nonlinear vanishing delays the paper concludes with a section on open problems these include the asymptotic stability of collocation solutions u h on uniform meshes for pantograph type functional equations and the analysis of collocation methods for pantograph type functional equations with advanced arguments

reliable approximate solution of systems of volterra integro differential equations with time dependent delays volterra integro differential equations with time dependent delay arguments can provide us with realistic models of many real world phenomena delayed lokta volterra predator prey systems arise in ecology and are well known examples of delay volterra integro differential equations dvides first introduced by volterra in 1928 we investigate the numerical solution of systems of dvides using an adaptive stepsize selection strategy we will present a generic variable stepsize approach for solving systems of neutral dvides based on an explicit continuous runge kutta method using defect error control and study the convergence of the resulting numerical method for various kinds of delay arguments we will show that the global error of the numerical solution can be effectively and reliably controlled by monitoring the size of the defect of the approximate solution and adjusting the stepsize on each step of the integration numerical results will be presented to demonstrate the effectiveness of this approach

existence of solutions for a nonlinear pde with an inverse square potential abstract via linking theorem and delicate energy estimates the existence of nontrivial solutions for a nonlinear pde with an inverse square potential and critical sobolev exponent is proved this result gives a partial positive answer to an open problem proposed in ferrero and gazzola j differential equations 177 2001 494

supremum self decomposable random vectors an intrinsic definition of sup self decomposable random vectors is given it is proved that they are precisely the limits in distribution of certain normalized partial maxima of sequences of independent random vectors the main further result is a representation of sup self decomposable random vectors as functions of poisson processes which is the analogue of wolfe s 1982 representation of additively self decomposable random variables

numerical stability of nonlinear delay differential equations of neutral type this paper is devoted to the stability analysis of both the true solutions and the numerical approximations for nonlinear systems of neutral delay differential equations nddes of the form y t f t y t g t y t t y t t this work extends the results recently obtained by the authors bellen et al bit 39 1999 1 24 for the linear case this is accomplished by considering a suitable reformulation of the given system which transforms it into a nonlinear differential system coupled with an algebraic functional recursion numerical processes preserving the qualitative properties of the solutions are also investigated

bayesian model comparison with the hyvarinen score computation and consistency the bayes factor is a widely used criterion in model comparison and its logarithm is a difference of out of sample predictive scores under the logarithmic scoring rule however when some of the ca

numerical modelling in biosciences using delay differential equations our principal purposes here are i to consider from the perspective of applied mathematics models of phenomena in the biosciences that are based on delay differential equations and for which numerical approaches are a major tool in understanding their dynamics ii to review the application of numerical techniques to investigate these models we show that there are prima facie reasons for using such models i they have a richer mathematical framework compared with ordinary differential equations for the analysis of biosystem dynamics ii they display better consistency with the nature of certain biological processes and predictive results we analyze both the qualitative and quantitative role that delays play in basic time lag models proposed in population dynamics epidemiology physiology immunology neural networks and cell kinetics we then indicate suitable computational techniques for the numerical treatment of mathematical problems emerging in the biosciences comparing them with those implemented by the bio modellers

arithmetic brownian motion subordinated by tempered stable and inverse tempered stable processes abstract in the last decade the subordinated processes have become popular and have found many practical applications therefore in this paper we examine two processes related to time changed subordinated classical brownian motion with drift called arithmetic brownian motion the first one so called normal tempered stable is related to the tempered stable subordinator while the second one to the inverse tempered stable process we compare the main properties such as probability density functions laplace transforms ensemble averaged mean squared displacements of such two subordinated processes and propose the parameters estimation procedures moreover we calibrate the analyzed systems to real data related to indoor air quality

the brezis nirenberg problem for the curl curl operator abstract we look for solutions e r 3 of the problem e e e p 2 e in e 0 on on a bounded lipschitz domain r 3 where denotes the curl operator in r 3 the equation describes the propagation of the time harmonic electric field e x e i t in a nonlinear isotropic material with e 2 0 where and e stand for the permeability and the linear part of the permittivity of the material the nonlinear term e p 2 e with p 2 is responsible for the nonlinear polarisation of and the boundary conditions are those for surrounded by a perfect conductor the problem has a variational structure and we deal with the critical value p for instance in convex domains or in domains with c 1 1 boundary p 6 2 is the sobolev critical exponent and we get the quintic nonlinearity in the equation we show that there exist a cylindrically symmetric ground state solution and a finite number of cylindrically symmetric bound states depending on 0 we develop a new critical point theory which allows to solve the problem and which enables us to treat more general anisotropic media as well as other variational problems

collocation methods for nonlinear volterra integro differential equations with infinite delay in this paper we study the numerical solution of nonlinear volterra integrodifferential equations with infinite delay by spline collocation and related runge kutta type methods the kernel function in these equations is of the form k t 8 y t y s with a representative example given by volterra s population equation where we have k t a y t y 8 a t s g y t y 8

a quasi maximum likelihood method for estimating the parameters of multivariate diffusions a quasi maximum likelihood procedure for estimating the parameters of multi dimensional diffusions is developed in which the transitional density is a multivariate gaussian density with first and second moments approximating the true moments of the unknown density for affine drift and diffusion functions the moments are exactly those of the true transitional density and for nonlinear drift and diffusion functions the approximation is extremely good and is as effective as alternative methods based on likelihood approximations the estimation procedure generalises to models with latent factors a conditioning procedure is developed that allows parameter estimation in the absence of proxies

exact simulation of the sabr model the stochastic alpha beta rho sabr model becomes popular in the financial industry because it is capable of providing good fits to various types of implied volatility curves observed in the marketplace however no analytical solution to the sabr model exists that can be simulated directly this paper explores the possibility of exact simulation for the sabr model our contribution is threefold i we propose an exact simulation method for the forward price and its volatility in two special but practically interesting cases i e when the elasticity 1 or when 1 and the price and volatility processes are instantaneously uncorrelated primary difficulties involved are how to simulate two random variables whose distributions can be expressed in terms of the hartman watson and the noncentral chi squared distribution functions respectively two novel simulation schemes are proposed to achieve numerical accuracy efficiency and stability one stems from numerical laplace inversion and asian option literature and the other is based on recent developments in evaluating the noncentral chi squared distribution functions in a robust way numerical examples demonstrate that our method is fast and accurate under various market environments ii when 1 but the price and volatility processes are correlated our simulation method becomes a semi exact one numerical results suggest that it is still quite accurate when the time horizon is not long e g no greater than one year for long time horizons a piecewise semi exact simulation scheme is developed that reduces the biases substantially iii for european option pricing under the sabr model we propose a conditional simulation method which reduces the variance of the plain simulation significantly e g by more than 99 the e companion is available at https doi org 10 1287 opre 2017 1617

critical growth problems for polyharmonic operators we prove that critical growth problems for polyharmonic operators admit nontrivial solutions for a wide class of lower order perturbations of the critical term the results highlight the phenomenon of bifurcation of the critical dimensions discovered by pucci and serrin moreover we show that another bifurcation seems to appear for nonresonant dimensions

time varying periodicity in intraday volatility abstractwe develop a nonparametric test for whether return volatility exhibits time varying intraday periodicity using a long time series of high frequency data our null hypothesis commonly adopt

subcritical perturbations of a singular quasilinear elliptic equation involving the critical hardy sobolev exponent abstract in this work we improve some known results for a singular operator and also for a wide class of lower order terms by proving a multiplicity result the proof is made by applying the generalized mountain pass theorem due to ambrosetti and rabinowitz to do this we show that the minimax levels are in a convenient range by combining a special class of approximating functions due to gazzola and ruf with the concentrating functions of the best sobolev constant

nonspectral relaxation in one dimensional ornstein uhlenbeck processes the relaxation of a dissipative system to its equilibrium state often shows a multiexponential pattern with relaxation rates which are typically considered to be independent of the initial condition the rates follow from the spectrum of a hermitian operator obtained by a similarity transformation of the initial fokker planck operator however some initial conditions are mapped by this similarity transformation to functions which growat infinity these cannot be expanded in terms of the eigenfunctions of a hermitian operator and show different relaxation patterns considering the exactly solvable examples of gaussian and generalized levy ornstein uhlenbeck processes oups we show that the relaxation rates belong to the hermitian spectrum only if the initial condition belongs to the domain of attraction of the stable distribution defining the noise while for an ordinary oup initial conditions leading to nonspectral relaxation can be considered exotic for generalized oups driven by levy noise such initial conditions are the rule doi 10 1103 physrevlett 110 150602

forecasting volatility of fuel oil futures in china garch type sv or realized volatility models abstract in most previous works on forecasting oil market volatility squared daily returns were taken as the proxy of unobserved actual volatility however as demonstrated by andersen and bollerslev 1998 22 this proxy with too high measurement noise could be perfectly outperformed by a so called realized volatility rv measure calculated by the cumulative sum of squared intraday returns with this motivation we further extend earlier works by employing intraday high frequency data to compare the performance of three typical volatility models in the daily out of sample volatility forecasting of fuel oil futures on the shanghai futures exchange shfe the garch type stochastic volatility sv and realized volatility models by taking rv as the proxy of actual daily volatility and then computing forecasting errors we find that the realized volatility model based on intraday high frequency data produces significantly more accurate volatility forecasts than the garch type and sv models based on daily returns furthermore the sv model outperforms many linear and nonlinear garch type models that capture long memory volatility and or the asymmetric leverage effect in volatility these results also prove that abundant volatility information is available in intraday high frequency data and can be used to construct more accurate oil volatility forecasting models

econometric analysis of realized covariation high frequency based covariance regression and correlation in financial economics this paper analyses multivariate high frequency financial data using realized covariation we provide a new asymptotic distribution theory for standard methods such as regression correlation analysis and covariance it will be based on a fixed interval of time e g a day or week allowing the number of high frequency returns during this period to go to infinity our analysis allows us to study how high frequency correlations regressions and covariances change through time in particular we provide confidence intervals for each of these quantities

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

analytic approach to the problem of convergence of truncated levy flights towards the gaussian stochastic process an analytic expression for characteristic function defining a truncated l evy flight is derived it is shown that the characteristic function yields results in agreement with recent simulations of truncated l evy flights by mantegna and stanley phys rev lett 73 2946 1994 with the analytic expression for the characteristic function the convergence of the l evy process towards the gaussian is demonstrated without simulations in the calculation of first return probability the simulations are replaced by numerical integration using simple quadratures

generalized arma models with martingale difference errors the analysis of non gaussian time series has been studied extensively and has many applications many successful models can be viewed as special cases or variations of the generalized autoregressive moving average garma models of benjamin et al 2003 where a link function similar to that used in generalized linear models is introduced and the conditional mean under the link function assumes an arma structure under such a model the transformed time series under the same link function assumes an arma form as well unfortunately unless the link function is an identity function the error sequence defined in the transformed arma model is usually not a martingale difference sequence in this paper we extend the garma model in such a way that the resulting arma model in the transformed space has a martingale difference sequence as its error sequence the benefit of such an extension are four folds it has easily verifiable conditions for stationarity and ergodicity its gaussian pseudo likelihood estimator is consistent standard time series model building tools are ready to use and its mle s asymptotic distribution can be established we also proposes two new classes of non gaussian time series models under the new framework the performance of the proposed models is demonstrated with simulated and real examples

the distribution of realized exchange rate volatility using high frequency data on deutschemark and yen returns against the dollar we construct model free estimates of daily exchange rate volatility and correlation that cover an entire decade our estimates termed realized volatilities and correlations are not only model free but also approximately free of measurement error under general conditions which we discuss in detail hence for practical purposes we may treat the exchange rate volatilities and correlations as observed rather than latent we do so and we characterize their joint distribution both unconditionally and conditionally noteworthy results include a simple normality inducing volatility transformation high contemporaneous correlation across volatilities high correlation between correlation and volatilities pronounced and persistent dynamics in volatilities and correlations evidence of long memory dynamics in volatilities and correlations and remarkably precise scaling laws under temporal aggregation

on the use of high frequency measures of volatility in midas regressions abstract many empirical studies link mixed data frequency variables such as low frequency macroeconomic or financial variables with high frequency financial indicators volatilities especially within a predictive regression model context the objective of this paper is threefold first we relate the standard least squares ls regression model with high frequency volatility predictors with the corresponding mixed data sampling nonlinear ls midas nls regression model ghysels et al 2005 ghysels et al 2006 and evaluate the properties of the regression estimators of these models we also consider alternative high frequency volatility measures as well as various continuous time models using their corresponding relevant higher order moments to further analyze the properties of these estimators second we derive the relative mse efficiency of the slope estimator in the standard ls and midas regressions we provide conditions for relative efficiency and present the numerical results for different continuous time models third we extend the analysis of the bias of the slope estimator in standard ls regressions with alternative realized measures of risk such as the realized covariance realized beta and the realized skewness when the true dgp is a midas model

on series representations of infinitely divisible random vectors general results on series representations involving arrival times in a poisson process are established for infinitely divisible banach space valued random vectors without gaussian components applying these results various generalization of lepage s representation are obtained in a unified way certain conditionally gaussian infinitely divisible random vectors are characterized and some problems related to a gaussian randomization method are investigated

analysis of error control strategies for continuous runge kutta methods there has been considerable recent progress in the analysis and development of interpolation schemes that can be associated with discrete runge kutta methods with the availability of these schemes it can now be asked that a numerical method provide a continuous approximation to the solution thispaper rather than view such a continuous method as an interpolant superimposed on a standard discrete method considers how the interpolant and its associated defect can be effectively used in the underlying error and stepsize control mechanism in particular four error control strategies are considered that can be used in methods based on runge kutta formula pairs with interpolants an asymptotic and a nonasymptotic analysis of each strategy are presented it is shown that a strategy based on direct defect control can provide significant advantages over existing strategies with only a modest increase in cost

filtering via simulation auxiliary particle filters this article analyses the recently suggested particle approach to filtering time series we suggest that the algorithm is not robust to outliers for two reasons the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution here we tackle the first of these problems

solutions of elliptic equations with critical sobolev exponent in dimension three theorem 1 for every a 72 4 there exists a solution of i the previously known results concerning this problem are the following 1 if 1 5 0 i has no solution this follows from pohozaev s identity see lo and from the principle of unique continuation when a 0 we will suppose in the following that i 0 2 every positive solution of i is radial see gidas et al 9 3 let a be the first eigenvalue of a in b with dirichlet boundary condition and p1 the associated eigenfunction then for every a 2 i i has no positive solution this result follows from multiplying i by cp 4 for every a e n2 4 rr there exists a positive solution of i see brezis and nirenberg 5 5 for i 5 n2 4 i has no radial solution see 5 6 for every k e n if 1 e zk with zk k t n k2n2 i has a radial solution with k 1 zeros see atkinson and peletier 2 31 7 the analogue of theorem 1 in dimension n 2 4 holds for general domains see capozzi et al 6 and ambrosetti and struwe l our method is very different and we do not know whether theorem 1 is valid for general domains in ir3

random integral representations for classes of limit distributions similar to levy class l0 iii for 1 0 subclasses u of the levy class l o of selfdecomposable measures on banach spaces are examined they are defined as limit distributions in certain summation schemes the main result in section 1 theorem 1 2 shows that each measure i from u is a convolution of a strictly stable measure with exponent and a probability distribution of random integral int 0 1 tdy t beta where y is a levy process with finite th moment the situation differs essentially from that with positive u theorem 2 2 in section 2 shows that the natural mapping pounds y 1 to pounds int 0 1 tdy t beta is a homeomorphism which immediately gives so called generators for the classu in addition potential applications of measures from u in the ising model for ferromagnetism are indicated finally remark 3 b shows that the classes u constitute a filtration of the semigroup id of all infinitely divisible measures

inference on fractal processes using multiresolution approximation we consider bayesian inference via markov chain monte carlo for a variety of fractal gaussian processes on the real line these models have unknown parameters in the covariance matrix requiring inversion of a new covariance matrix at each markov chain monte carlo iteration the processes have no suitable independence properties so this becomes computationally prohibitive we surmount these difficulties by developing a computational algorithm for likelihood evaluation based on a multiresolution approximation to the original process the method is computationally very efficient and widely applicable making likelihood based inference feasible for large datasets a simulation study indicates that this approach leads to accurate estimates for underlying parameters in fractal models including fractional brownian motion and fractional gaussian noise and functional parameters in the recently introduced multifractional brownian motion we apply the method to a variety of real datasets and illustrate its application to prediction and to model selection

a new factorization property of the selfdecomposable probability measures we prove that the convolution of a selfdecomposable dis tribution with its background driving law is again selfdecomposable if and only if the background driving law is s selfdecomposable we will refer to this as the factorization property of a selfdecomposable distribution let l f denote the set of all these distributions the algebraic structure and various characterizations of l f are studied some examples are discussed the most interesting one being given by the levy stochastic area integral a nested family of subclasses l f n 0 or a filtration of the class l f is given

out of sample forecasts of quadratic variation we compare the forecasts of quadratic variation given by the realized volatility rv and the two scales realized volatility tsrv computed from high frequency data in the presence of market microstructure noise under several different dynamics for the volatility process and assumptions on the noise we show that tsrv largely outperforms rv whether looking at bias variance rmse or out of sample forecasting ability an empirical application to all djia stocks confirms the simulation results

general optimized lower and upper bounds for discrete and continuous arithmetic asian options we propose an accurate method for pricing arithmetic asian options on the discrete or continuous average in a general model setting by means of a lower bound approximation in particular we derive analytical expressions for the lower bound in the fourier domain this is then recovered by a single univariate inversion and sharpened using an optimization technique in addition we derive an upper bound to the error from the lower bound price approximation our proposed method can be applied to computing the prices and price sensitivities of asian options with fixed or floating strike price discrete or continuous averaging under a wide range of stochastic dynamic models including exponential levy models stochastic volatility models and the constant elasticity of variance diffusion our extensive numerical experiments highlight the notable performance and robustness of our optimized lower bound for different test cases

convergence analysis of an arnoldi order reduced runge kutta method for integro differential equations of pantograph type in this paper we consider a numerical method for linear functional integro differential equations with pantograph delays to deal with the pantograph delays we introduce a geometrically increasing mesh and propose a new kind of runge kutta methods based on the arnoldi order reduced technique the convergence analysis of the new method is presented and the method is proved to be at least first order the numerical experiments attached show that the new method can achieve almost the same accuracy as the corresponding runge kutta method for some properly chosen krylov subspaces

analysis of high dimensional multivariate stochastic volatility models this paper is concerned with the bayesian estimation and comparison of flexible high dimensional multivariate time series models with time varying correlations the model proposed and considered here combines features of the classical factor model with that of the heavy tailed univariate stochastic volatility model a unified analysis of the model and its special cases is developed that encompasses estimation filtering and model choice the centerpieces of the estimation algorithm which relies on mcmc methods are 1 a reduced blocking scheme for sampling the free elements of the loading matrix and the factors and 2 a special method for sampling the parameters of the univariate sv process the resulting algorithm is scalable in terms of series and factors and simulation efficient methods for estimating the log likelihood function and the filtered values of the time varying volatilities and correlations are also provided the performance and effectiveness of the inferential methods are extensively tested using simulated data where models up to 50 dimensions and 688 parameters are fit and studied the performance of our model in relation to various multivariate garch models is also evaluated using a real data set of weekly returns on a set of 10 international stock indices we consider the performance along two dimensions the ability to correctly estimate the conditional covariance matrix of future returns and the unconditional and conditional coverage of the 5 and 1 value at risk var measures of four pre defined portfolios

the euler scheme for levy driven stochastic differential equations in relation with monte carlo methods to solve some integro differential equations we study the approximation problem of ee g x t by ee g bar x t n where x t 0 leq t leq t is the solution of a stochastic differential equation governed by a levy process z t bar x n t is defined by the euler discretization scheme with step fractn with appropriate assumptions we show that the error ee g x t ee g bar x t n can be expanded in powers of frac1n if the levy measure of z has finite moments of order high enough otherwise the rate of convergence is slower and its speed depends on the behavior of the tails of the levy measure the simulation of the increments of z t is also discussed

non gaussian ornstein uhlenbeck based models and some of their uses in financial economics non gaussian processes of ornstein uhlenbeck ou type offer the possibility of capturing important distributional deviations from gaussianity and for flexible modelling of dependence structures this paper develops this potential drawing on and extending powerful results from probability theory for applications in statistical analysis their power is illustrated by a sustained application of ou processes within the context of finance and econometrics we construct continuous time stochastic volatility models for financial assets where the volatility processes are superpositions of positive ou processes and we study these models in relation to financial data and theory

econometric analysis of realized volatility and its use in estimating stochastic volatility models summary the availability of intraday data on the prices of speculative assets means that we can use quadratic variation like measures of activity in financial markets called realized volatility to study the stochastic properties of returns here under the assumption of a rather general stochastic volatility model we derive the moments and the asymptotic distribution of the realized volatility error the difference between realized volatility and the discretized integrated volatility which we call actual volatility these properties can be used to allow us to estimate the parameters of stochastic volatility models without recourse to the use of simulation intensive methods

modeling high frequency financial data by pure jump processes hk rgc hkust6011 07p hkust6015 08p hkust6019 10p humanity and social science youth foundation of chinese ministry of education 12yjc910003

ornstein uhlenbeck processes for geophysical data analysis abstract in this work a three parameter stochastic process termed the gamma ornstein uhlenbeck process has been implemented to analyze geophysical data such non gaussian ornstein uhlenbeck processes offer the possibility of capturing important distributional deviations from gaussianity and make the model flexible of dependence structures it is shown that the gamma ornstein uhlenbeck process is a possible candidate for earthquake data modeling rigorous regression analysis is provided and based on that the first passage times are computed for different sets of data it is shown that this model may be used to estimate parameters related to some major events namely major earthquakes

extremes and local dependence in stationary sequences extensions of classical extreme value theory to apply to stationary sequences generally make use of two types of dependence restriction a a weak mixing condition restricting long range dependence b a local condition restricting the clustering of high level exceedances

temporal aggregation of volatility models in this paper we consider temporal aggregation of volatility models we introduce semiparametric volatility models termed square root stochastic autoregressive volatility sr sarv which are characterized by autoregressive dynamics of the stochastic variance our class encompasses the usual garch models and various asymmetric garch models moreover our stochastic volatility models are characterized by multiperiod conditional moment restrictions in terms of observables the sr sarv class is a natural extension of the class of weak garch models this extension has four advantages i we do not assume that fourth moments are finite ii we allow for asymmetries skewness leverage effect that are excluded from weak garch models iii we derive conditional moment restrictions and iv our framework allows us to study temporal aggregation of igarch models

on the linearity of bayesian interpolators for non gaussian continuous time ar 1 processes bayesian estimation problems involving gaussian distributions often result in linear estimation techniques nevertheless there are no general statements as to whether the linearity of the bayesian estimator is restricted to the gaussian case the two common strategies for non gaussian models are either finding the best linear estimator or numerically evaluating the bayesian estimator by monte carlo methods in this paper we focus on bayesian interpolation of non gaussian first order autoregressive ar processes where the driving innovation can admit any symmetric infinitely divisible distribution characterized by the levy khintchine representation theorem we redefine the bayesian estimation problem in the fourier domain with the help of characteristic forms by providing analytic expressions we show that the optimal interpolator is linear for all symmetric stable distributions the bayesian interpolator can be expressed in a convolutive form where the kernel is described in terms of exponential splines we also show that the limiting case of levy type ar 1 processes the system of which has a pole at the origin always corresponds to a linear bayesian interpolator made of a piecewise linear spline irrespective of the innovation distribution finally we show the two mentioned cases to be the only ones within the family for which the bayesian interpolator is linear

levy processes in free probability this is the continuation of a previous article that studied the relationship between the classes of infinitely divisible probability measures in classical and free probability respectively via the bercovici pata bijection drawing on the results of the preceding article the present paper outlines recent developments in the theory of levy processes in free probability

bounds on the spectrum for markov chains and markov processes a generalization of cheeger s inequality we prove a general version of cheeger s inequality for discrete time markov chains and continuous time markovian jump processes both reversible and nonreversible with general state space we also prove a version of cheeger s inequality for markov chains and processes with killing as an application we prove l 2 exponential convergence to equilibrium for random walk with inward drift on a class of countable rooted graphs