estimating dynamic equilibrium models using mixed frequency macro and financial data abstract we provide a framework for inference in dynamic equilibrium models including financial market data at daily frequency along with macro series at standard lower frequency our formulation of the macro finance model in continuous time conveniently accounts for the difference in observation frequency we suggest the use of martingale estimating functions mef to infer the structural parameters of the model directly through a nonlinear scheme this method is compared to regression based methods and the generalized method of moments gmm we illustrate our approaches by estimating various versions of the ak vasicek model with mean reverting interest rates we provide asymptotic theory and monte carlo evidence on the small sample behavior of the estimators and report empirical estimates using 30 years of us macro and financial data

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

oscillation criteria for a class of second order neutral delay differential equations in this article we investigate oscillation and asymptotic behaviour of all solutions of a class of neutral delay differential equations of second order with several positive and negative coefficients having the formx t email protected email protected rr i t x a i t email protected email protected pp i t x b i t email protected email protected qq i t x c i t f t fort t 0 where r p q are bounded beginning segments of positive integers r email protected c t 0 r p i q email protected c t 0 r a i b i c email protected c t 0 r are delay functions and f is a continuous function our results improve and extend the recent results given in the papers j manojlovic y shoukaku t tanigawa n yoshida oscillation criteria for second order differential equations with positive and negative coefficients appl math comput 181 2006 853 863 and a weng j sun oscillation of second order delay differential equations appl math comput 198 2 2008 930 935

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

efficiency bounds implied by multiperiod conditional moment restrictions abstract in this article we study a class of econometric models that imply a set of multiperiod conditional moment restrictions these restrictions depend on an unknown parameter vector we construct an extensive class of consistent asymptotically normal estimators of this parameter vector and calculate the greatest lower bound for the asymptotic covariance matrices of estimators in this class in so doing we extend results reported by hansen 1985 and stoica soderstrom and friedlander 1985 by allowing for more general forms of nonlinearities and temporal dependence many dynamic econometric models imply that the expectation of a function of a currently observed data vector and an unknown parameter vector conditioned on information available at some point in the past is 0 we focus on models in which the conditioning information is lagged more than one time period as in the models considered by barro 1981 dunn and singleton 1986 eichenbaum and hansen 1987 eichenbaum hansen and singleto

oscillation of second order delay differential equations abstract we establish the oscillation criteria for the second order functional equation x t i 1 l c i t x t i i 1 m p i t x t i i 1 n q i t x t i 0 and x t i 1 l c i t x t i i 1 m p i t x t i i 1 n q i t x t i f t new oscillation criteria improve the one recently established by manojlovic et al j manojlovic y shoukaku t tanigawa n yoshida oscillation criteria for second order differential equations with positive and negative coefficients appl math comp 181 2006 853 863

research on the relationship between the multifractality and long memory of realized volatility in the sseci abstract we examine the multifractal properties of the realized volatility rv and realized bipower variation rbv series in the shanghai stock exchange composite index sseci by using the multifractal detrended fluctuation analysis mf dfa method we find that there exist distinct multifractal characteristics in the volatility series the contributions of two different types of source of multifractality namely fat tailed probability distributions and nonlinear temporal correlations are studied by using the unit root test we also find the strength of the multifractality of the volatility time series is insensitive to the sampling frequency but that the long memory of these series is sensitive

estimation of affine asset pricing models using the empirical characteristic function abstract the known functional form of the conditional characteristic function ccf of discretely sampled observations from an affine diffusion is used to develop computationally tractable and asymptotically efficient estimators of the parameters of affine diffusions and of asset pricing models in which the state vectors follow affine diffusions both time domain estimators based on fourier inversion of the ccf and frequency domain estimators based directly on the ccf are constructed a method of moments estimator based on the ccf is shown to approximate the efficiency of maximum likelihood for affine diffusion and asset pricing models

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

diagnostic testing and evaluation of maximum likelihood models abstract the paper develops a unified theory of likelihood specification testing based on m estimators of auxiliary parameters the theory is sufficiently general to encompass a wide class of specification tests including moment based tests pearson type goodness of fit tests the information matrix test and the cox test the paper also presents a framework based on frechet differentiation for determining the effects of misspecification on the almost sure limits of parameter estimates and specification test statistics

necessary and sufficient conditions on asymptotic behaviour of solutions of forced neutral delay dynamic equations abstract in this article we first study the asymptotic behavior of delay dynamic equations having the following form x t a t x t b t f x t c t g x t t for t t 0 t where t is a time scale unbounded from above t 0 t f g c rd r r a c rd t 0 t r b c c rd t 0 t 0 r and are delay functions then we extend our results to equations of the form x t a t x t b t f x t t for t t 0 t where b c rd t 0 t r is allowed to oscillate our results state necessary and sufficient conditions on all solutions of the equations to be oscillatory or convergent 0 or divergent depending on various ranges of the coefficient a we generalize and improve some of the results for differential and difference equations using the time scale theory most of our results for the equations are not thus far presented in the literature not even for the discrete or the continuous cases

estimating stochastic volatility diffusion using conditional moments of integrated volatility we exploit the distributional information contained in high frequency intraday data in constructing a simple conditional moment estimator for stochastic volatility diffusions the estimator is based on the analytical solutions of the first two conditional moments for the latent integrated volatility the realization of which is effectively approximated by the sum of the squared high frequency increments of the process our simulation evidence indicates that the resulting gmm estimator is highly reliable and accurate our empirical implementation based on high frequency five minute foreign exchange returns suggests the presence of multiple latent stochastic volatility factors and possible jumps

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

a method for calculating bounds on the asymptotic covariance matrices of generalized method of moments estimators abstract for many time series estimation problems there is an infinite dimensional class of generalized method of moments estimators that are consistent and asymptotically normal this paper suggests a procedure for calculating the greatest lower bound for the asymptotic covariance matrices of such estimators the analysis focuses on estimation problems in which the data are generated by a stochastic process that is stationary and ergodic the calculation of the bound uses martingale difference approximations as suggested by gordon 1969 and a matrix version of hilbert space methods

notes on financial econometrics the first part of the discussion reviews recent successes in modeling of discrete time financial data and argues that a direct approach is better suited than stochastic volatility the second part reviews recent work on estimating continuous time models with emphasis on simulation based techniques and joint estimation of the risk neutral and objective probability distributions

trim loss pattern rearrangement and its relevance to the flat glass industry abstract an additional restriction upon the conventional two dimensional trim loss problem arises in the glass industry this restriction imposes limitations upon the positioning of cuts within the stock plate relative to other cuts two procedures are presented which take an existing pattern and attempt to rearrange it to meet the restrictions one procedure is a heuristic while the other is a complete enumeration

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

oscillation criteria for second order differential equations with positive and negative coefficients some oscillation criteria for the second order neutral delay differential equationsx t email protected i 1lc i t x email protected i email protected i 1mp i t x email protected i email protected i 1nq i t x email protected i 0 t 0are established new oscillation criteria are different from one recently established in the sense that the boundedness of the solution in the results of parhi and chand oscillation of second order neutral delay differential equations with positive and negative coefficients j indian math soc 66 1999 227 235 has been erased i e we give sufficient conditions for the oscillation of all solutions

quasi maximum likelihood estimation of stochastic volatility models abstract changes in variance or volatility over time can be modelled using stochastic volatility sv models this approach is based on treating the volatility as an unobserved vatiable the logarithm of which is modelled as a linear stochastic process usually an autoregression this article analyses the asymptotic and finite sample properties of a quasi maximum likelihood qml estimator based on the kalman filter the relative efficiency of the qml estimator when compared with estimators based on the generalized method of moments is shown to be quite high for parameter values often found in empirical applications the qml estimator can still be employed when the sv model is generalized to allow for distributions with heavier tails than the normal sv models are finally fitted to daily observations on the yen dollar exchange rate

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

filtering and forecasting with misspecified arch models i getting the right variance with the wrong model this paper investigates the properties of the conditional covariance estimates generated by a misspecified arch model for example suppose that we observe a diffusion process at discrete time intervals of length h for each h we use a garch 1 1 model to estimate the instantaneous conditional covariance matrix of the diffusion under mild regularity conditions the difference between these conditional covariance estimates and the true conditional covariance converges to zero in probability as h 0 many other arch models for example exponential arch have similar consistency properties this may well account for the success of arch models in short term forecasting using high frequency data since even misspecified arch models can produce good estimates of volatility

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

predictive inference for integrated volatility numerous volatility based derivative products have been engineered in recent years this has led to interest in constructing conditional predictive densities and confidence intervals for integrated volatility in this article we propose nonparametric estimators of the aforementioned quantities based on model free volatility estimators we establish consistency and asymptotic normality for the feasible estimators and study their finite sample properties through a monte carlo experiment finally using data from the new york stock exchange we provide an empirical application to volatility directional predictability

on nonoscillation of mixed advanced delay differential equations with positive and negative coefficients for a mixed advanced delay differential equation with variable delays and coefficients email protected t a t x g t b t x h t 0 t t 0 where a t 0 b t 0 g t t h t t explicit nonoscillation conditions are obtained

probabilistic forecasts of volatility and its risk premia abstract the object of this paper is to produce distributional forecasts of asset price volatility and its associated risk premia using a non linear state space approach option and spot market information on the latent variance process is captured by using dual model free variance measures to define a bivariate observation equation in the state space model the premium for variance diffusive risk is defined as linear in the latent variance in the usual fashion whilst the premium for variance jump risk is specified as a conditionally deterministic dynamic process driven by a function of past measurements the inferential approach adopted is bayesian implemented via a markov chain monte carlo algorithm that caters for the multiple sources of non linearity in the model and for the bivariate measure the method is applied to spot and option price data on the s p500 index from 1999 to 2008 with conclusions drawn about investors required compensation for variance risk during the recent financial turmoil the accuracy of the probabilistic forecasts of the observable variance measures is demonstrated and compared with that of forecasts yielded by alternative methods to illustrate the benefits of the approach it is used to produce forecasts of prices of derivatives on volatility itself in addition the posterior distribution is augmented by information on daily returns to produce value at risk predictions linking the variance risk premia to the risk aversion parameter in a representative agent model probabilistic forecasts of approximate relative risk aversion are also produced

predictive density estimators for daily volatility based on the use of realized measures abstract the main objective of this paper is to propose a feasible model free estimator of the predictive density of integrated volatility in this sense we extend recent papers by andersen et al andersen t g bollerslev t diebold f x labys p 2003 modelling and forecasting realized volatility econometrica 71 579 626 and by andersen et al andersen t g bollerslev t meddahi n 2004 analytic evaluation of volatility forecasts international economic review 45 1079 1110 andersen t g bollerslev t meddahi n 2005 correcting the errors volatility forecast evaluation using high frequency data and realized volatilities econometrica 73 279 296 who address the issue of pointwise prediction of volatility via arma models based on the use of realized volatility our approach is to use a realized volatility measure to construct a non parametric kernel estimator of the predictive density of daily volatility we show that by choosing an appropriate realized measure one can achieve consistent estimation even in the presence of jumps and microstructure noise in prices more precisely we establish that four well known realized measures i e realized volatility bipower variation and two measures robust to microstructure noise satisfy the conditions required for the uniform consistency of our estimator furthermore we outline an alternative simulation based approach to predictive density construction finally we carry out a simulation experiment in order to assess the accuracy of our estimators and provide an empirical illustration that underscores the importance of using microstructure robust measures when using high frequency data

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

cutting stock problems and solution procedures this paper discusses some of the basic formulation issues and solution procedures for solving one and two dimensional cutting stock problems linear programming sequential heuristic and hybrid solution procedures are described for two dimensional cutting stock problems with rectangular shapes we also propose an approach for solving large problems with limits on the number of times an ordered size may appear in a pattern

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

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

an interactive technique for the cutting stock problem with multiple objectives abstract this paper deals with the two dimensional cutting stock problem in which a specified number of different rectangular pieces are required to be cut from a stock of sheets of finite dimensions in such a way that several objectives will be satisfied simultaneously it is shown how this problem can be expressed as a large scale multiple objective integer linear programming and solved by applying an interactive technique known from multiple criteria decision making furthermore a new cutting procedure is proposed based on homogeneous strips to generate cutting patterns with minimum waste the effectiveness of the interactive technique as well as the cutting procedure is illustrated in detail by a numerical example all the given approaches are implemented on a microcomputer and experimented using a real data from automotive company sample of the input output computer screens and the suggestions for future work are also reported

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

dynamic integration of time and state domain methods for volatility estimation time and state domain methods are two common approaches to nonparametric prediction whereas the former uses data predominantly from recent history the latter relies mainly on historical information combining these two pieces of valuable information is an interesting challenge in statistics we surmount this problem by dynamically integrating information from both the time and state domains the estimators from these two domains are optimally combined based on a data driven weighting strategy which provides a more efficient estimator of volatility asymptotic normality is separately established for the time domain the state domain and the integrated estimators by comparing the efficiency of the estimators we demonstrate that the proposed integrated estimator uniformly dominates the other two estimators the proposed dynamic integration approach is also applicable to other estimation problems in time series extensive simulations are conducted to demonstrate that the newly proposed procedure outper