violation of the fluctuation dissipation theorem in glassy systems basic notions and the numerical evidence this review reports on the research done during past years on violations of the fluctuation dissipation theorem fdt in glassy systems it is focused on the existence of a quasi fluctuation dissipation theorem qfdt in glassy systems and the current supporting knowledge gained from numerical simulation studies it covers a broad range of non stationary aging and stationary driven systems such as structural glasses spin glasses coarsening systems ferromagnetic models at criticality trap models models with entropy barriers kinetically constrained models sheared systems and granular media the review is divided into four main parts 1 an introductory section explaining basic notions related to the existence of the fdt in equilibrium and its possible extension to the glassy regime qfdt 2 a description of the basic analytical tools and results derived in the framework of some exactly solvable models 3 a detailed report of the current evidence in favour of the qfdt and 4 a brief digression on the experimental evidence in its favour this review is intended for inexpert readers who want to learn about the basic notions and concepts related to the existence of the qfdt as well as for the more expert readers who may be interested in more specific results

generic features of the fluctuation dissipation relation in coarsening systems the integrated response function in phase ordering systems with scalar vector conserved and nonconserved order parameter is studied at various space dimensionalities assuming scaling of the aging contribution ensuremath chi ag t t w t w ensuremath a ensuremath chi stackrel ifmmode hat else fi ensuremath chi t t w we obtain by numerical simulations and analytical arguments the phenomenological formula describing the dimensionality dependence of a ensuremath chi in all cases considered the primary result is that a ensuremath chi vanishes continuously as d approaches the lower critical dimensionality d l this implies that i the existence of a nontrivial fluctuation dissipation relation and ii the failure of the connection between statics and dynamics are generic features of phase ordering at d l

spectral gmm estimation of continuous time processes abstract this paper derives a methodology for the estimation of continuous time stochastic models based on the characteristic function the estimation method does not require discretization of the stochastic process and it is simple to apply in practice the method is essentially generalized method of moments on the complex plane hence it shares the efficiency and distribution properties of gmm estimators we illustrate the method with some applications to relevant estimation problems in continuous time finance we estimate a model of stochastic volatility a jump diffusion model with constant volatility and a model that nests both the stochastic volatility model and the jump diffusion model we find that negative jumps are important to explain skewness and asymmetry in excess kurtosis of the stock return distribution while stochastic volatility is important to capture the overall level of this kurtosis positive jumps are not statistically significant once we allow for stochastic volatility in the model we also estimate a non affine model of stochastic volatility and find that the power of the diffusion coefficient appears to be between one and two rather than the value of one half that leads to the standard affine stochastic volatility model however we find that including jumps into this non affine stochastic volatility model reduces the power of the diffusion coefficient to one half finally we offer an explanation for the observation that the estimate of persistence in stochastic volatility increases dramatically as the frequency of the observed data falls based on a multiple factor stochastic volatility model

large deviations condensation and giant response in a statistical system we study the probability distribution p of the sum of a large number of non identically distributed random variables n m condensation of fluctuations the phenomenon whereby one of such variables provides a macroscopic contribution to the global probability is discussed and interpreted by analogy with phase transitions in statistical mechanics a general expression for p is derived and its sensitivity to the details of the distribution of a single n m is worked out these general results are verified by the analytical and numerical solution of some specific examples

efficient implementation of markov chain monte carlo when using an unbiased likelihood estimator summary when an unbiased estimator of the likelihood is used within a metropolis hastings chain it is necessary to trade off the number of monte carlo samples used to construct this estimator against the asymptotic variances of the averages computed under this chain using many monte carlo samples will typically result in metropolis hastings averages with lower asymptotic variances than the corresponding averages that use fewer samples however the computing time required to construct the likelihood estimator increases with the number of samples under the assumption that the distribution of the additive noise introduced by the loglikelihood estimator is gaussian with variance inversely proportional to the number of samples and independent of the parameter value at which it is evaluated we provide guidelines on the number of samples to select we illustrate our results by considering a stochastic volatility model applied to stock index returns

slow relaxation in the large n model for phase ordering the basic features of the slow relaxation phenomenology arising in phase ordering processes are obtained analytically in the large n model through the exact separation of the order parameter into the sum of thermal and condensation components the aging contribution in the response function x a g t t w is found to ohey a pattern of behavior under variation of dimensionality qualitatively similar to the one observed in ising systems there exists a critical dimensionality d 4 above which x a g t t w is proportional to the defect density d t while for d 4 it vanishes more slowly than d t and at d 2 does not vanish as in the ising case this behavior can be understood in terms of the dependence on dimensionality of the interplay between the defect density and the effective response associated to a single defect

traveling wave solutions for gause type predator prey systems with density dependence a heteroclinic orbit in r4 abstract this paper investigates the existence of traveling wave solutions for a class of diffusive gause type predator prey systems with linear density dependence for predator using the shooting method we establish the existence of a non negative traveling wave solution connecting a boundary equilibrium point to the coexistence equilibrium point with the help of topological method of wazewski theorem and lasalle s invariance principle

scaling in the aging dynamics of the site diluted ising model we study numerically the phase ordering kinetics of the two dimensional site diluted ising model the data can be interpreted in a framework motivated by renormalization group concepts apart from the usual fixed point of the nondiluted system there exist two disorder fixed points characterized by logarithmic and power law growth of the ordered domains this structure gives rise to a rich scaling behavior with an interesting crossover due to the competition between fixed points and violation of superuniversality

threshold bipower variation and the impact of jumps on volatility forecasting this study reconsiders the role of jumps for volatility forecasting by showing that jumps have a positive and mostly significant impact on future volatility this result becomes apparent once volatility is separated into its continuous and discontinuous components using estimators which are not only consistent but also scarcely plagued by small sample bias with the aim of achieving this we introduce the concept of threshold bipower variation which is based on the joint use of bipower variation and threshold estimation we show that its generalization threshold multipower variation admits a feasible central limit theorem in the presence of jumps and provides less biased estimates with respect to the standard multipower variation of the continuous quadratic variation in finite samples we further provide a new test for jump detection which has substantially more power than tests based on multipower variation empirical analysis on the s p500 index individual stocks and us bond yields shows that the proposed techniques improve significantly the accuracy of volatility forecasts especially in periods following the occurrence of a jump

spin bond and global fluctuation dissipation relations in the non equilibrium spherical ferromagnet we study the out of equilibrium dynamics of the spherical ferromagnet after a quench to its critical temperature we calculate correlation and response functions for spin observables which probe length scales much larger than the lattice spacing but smaller than the system size and find that the asymptotic fluctuation dissipation ratio fdr x is the same as for local observables this is consistent with our earlier results for the ising model in dimension d 1 and d 2 we also check that bond observables both local and long range give the same asymptotic fdr in the second part of the paper the analysis is extended to global observables which probe correlations among all n spins here non gaussian fluctuations arising from the spherical constraint need to be accounted for and we develop a systematic expansion in to do this applying this to the global bond observable i e the energy we find that non gaussian corrections change its fdr to a nontrivial value which we calculate exactly for all dimensions d 2 finally we consider quenches from magnetized initial states here even the fdr for the global spin observable i e the magnetization is nontrivial it differs from the one for unmagnetized states even in d 4 signalling the appearance of a distinct dynamical universality class of magnetized critical coarsening for lower d the fdr is irrational even to first order in 4 d and d 2 the latter in contrast to recent results for the transverse fdr in the n vector model

bootstrapping realized volatility we propose bootstrap methods for a general class of nonlinear transformations of realized volatility which includes the raw version of realized volatility and its logarithmic transformation as special cases we consider the independent and identically distributed i i d bootstrap and the wild bootstrap wb and prove their first order asymptotic validity under general assumptions on the log price process that allow for drift and leverage effects we derive edgeworth expansions in a simpler model that rules out these effects the i i d bootstrap provides a second order asymptotic refinement when volatility is constant but not otherwise the wb yields a second order asymptotic refinement under stochastic volatility provided we choose the external random variable used to construct the wb data appropriately none of these methods provides third order asymptotic refinements both methods improve upon the first order asymptotic theory in finite samples

pricing formula for european currency option and exchange option in a generalized jump mixed fractional brownian motion with time varying coefficients abstract in this paper a new framework for pricing the european currency option is developed in the case where the spot exchange rate follows a generalized mixed fractional brownian motion with jumps hereafter gjmfbm in addition we consider a general case that the coefficients of the model are time varying to capture the behaviors of exchange rate the combination of poisson jumps and generalized mixed fractional brownian motion is introduced to derive the pricing formula for some options we firstly derive a generalized mixed fractional girsanov theorem and some results regarding the quasi conditional expectation that we will need for the rest of the paper then analytic pricing formulas for european currency option and exchange option are obtained using the equivalent martingale measure finally through some numerical experiments and discussion we show that the gjmfbm model is different with the other previous ones

exact simulation of stochastic volatility and other affine jump diffusion processes the stochastic differential equations for affine jump diffusion models do not yield exact solutions that can be directly simulated discretization methods can be used for simulating security prices under these models however discretization introduces bias into the simulation results and a large number of time steps may be needed to reduce the discretization bias to an acceptable level this paper suggests a method for the exact simulation of the stock price and variance under hestons stochastic volatility model and other affine jump diffusion processes the sample stock price and variance from the exact distribution can then be used to generate an unbiased estimator of the price of a derivative security we compare our method with the more conventional euler discretization method and demonstrate the faster convergence rate of the error in our method specifically our method achieves an o s 1 2 convergence rate where s is the total computational budget the convergence rate for the euler discretization method is o s 1 3 or slower depending on the model coefficients and option payoff function

empirical reverse engineering of the pricing kernel abstract this paper proposes an econometric procedure that allows the estimation of the pricing kernel without either any assumptions about the investors preferences or the use of the consumption data we propose a model of equity price dynamics that allows for i simultaneous consideration of multiple stock prices ii analytical formulas for derivatives such as futures options and bonds and iii a realistic description of all of these assets the analytical specification of the model allows us to infer the dynamics of the pricing kernel the model calibrated to a comprehensive dataset including the s p 500 index individual equities t bills and gold futures yields the conditional filter of the unobservable pricing kernel as a result we obtain the estimate of the kernel that is positive almost surely i e precludes arbitrage consistent with the equity risk premium the risk free discounting and with the observed asset prices by construction the pricing kernel estimate involves a highly nonlinear function of the contemporaneous and lagged returns on the s p 500 index this contradicts typical implementations of capm that use a linear function of the market proxy return as the pricing kernel hence the s p 500 index does not have to coincide with the market portfolio if it is used in conjunction with nonlinear asset pricing models we also find that our best estimate of the pricing kernel is not consistent with the standard time separable utilities but potentially could be cast into the stochastic habit formation framework of campbell and cochrane j political economy 107 1999 205

financial asset returns direction of change forecasting and volatility dynamics we consider three sets of phenomena that feature prominently in the financial economics literature 1 conditional mean dependence or lack thereof in asset returns 2 dependence and hence forecastability in asset return signs and 3 dependence and hence forecastability in asset return volatilities we show that they are very much interrelated and explore the relationships in detail among other things we show that 1 volatility dependence produces sign dependence so long as expected returns are nonzero so that one should expect sign dependence given the overwhelming evidence of volatility dependence 2 it is statistically possible to have sign dependence without conditional mean dependence 3 sign dependence is not likely to be found via analysis of sign autocorrelations runs tests or traditional market timing tests because of the special nonlinear nature of sign dependence so that traditional market timing tests are best viewed as tests for sign dependence arising from variation in expected returns rather than from variation in volatility or higher moments 4 sign dependence is not likely to be found in very high frequency e g daily or very low frequency e g annual returns instead it is more likely to be found at intermediate return horizons and 5 the link between volatility dependence and sign dependence remains intact in conditionally non gaussian environments for example with time varying conditional skewness and or kurtosis

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

correlation functions and fluctuation dissipation relation in driven phase ordering systems an exactly solvable model the dynamics of a phase ordering system with non conserved order parameter under a plain shear flow with rate is solved analytically in the large n limit a phase transition is observed at a critical temperature tc after a quench from a high temperature equilibrium state to a lower temperature t a non equilibrium stationary state is entered when t tc while aging dynamics characterizes the phases with t tc two time quantities are computed and the off equilibrium generalization of the fluctuation dissipation theorem is provided

consistency and asymptotic normality of the quasi maximum likelihood estimator in igarch 1 1 and covariance stationary garch 1 1 models this paper provides a proof of the consistency and asymptotic normality of the quasi maximum likelihood estimator in garch 1 1 and igarch 1 1 models in contrast to the case of a unit root in the conditional mean the presence of a unit root in the conditional variance does not affect the limiting distribution of the estimators in both models estimators are normally distributed in addition a consistent estimator of the covariance matrix is available enabling the use of standard test statistics for inference

investigating market efficiency through a forecasting model based on differential equations abstract a new differential equation based model for stock price trend forecast is proposed as a tool to investigate efficiency in an emerging market its predictive power showed statistically to be higher than the one of a completely random model signaling towards the presence of arbitrage opportunities conditions for accuracy to be enhanced are investigated and application of the model as part of a trading strategy is discussed

contemporaneous asymmetry in garch processes abstract the paper introduces a new concept of asymmetry contemporaneous asymmetry in conditional heteroskedasticity models we propose an original class of models aimed to capture the leverage effect contemporaneous asymmetry as well as time varying skewness and kurtosis not only past up and down moves have different impacts on the conditional variance but also positive and negative changes are governed by different conditional variances we give conditions for the existence of a second order and strictly stationary solution the paper also provides consistency results on the quasi maximum likelihood estimation finally an empirical analysis on the french cac 40 stock index is proposed

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

increased correlation among asset classes are volatility or jumps to blame or both abstract we develop estimators and asymptotic theory to decompose the quadratic covariation between two assets into its continuous and jump components in a manner that is robust to the presence of market microstructure noise using high frequency data on different assets classes we find that the recent financial crisis led to an increase in both the quadratic variations of the assets and their correlations however we find little evidence to suggest a change between the relative contributions of the brownian and jump components as both comove co jumps stem from surprising news announcements that occur primarily before the opening of the us market and are also accompanied by an increase in brownian driven correlations

stationarity of garch processes and of some nonnegative time series abstract two time series models are considered garch processes and generalized multivariate autoregressive equations x n 1 a n 1 x n b n 1 with nonnegative i i d coefficients in each case a necessary and sufficient condition ensuring the existence of a strictly stationary solution is given

smc 2 an efficient algorithm for sequential analysis of state space models we consider the generic problem of performing sequential bayesian inference in a state space model with observation process y state process x and fixed parameter theta an idealized approach would be to apply the iterated batch importance sampling ibis algorithm of chopin 2002 this is a sequential monte carlo algorithm in the theta dimension that samples values of theta reweights iteratively these values using the likelihood increments p y t y 1 t 1 theta and rejuvenates the theta particles through a resampling step and a mcmc update step in state space models these likelihood increments are intractable in most cases but they may be unbiasedly estimated by a particle filter in the x dimension for any fixed theta this motivates the smc 2 algorithm proposed in this article a sequential monte carlo algorithm defined in the theta dimension which propagates and resamples many particle filters in the x dimension the filters in the x dimension are an example of the random weight particle filter as in fearnhead et al 2010 on the other hand the particle markov chain monte carlo pmcmc framework developed in andrieu et al 2010 allows us to design appropriate mcmc rejuvenation steps thus the theta particles target the correct posterior distribution at each iteration t despite the intractability of the likelihood increments we explore the applicability of our algorithm in both sequential and non sequential applications and consider various degrees of freedom as for example increasing dynamically the number of x particles we contrast our approach to various competing methods both conceptually and empirically through a detailed simulation study included here and in a supplement and based on particularly challenging examples

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

traveling waves in diffusive predator prey equations periodic orbits and point to periodic heteroclinic orbits we demonstrate the existence of periodic traveling wave train and traveling front solutions for a diffusive predator prey system the analysis is in the three dimensional phase space of the nonlinear ordinary differential equation system given by the diffusive predator prey system in the traveling wave variable the analysis shows the existence of periodic orbits heteroclinic orbits and a heteroclinic connection of a point and a periodic orbit the proof uses shooting techniques invariant manifold theory and the qualitative theory of ordinary differential equations

crossover in growth law and violation of superuniversality in the random field ising model we study the nonconserved phase ordering dynamics of the d 2 3 random field ising model quenched to below the critical temperature motivated by the puzzling results of previous work in two and three dimensions reporting a crossover from power law to logarithmic growth together with superuniversal behavior of the correlation function we have undertaken a careful investigation of both the domain growth law and the autocorrelation function our main results are as follows we confirm the crossover to asymptotic logarithmic behavior in the growth law but at variance with previous findings we find the exponent in the preasymptotic power law to be disorder dependent rather than being that of the pure system furthermore we find that the autocorrelation function does not display superuniversal behavior this restores consistency with previous results for the d 1 system and fits nicely into the unifying scaling scheme we have recently proposed in the study of the random bond ising model

traveling wave solutions of diffusive lotka volterra equations a heteroclinic connection in we establish the existence of traveling wave solutions for a reaction dif fusion system based on the lotka volterra differential equation model of a predator and prey interaction the waves are of transition front type analogous to the solutions discussed by fisher and kolmogorov et al for a scalar reaction diffusion equation the waves discussed here are not necessarily monotone there is a speed c 0 such that for c c there is a traveling wave moving with speed c the proof uses a shooting argument based on the nonequivalence of a simply connected region and a nonsimply connected region together with a liapunov function to guarantee the existence of the traveling wave solution the traveling wave solution is equivalent to a heteroclinic orbit in 4 dimensional phase space

bootstrapping realized multivariate volatility measures we study bootstrap methods for statistics that are a function of multivariate high frequency returns such as realized regression coefficients and realized covariances and correlations for these measures of covariation the monte carlo simulation results of barndorff nielsen and shephard 2004 show that finite sample distortions associated with their feasible asymptotic theory approach may arise if sampling is not too frequent this motivates our use of the bootstrap as an alternative tool of inference for covariation measures we consider an i i d bootstrap applied to the vector of returns we show that the finite sample performance of the bootstrap is superior to the existing first order asymptotic theory nevertheless and contrary to the existing results in the bootstrap literature for regression models subject to heteroskedasticity in the error term the edgeworth expansion for the i i d bootstrap that we develop here shows that this method is not second order accurate we argue that this is due to the fact that the conditional mean parameters of realized regression models are heterogeneous under stochastic volatility

bootstrapping the box pierce q test a robust test of uncorrelatedness abstract this paper describes a test of the null hypothesis that the first k autocorrelations of a covariance stationary time series are zero in the presence of statistical dependence the test is based on the box pierce q statistic with bootstrap based p values the bootstrap is implemented using a double blocks of blocks procedure with prewhitening the finite sample performance of the bootstrap q test is investigated by simulation in our experiments the performance is satisfactory for samples of n 500 at this sample size the differences between the empirical and nominal rejection probabilities are essentially eliminated

stochastic volatility with leverage fast and efficient likelihood inference this paper is concerned with the bayesian analysis of stochastic volatility sv models with leverage specifically the paper shows how the often used kim et al 1998 stochastic volatility likelihood inference and comparison with arch models review of economic studies 65 361 393 method that was developed for sv models without leverage can be extended to models with leverage the approach relies on the novel idea of approximating the joint distribution of the outcome and volatility innovations by a suitably constructed ten component mixture of bivariate normal distributions the resulting posterior distribution is summarized by mcmc methods and the small approximation error in working with the mixture approximation is corrected by a reweighting procedure the overall procedure is fast and highly efficient we illustrate the ideas on daily returns of the tokyo stock price index finally extensions of the method are described for superposition models where the log volatility is made up of a linear combination of heterogenous and independent autoregressions and heavy tailed error distributions student and log normal

integrated variance forecasting model based vs reduced form abstract this paper compares model based and reduced form forecasts of financial volatility when high frequency return data are available we derived exact formulas for the forecast errors and analyzed the contribution of the wrong data modeling and errors in forecast inputs the comparison is made for feasible forecasts i e we assumed that the true data generating process latent states and parameters are unknown as an illustration the same comparison is carried out empirically for spot 5 min returns of dm usd exchange rates it is shown that the comparison between feasible reduced form and model based forecasts is not always in favor of the latter in contrast to their infeasible versions the reduced form approach is generally better for long horizon forecasting and for short horizon forecasting in the presence of microstructure noise

econometric analysis of jump driven stochastic volatility models abstract this paper introduces and studies the econometric properties of a general new class of models which i refer to as jump driven stochastic volatility models in which the volatility is a moving average of past jumps i focus attention on two particular semiparametric classes of jump driven stochastic volatility models in the first the price has a continuous component with time varying volatility and time homogeneous jumps the second jump driven stochastic volatility model analyzed here has only jumps in the price which have time varying size in the empirical application i model the memory of the stochastic variance with a carma 2 1 kernel and set the jumps in the variance to be proportional to the squared price jumps the estimation which is based on matching moments of certain realized power variation statistics calculated from high frequency foreign exchange data shows that the jump driven stochastic volatility model containing continuous component in the price performs best it outperforms a standard two factor affine jump diffusion model but also the pure jump jump driven stochastic volatility model for the particular jump specification

the fluctuation dissipation relation in phase ordering kinetics abstract the properties of the response function and the fluctuation dissipation relation in phase ordering systems are discussed these issues are shown to be highly nontrivial even in the relatively simple case of coarsening dynamics considered here it is discussed how the connection between statics and dynamics fails in particular cases and the origin of this phenomenon is considered

a rational route to randomness the concept of adaptively rational equilibrium a r e is introduced agents adapt their beliefs over time by choosing from a finite set of different predictor or expectations functions each predictor is a function of past observations and has a performance or fitness measure which is publicly available agents make a rational choice concerning the predictors based upon their past performance this results in a dynamics across predictor choice which is coupled to the equilibrium dynamics of the endogenous variables as a simple but typical example we consider a cobweb type demand supply model where agents can choose between rational and naive expectations in an unstable market with small positive information costs for rational expectations a high intensity of choice to switch predictors leads to highly irregular equilibrium prices converging to a strange attractor the irregularity of the equilibrium time paths is explained by the existence of a so called homoclinic orbit and its associated complicated dynamical phenomena thus local instability and global complicated dynamics may be a feature of a fully rational notion of equilibrium

a far from equilibrium fluctuation dissipation relation for an ising glauber like model we derive an exact expression of the response function to an infinitesimal magnetic field for an ising glauber like model with arbitrary exchange couplings the result is expressed in terms of thermodynamic averages and does not depend on the initial conditions or on the dimension of the space the response function is related to time derivatives of a complicated correlation function and so the expression is a generalization of the equilibrium fluctuation dissipation theorem in the special case of this model correspondence with the ising glauber model is discussed a discrete time version of the relation is implemented in monte carlo simulations and then used to study the ageing regime of the ferromagnetic two dimensional ising glauber model quenched from the paramagnetic phase to the ferromagnetic one our approach has the originality to give direct access to the response function and the fluctuation dissipation ratio

realised quantile based estimation of the integrated variance in this paper we propose a new jump robust quantile based realised variance measure of ex post return variation that can be computed using potentially noisy data the estimator is consistent for the integrated variance and we present feasible central limit theorems which show that it converges at the best attainable rate and has excellent efficiency asymptotically the quantile based realised variance is immune to finite activity jumps and outliers in the price series while in modified form the estimator is applicable with market microstructure noise and therefore operational on high frequency data simulations show that it has superior robustness properties in finite sample while an empirical application illustrates its use on equity data

neglecting parameter changes in garch models if a garch model is estimated on a time series that contains parameter changes in the conditional volatility process and these parameter changes are not accounted for a distinct error in the estimation occurs the sum of the estimated autoregressive parameters of the conditional variance converges to one in finite samples the sum of the estimated autoregressive parameters is heavily biased towards one this paper shows that this convergence holds for all common estimators of garch simulations of the garch model show that the effect occurs for realistic parameter changes and sample sizes for financial volatility data

existence of traveling wave solutions for gause type models of predator prey systems this paper deals with the existence of three types of traveling waves for a general predator prey systems of gause type traveling wave train solution point to point and point to periodic traveling wave solutions applying the methods of wazewski theorem lasalle s invariance principle and hopf bifurcation theorem we obtain the existence results also the minimal wave speed for biological invasion is obtained furthermore some applications are given to illustrate our results

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

variance function estimation abstract heteroscedastic regression models are used in fields including economics engineering and the biological and physical sciences often the heteroscedasticity is modeled as a function of the covariates or the regression and other structural parameters standard asymptotic theory implies that how one estimates the variance function in particular the structural parameters has no effect on the first order properties of the regression parameter estimates there is evidence however both in practice and higher order theory to suggest that how one estimates the variance function does matter further in some settings estimation of the variance function is of independent interest or plays an important role in estimation of other quantities in this article we study variance function estimation in a unified way focusing on common methods proposed in the statistical and other literature to make both general observations and compare different estimation schemes we show that there are significant di

reprojecting partially observed systems with application to interest rate diffusions abstract we introduce reprojection as a general purpose technique for characterizing the dynamic response of a partially observed nonlinear system to its observable history reprojection is the third step of a procedure wherein first data are summarized by projection onto a hermite series representation of the unconstrained transition density for observables second system parameters are estimated by minimum chi squared where the chi squared criterion is a quadratic form in the expected score of the projection and third the constraints on dynamics implied by the nonlinear system are imposed by projecting a long simulation of the estimated system onto a hermite series representation of the constrained transition density for observables the constrained transition density can be used to study the response of the system to its observable history we utilize the technique to assess the dynamics of several diffusion models for the short term interest rate that have been proposed and to compare them to a ne

arch models as diffusion approximations abstract this paper investigates the convergence of stochastic difference equations e g arch to stochastic differential equations as the length of the discrete time intervals between observations goes to zero these results are applied to the garch 1 1 model of bollerslev 1986 and to the ar 1 exponential arch model of nelson 1989 in their continuous time limits the conditional variance processes in these models have stationary distributions that are inverted gamma and lognormal respectively in addition a class of diffusion approximations based on the exponential arch model is developed

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

exact and asymptotic tests for possibly non regular hypotheses on stochastic volatility models abstract we study the problem of testing hypotheses on the parameters of one and two factor stochastic volatility models sv allowing for the possible presence of non regularities such as singular moment conditions and unidentified parameters which can lead to non standard asymptotic distributions we focus on the development of simulation based exact procedures whose level can be controlled in finite samples as well as on large sample procedures which remain valid under non regular conditions we consider wald type score type and likelihood ratio type tests based on a simple moment estimator which can be easily simulated we also propose a c type test which is very easy to implement and exhibits relatively good size and power properties besides usual linear restrictions on the sv model coefficients the problems studied include testing homoskedasticity against a sv alternative which involves singular moment conditions under the null hypothesis and testing the null hypothesis of one factor driving the dynamics of the volatility process against two factors which raises identification difficulties three ways of implementing the tests based on alternative statistics are compared asymptotic critical values when available a local monte carlo or parametric bootstrap test procedure and a maximized monte carlo mmc procedure the size and power properties of the proposed tests are examined in a simulation experiment the results indicate that the c based tests built upon the simple moment estimator available in closed form have good size and power properties for regular hypotheses while monte carlo tests are much more reliable than those based on asymptotic critical values further in cases where the parametric bootstrap appears to fail for example in the presence of identification problems the mmc procedure easily controls the level of the tests moreover mmc based tests exhibit relatively good power performance despite the conservative feature of the procedure finally we present an application to a time series of returns on the standard and poor s composite price index

generalized spectral testing for multivariate continuous time models we develop an omnibus specification test for multivariate continuous time models using the conditional characteristic function which often has a convenient closed form or can be accurately approximated for many multivariate continuous time models in finance and economics the proposed test fully exploits the information in the joint conditional distribution of underlying economic processes and hence is expected to have good power in a multivariate context a class of easy to interpret diagnostic procedures is supplemented to gauge possible sources of model misspecification our tests are also applicable to discrete time distribution models simulation studies show that the tests provide reliable inference in finite samples

is the diurnal pattern sufficient to explain intraday variation in volatility a nonparametric assessment abstract in this paper we propose a nonparametric way to test the hypothesis that time variation in intraday volatility is caused solely by a deterministic and recurrent diurnal pattern we assume that noisy high frequency data from a discretely sampled jump diffusion process are available the test is then based on asset returns which are deflated by the seasonal component and therefore homoskedastic under the null to construct our test statistic we extend the concept of pre averaged bipower variation to a general ito semimartingale setting via a truncation device we prove a central limit theorem for this statistic and construct a positive semi definite estimator of the asymptotic covariance matrix the t statistic after pre averaging and jump truncation diverges in the presence of stochastic volatility and has a standard normal distribution otherwise we show that replacing the true diurnal factor with a model free jump and noise robust estimator does not affect the asymptotic theory a monte carlo simulation also shows this substitution has no discernable impact in finite samples the test is however distorted by small infinite activity price jumps to improve inference we propose a new bootstrap approach which leads to almost correctly sized tests of the null hypothesis we apply the developed framework to a large cross section of equity high frequency data and find that the diurnal pattern accounts for a rather significant fraction of intraday variation in volatility but important sources of heteroskedasticity remain present in the data

scaling of the linear response function from zero field cooled and thermoremanent magnetization in phase ordering kinetics in this paper we investigate the relation between the scaling properties of the linear response function r t s of the thermoremanent magnetization trm and of the zero field cooled zfc magnetization in the context of phase ordering kinetics we explain why the retrieval of the scaling properties of r t s from those of trm and zfc magnetization is not trivial preasymptotic contributions generate a long crossover in trm while zfc magnetization is affected by a dangerous irrelevant variable lack of understanding of both these points has generated some confusion in the literature the full picture relating the exponents of all the quantities involved is explicitly illustrated in the framework of the large n model following this scheme an assessment of the present status of numerical simulations for the ising model can be made we reach the conclusion that on the basis of the data available up to now statements on the scaling properties of r t s can be made from zfc magnetization but not from trm from zfc data for the ising model with d 2 3 4 we confirm the previously found linear dependence on dimensionality of the exponent a entering r t s ensuremath sim s ensuremath 1 a f t s we also find evidence that a recently derived form of the scaling function f x using local scale invariance arguments m henkel m pleimling c godr eche and j m luck phys rev lett 87 265701 2001 does not hold for the ising model

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

off equilibrium generalization of the fluctuation dissipation theorem for ising spins and measurement of the linear response function we derive for ising spins an off equilibrium generalization of the fluctuation dissipation theorem which is formally identical to the one previously obtained for soft spins with langevin dynamics l f cugliandolo j kurchan and g parisi j phys i 4 1641 1994 the result is quite general and holds both for dynamics with conserved and nonconserved order parameters on the basis of this fluctuation dissipation relation we construct an efficient numerical algorithm for the computation of the linear response function without imposing the perturbing field which is alternative to those of chatelain j phys a 36 10 739 2003 and ricci tersenghi phys rev e 68 065104 r 2003 as applications of the new algorithm we present very accurate data for the linear response function of the ising chain with conserved and nonconserved order parameter dynamics finding that in both cases the structure is the same with a very simple physical interpretation we also compute the integrated response function of the two dimensional ising model confirming that it obeys scaling ensuremath chi t t w ensuremath simeq t w ensuremath a f t t w with a 0 26 ifmmode pm else textpm fi 0 01 as previously found with a different method

singular perturbations for boundary value problems arising from exotic options we study the pricing of three exotic derivative securities barrier lookback and passport options which can be characterized by boundary value pde problems in the context of popular markovian sv models of stock prices by extending the fast mean reverting asymptotic analysis in j p fouque g papanicolaou and k r sircar derivatives in financial markets with stochastic volatility cambridge university press london 2000 the usual greek correction to the black scholes prices of these contracts is further corrected by a boundary integral term that is rapidly computed numerically in the case of the passport option the asymptotic method is effective in accounting for sv effects in a simple and robust fashion even in the presence of a highly nonlinear embedded stochastic control problem

estimating stochastic differential equations efficiently by minimum chi squared summary we propose a minimum chi squared estimator for the parameters of an ergodic system of stochastic differential equations with partially observed state we prove that the efficiency of the estimator approaches that of maximum likelihood as the number of moment functions entering the chi squared criterion increases and as the number of past observations entering each moment function increases the minimised criterion is asymptotically chi squared and can be used to test system adequacy when a fitted system is rejected inspecting studentised moments suggests how the fitted system might be modified to improve the fit the method and diagnostic tests are applied to daily observations on the u s dollar to deutschmark exchange rate from 1977 to 1992

asymptotic bias for quasi maximum likelihood estimators in conditional heteroskedasticity models virtually all applications of time varying conditional variance models use a quasimaximum likelihood estimator qmle consistency of a qmle requires an identification condition that the quasi log likelihood have a unique maximum at the true conditional mean and relative scale parameters we show that the identification condition holds for a non gaussian qmle if the conditional mean is identically zero or if a symmetry condition is satisfied without symmetry an additional parameter for the location of the innovation density must be added for identification we calculate the efficiency loss from adding such a parameter under symmetry when the parameter is not needed we also show that there is no efficiency loss for the conditional variance parameters of a garch process

alternative models for stock price dynamics abstract this paper evaluates the role of various volatility specifications such as multiple stochastic volatility sv factors and jump components in appropriate modeling of equity return distributions we use estimation technology that facilitates nonnested model comparisons and use a long data set which provides rich information about the conditional and unconditional distribution of returns we consider two broad families of models 1 the multifactor loglinear family and 2 the affine jump family both classes of models have attracted much attention in the derivatives and econometrics literatures there are various tradeoffs in considering such diverse specifications if pure diffusion sv models are chosen over jump diffusions it has important implications for hedging strategies if logarithmic models are chosen over affine ones it may seriously complicate option pricing comparing many different specifications of pure diffusion multifactor models and jump diffusion models we find that 1 log linear models have to be extended to two factors with feedback in the mean reverting factor 2 affine models have to have a jump in returns stochastic volatility or probably both models 1 and 2 are observationally equivalent on the data set in hand in either 1 or 2 the key is that the volatility can move violently as we obtain models with comparable empirical fit one must make a choice based on arguments other than statistical goodness of fit criteria the considerations include facility to price options to hedge and parsimony the affine specification with jumps in volatility might therefore be preferred because of the closed form derivatives prices

nonlinear response and fluctuation dissipation relations a unified derivation of the off equilibrium fluctuation dissipation relations fdrs is given for ising and continuous spins to arbitrary order within the framework of markovian stochastic dynamics knowledge of the fdrs allows one to develop zero field algorithms for the efficient numerical computation of the response functions two applications are presented in the first one the problem of probing for the existence of a growing cooperative length scale is considered in those cases like in glassy systems where the linear fdr is of no use the effectiveness of an appropriate second order fdr is illustrated in the test case of the edwards anderson spin glass in one and two dimensions in the second application the important problem of the definition of an off equilibrium effective temperature through the nonlinear fdr is considered it is shown that in the case of coarsening systems the effective temperature derived from the second order fdr is consistent with the one obtained from the linear fdr

estimation of stochastic volatility models with diagnostics abstract efficient method of moments emm is used to fit the standard stochastic volatility model of various extensions to several daily financial time series emm matches to the score of the model determined by data analysis called the score generator discrepancies reveal characteristics of data that stochastic volatility models cannot approximate the two score generators employed here are semiparametric arch and nonlinear nonparametric with the first the standard model is rejected although some extensions are accepted with the second all versions are rejected the extensions required for an adequate fit are so elaborate that nonparametric specifications are probably more convenient

comment on scaling of the linear response in simple aging systems without disorder we have repeated the simulations of henkel paessens and pleimling hpp phys rev e 69 056109 2004 for the field cooled susceptibility ensuremath chi mathit fc t ensuremath ensuremath chi 0 ensuremath sim t ensuremath a in the quench of ferromagnetic systems to and below t c we show that contrary to the statement made by hpp the exponent a coincides with the exponent a of the linear response function r t s ensuremath sim s ensuremath 1 a f r t s we point out what are the assumptions in the argument of hpp that lead them to the conclusion ala

kinetics of the long range spherical model the kinetic spherical model with long range interactions is studied after a quench to t tc or to t tc for the two time response and correlation functions of the order parameter as well as for composite fields such as the energy density the ageing exponents and the corresponding scaling functions are derived the results are compared to the predictions which follow from local scale invariance

existence of travelling wave solutions of predator prey systems via the connection index we consider a reaction diffusion system which arises as a model of predator prey interactions in mathematical ecology the system admits four constant equilibria two of which are stable the main result is an existence theorem for travelling wave solutions which connect the two stable equilibria most previous efforts with regard to travelling waves for systems employ singular perturbations to locate the connecting orbit the new aspect of the present discussion lies in devising some novel methods for locating the connecting solution in phase space which do not require that the equations be singularly perturbed in certain cases the main result holds for an arbitrary choice of diffusion coefficients

off equilibrium response function in coarsening systems abstract in the late stage dynamics of systems evolving via domain coarsening the linear response function splits into the sum of a stationary term due to thermal fluctuations within domains and of an aging term due to off equilibrium interface dynamics the latter contribution is analyzed in the pure ising model under variation of space dimensionality and in the random field ising model in one dimension the variety of behaviors observed can be accounted for in terms of the effective response associated to a single interface implications for the connection between static and dynamic properties are discussed

on the functional estimation of jump diffusion models abstract we provide a general asymptotic theory for the fully functional estimates of the infinitesimal moments of continuous time models with discontinuous sample paths of the jump diffusion type minimal requirements are placed on the dynamic properties of the underlying jump diffusion process i e stationarity is not required our theoretical framework justifies consistent in a statistical sense nonparametric extraction of the parameters and functions that drive the dynamic evolution of the process of interest i e the potentially nonaffine and level dependent intensity of the jump arrival being an example from the estimated infinitesimal conditional moments as suggested in johannes 2003 the statistical and economic role of jumps in continuous time interest rate models journal of finance forthcoming

a discrete time model for daily s p500 returns and realized variations jumps and leverage effects abstract we develop an empirically highly accurate discrete time daily stochastic volatility model that explicitly distinguishes between the jump and continuous time components of price movements using nonparametric realized variation and bipower variation measures constructed from high frequency intraday data the model setup allows us to directly assess the structural inter dependencies among the shocks to returns and the two different volatility components the model estimates suggest that the leverage effect or asymmetry between returns and volatility works primarily through the continuous volatility component the excellent fit of the model makes it an ideal candidate for an easy to implement auxiliary model in the context of indirect estimation of empirically more realistic continuous time jump diffusion and levy driven stochastic volatility models effectively incorporating the interdaily dependencies inherent in the high frequency intraday data

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

efficient hedging currency options in fractional brownian motion model with jumps abstract this paper deals with the problem of efficient hedging for european currency option and exchange option in case that exchange rate is driven by a fractional brownian motion with jumps in a complete market as long as a seller receives a price of the option equal to the expectation under the risk neutral probability measure of the discounted payoff the seller can hedge this payoff perfectly as the price is often quite expensive the investors need partial hedges which require less capital and reduce the risk the efficient hedge is one of partial hedges the efficient hedging results for options are obtained under fractional brownian motion model with jumps using the equivalent martingale measure simulation results and empirical studies confirm the theoretical findings and show that the fractional brownian motion model with jumps is reasonable

existence of traveling wave solutions for diffusive predator prey type systems abstract in this work we investigate the existence of traveling wave solutions for a class of diffusive predator prey type systems whose each nonlinear term can be separated as a product of suitable smooth functions satisfying some monotonic conditions the profile equations for the above system can be reduced as a four dimensional ode system and the traveling wave solutions which connect two different equilibria or the small amplitude traveling wave train solutions are equivalent to the heteroclinic orbits or small amplitude periodic solutions of the reduced system applying the methods of wazewski theorem lasalle s invariance principle and hopf bifurcation theory we obtain the existence results our results can apply to various kinds of ecological models

testing for jumps when asset prices are observed with noise a swap variance approach abstract this paper proposes a new test for jumps in asset prices that is motivated by the literature on variance swaps formally the test follows by a direct application of ito s lemma to the semi martingale process of asset prices and derives its power from the impact of jumps on the third and higher order return moments intuitively the test statistic reflects the cumulative gain of a variance swap replication strategy which is known to be minimal in the absence of jumps but substantial in the presence of jumps simulations show that the jump test has nice properties and is generally more powerful than the widely used bi power variation test an important feature of our test is that it can be applied in analytically modified form to noisy high frequency data and still retain power as a by product of our analysis we obtain novel analytical results regarding the impact of noise on bi power variation an empirical illustration using ibm trade data is also included

fluctuation dissipation relations for markov processes the fluctuation dissipation relation is calculated for stochastic models obeying a master equation with continuous time in the general case of a nonstationary process there appears to be no simple relation between the response and the correlation also if one considers stationary processes the linear response cannot be expressed via time derivatives of the correlation function alone in this case an additional function which has rarely been discussed previously is required this so called asymmetry depends on the two times also relevant for the response and the correlation and it vanishes under equilibrium conditions the asymmetry can be expressed in terms of the propagators and the transition rates of the master equation but it is not related to any physical observable in an obvious way it is found that the behavior of the asymmetry strongly depends on the nature of the dynamical variable considered in the calculation of the correlation and the response if one is concerned with a variable which randomizes with any transition among the states of the system the asymmetry vanishes in most cases this is in contrast to the situation for other classes of variables in particular for trap models of glassy relaxation the fluctuation dissipation ratio strongly depends on the observable and the asymmetry plays a dominant role in the determination of this ratio also if only neutral variables are considered some implications of a nonvanishing asymmetry with regard to the definition of an effective temperature are discussed

ageing properties of critical systems in the past few years systems with slow dynamics have attracted considerable theoretical and experimental interest ageing phenomena are observed during this everlasting non equilibrium evolution a simple instance of such a behaviour is provided by the dynamics that takes place when a system is quenched from its high temperature phase to the critical point the aim of this review is to summarize the various numerical and analytical results that have been recently obtained for this case particular emphasis is put on the field theoretical methods that can be used to provide analytical predictions for the relevant dynamical quantities fluctuation dissipation relations are discussed and in particular the concept of fluctuation dissipation ratio fdr is reviewed emphasizing its connection with the definition of a possible effective temperature the renormalization group approach to critical dynamics is summarized and the scaling forms of the time dependent non equilibrium correlation and response functions of a generic observable are discussed from them the universality of the associated fdr follows as an amplitude ratio it is then possible to provide predictions for ageing quantities in a variety of different models in particular the results for models a b and c dynamics of the o n ginzburg landau hamiltonian and model a dynamics of the weakly dilute ising magnet and of the 3 theory are reviewed and compared with the available numerical results and exact solutions the effect of a planar surface on the ageing behaviour of model a dynamics is also addressed within the mean field approximation