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

a new class of nonlinear generalizations of the schrodinger equation we propose a new nonlinear representation independent generalized schrodinger equation satisfying the homogeneity condition which is valid for arbitrary representations and arbitrary operators this is a generalization of the equation recently proposed by doebner and goldin 1992 for the wavefunction written in cartesian coordinates the new model leads to simple exact solutions describing for instance the relaxation of the two level system and the harmonic oscillator both in fock and in coherent states bases

exponential stability for a class of boundary conditions on a euler bernoulli beam subject to disturbances via boundary control abstract this paper outlines the procedure for applying a sliding mode backstepping boundary control technique to a euler bernoulli beam subject to unknown bounded disturbances on the boundary for four different types of boundary conditions referred to in this paper as a class of boundary conditions these boundary conditions include all combinations of pinned and sliding types with control and disturbances on one boundary i e pinned pinned pinned sliding sliding pinned and sliding sliding with input on the second boundary the technique was developed for the specific case of a pinned pinned beam in the literature and in this paper the technique is generalized to the degree that it is possible to cover all four of the aforementioned cases furthermore a proof of the fully arbitrary exponential stability of the closed loop system is provided in this paper to this point only asymptotic stability was shown for the closed loop system for one case the technique outlined in this paper provides for a class of boundary conditions a controller that exponentially stabilizes the vibrations in a beam in the presence of bounded unknown disturbances the beam displacement returns to the origin and its decay is bounded by a known exponential decay function after a known finite time reaching phase

testing for jumps in noisy high frequency data a b s t r a c t this paper proposes a robustification of the test statistic of ait sahalia and jacod 2009b for the presence of market microstructure noise in high frequency data based on the pre averaging method of jacod et al 2010 we show that the robustified statistic restores the test s discriminating power between jumps and no jumps despite the presence of market microstructure noise in the data

discontinuous unit feedback control of uncertain infinite dimensional systems control systems driven by a discontinuous unit feedback in a hilbert space are studied the equation which describes a system motion taking place in the discontinuity manifold and further referred to as a sliding mode is derived by means of a special regularization technique based on the sliding mode equation the procedure of synthesis of a discontinuous unit control signal is developed restricted to a class of infinite dimensional systems with finite dimensional unstable part this procedure generates the control law which ensures desired dynamic properties as well as robustness of the closed loop system with respect to matched disturbances as an illustration of the capabilities of the procedure proposed a scalar unit controller of an uncertain exponentially minimum phase dynamic system is constructed and applied to heat processes and distributed mechanical oscillators

asymptotic error distributions for the euler method for stochastic differential equations we are interested in the rate of convergence of the euler scheme approximation of the solution to a stochastic differential equation driven by a general possibly discontinuous semimartingale and by the asymptotic behavior of the associated normalized error it is well known that for ito s equations the rate is 1 sqrt n we provide a necessary and sufficient condition for this rate to be 1 sqrt n when the driving semimartingale is a continuous martingale or a continuous semimartingale under a mild additional assumption we also prove that in these cases the normalized error processes converge in law the rate can also differ from 1 sqrt n this is the case for instance if the driving process is deterministic or if it is a levy process without a brownian component it is again 1 sqrt n when the driving process is levy with a nonvanishing brownian component but then the normalized error processes converge in law in the finite dimensional sense only while the discretized normalized error processes converge in law in the skorohod sense and the limit is given an explicit form

lyapunov approach to output feedback stabilization for the euler bernoulli beam equation with boundary input disturbance we propose a boundary output feedback control law for a one dimensional euler bernoulli beam equation with general external disturbance entering the control end a galerkin approximation scheme is constructed to show the existence of solution to the closed loop system the exponential stability of the closed loop system is obtained by the lyapunov functional method numerical simulations are presented for illustration

multivariate realised kernels consistent positive semi definite estimators of the covariation of equity prices with noise and non synchronous trading we propose a multivariate realised kernel to estimate the ex post covariation of log prices we show this new consistent estimator is guaranteed to be positive semi definite and is robust to measurement noise of certain types and can also handle non synchronous trading it is the first estimator which has these three properties which are all essential for empirical work in this area we derive the large sample asymptotics of this estimator and assess its accuracy using a monte carlo study we implement the estimator on some us equity data comparing our results to previous work which has used returns measured over 5 or 10 minutes intervals we show the new estimator is substantially more precise

exact controllability of the euler bernoulli equation with boundary controls for displacement and moment abstract we consider the euler bernoulli problem 1 1 in the solution w t with boundary controls g1 and g2 acting in the dirichlet traces for w and w respectively we show two main exact controllability results both in the spaces of maximal regularity of the solution at t t see i lasiecka and r triggiani regularity theory for a class of euler bernoulli equations a cosine operator approach boll unione mat ital 7 3 b 1989 and both without geometrical conditions on the open bounded domain except for smoothness of its boundary one with g1 l2 0 t l2 and g2 h1 0 t l2 for any t 0 arbitrarily short and one with g1 h01 0 t l2 and g2 l2 0 t l2 for all t 0 sufficiently large an interpolation result between these two cases is also presented a direct approach is given based on two main steps first by means of an operator model i lasiecka and r triggiani regularity theory for a class of euler bernoulli equations a cosine operator approach boll unione mat ital 7 3 b 1989 for problem 1 1 and a functional analytic approach the question of exact controllability is shown to be equivalent to an a priori inequality for the corresponding homogeneous problem next this a priori inequality is proved to hold true by means of multiplier techniques these are inspired by recent progress on the maximal regularity exact controllability and uniform stabilization questions for second order hyperbolic equations

is brownian motion necessary to model high frequency data this paper considers the problem of testing for the presence of a continuous part in a semimartingale sampled at high frequency we provide two tests one where the null hypothesis is that a continuous component is present the other where the continuous component is absent and the model is then driven by a pure jump process when applied to high frequency individual stock data both tests point toward the need to include a continuous component in the model

econometrics of co jumps in high frequency data with noise abstract we establish estimation methods to determine co jumps in multivariate high frequency data with non synchronous observations and market microstructure a rate optimal estimator of the entire quadratic covariation of an ito semimartingale is constructed by a locally adaptive spectral approach thresholding allows to disentangle the co jump from the continuous part we derive a feasible limit theorem for a truncated estimator of integrated covolatility which facilitates asymptotically efficient co volatility estimation in the presence of jumps a test for common jumps is presented simulations and an empirical application to intra day tick data from eurex futures demonstrate the practical value of the approach

large dimensional factor modeling based on high frequency observations abstract this paper develops a statistical theory to estimate an unknown factor structure based on financial high frequency data we derive an estimator for the number of factors and consistent and asymptotically mixed normal estimators of the loadings and factors under the assumption of a large number of cross sectional and high frequency observations the estimation approach can separate factors for continuous and rare jump risk the estimators for the loadings and factors are based on the principal component analysis of the quadratic covariation matrix the estimator for the number of factors uses a perturbed eigenvalue ratio statistic in an empirical analysis of the s p 500 firms we estimate four stable continuous systematic factors which can be approximated very well by a market and industry portfolios jump factors are different from the continuous factors

adaptive boundary iterative learning control for an euler bernoulli beam system with input constraint this paper addresses the vibration control and the input constraint for an euler bernoulli beam system under aperiodic distributed disturbance and aperiodic boundary disturbance hyperbolic tangent functions and saturation functions are adopted to tackle the input constraint a restrained adaptive boundary iterative learning control abilc law is proposed based on a time weighted lyapunov krasovskii like composite energy function in order to deal with the uncertainty of a system parameter and reject the external disturbances three adaptive laws are designed and learned in the iteration domain all the system states of the closed loop system are proved to be bounded in each iteration along the iteration axis the displacements asymptotically converge toward zero simulation results are provided to illustrate the effectiveness of the proposed abilc scheme

estimating the quadratic covariation matrix from noisy observations local method of moments and efficiency an efficient estimator is constructed for the quadratic covariation or integrated covolatility matrix of a multivariate continuous martingale based on noisy and non synchronous observations under high frequency asymptotics our approach relies on an asymptotically equivalent continuous time observation model where a local generalised method of moments in the spectral domain turns out to be optimal asymptotic semiparametric efficiency is established in the cramer rao sense main findings are that non synchronicity of observation times has no impact on the asymptotics and that major efficiency gains are possible under correlation simulations illustrate the finite sample behaviour

on a class of homogeneous nonlinear schrodinger equations a class of homogeneous norm conserving nonlinear wave equations of the schrodinger type is studied it is shown that those equations which derive from a lagrangian can be linearized but have no regular confined solutions whereas the equations which cannot be obtained from a local lagrangian do admit such confined solutions the latter however are unstable against small perturbations of the initial data

arbitrary decay rate for euler bernoulli beam by backstepping boundary feedback we consider a problem of stabilization of the euler bernoulli beam the beam is controlled at one end using position and moment actuators and has the ldquoslidingrdquo boundary condition at the opposite end we design the controllers that achieve any prescribed decay rate of the closed loop system removing a long standing limitation of classical ldquoboundary damperrdquo controllers the idea of the control design is to use the well known representation of the euler bernoulli beam model through the schrodinger equation and then adapt recently developed backstepping designs for the latter in order to stabilize the beam we derive the explicit integral transformation and its inverse of the closed loop system into an exponentially stable target system the transformation is of a novel volterra fredholm type the design is illustrated with simulations

modulational instabilities and soliton solutions of a generalized nonlinear schrodinger equation previous forms of the generalized nonlinear schrodinger equation are ambiguously related to the corresponding nonlinear dispersion relation the authors therefore propose a hamiltonian equation which is determined in a unique way soliton solutions of the nonlinear schrodinger equations are found and modulational instabilities are investigated

quasi maximum likelihood estimation of volatility with high frequency data this paper investigates the properties of the well known maximum likelihood estimator in the presence of stochastic volatility and market microstructure noise by extending the classic asymptotic results of quasi maximum likelihood estimation when trying to estimate the integrated volatility and the variance of noise this parametric approach remains consistent efficient and robust as a quasi estimator under misspecified assumptions moreover it shares the model free feature with nonparametric alternatives for instance realized kernels while being advantageous over them in terms of finite sample performance in light of quadratic representation this estimator behaves like an iterative exponential realized kernel asymptotically comparisons with a variety of implementations of the tukey hanning2 kernel are provided using monte carlo simulations and an empirical study with the euro us dollar future illustrates its application in practice

designing realised kernels to measure the ex post variation of equity prices in the presence of noise this paper shows how to use realised kernels to carry out efficient feasible inference on the expost variation of underlying equity prices in the presence of simple models of market frictions the issue is subtle with only estimators which have symmetric weights delivering consistent estimators with mixed gaussian limit theorems the weights can be chosen to achieve the best possible rate of convergence and to have an asymptotic variance which is close to that of the maximum likelihood estimator in the parametric version of this problem realised kernels can also be selected to i be analysed using endogenously spaced data such as that in databases on transactions ii allow for market frictions which are endogenous iii allow for temporally dependent noise the finite sample performance of our estimators is studied using simulation while empirical work illustrates their use in practice

dynamics of transversely vibrating beams using four engineering theories abstract in this paper the full development and analysis of four models for the transversely vibrating uniform beam are presented the four theories are the euler bernoulli rayleigh shear and timoshenko first a brief history of the development of each beam model is presented second the equation of motion for each model and the expressions for boundary conditions are obtained using hamilton s variational principle third the frequency equations are obtained for four sets of end conditions free free clamped clamped hinged hinged and clamped free the roots of the frequency equations are presented in terms of normalized wave numbers the normalized wave numbers for the other six sets of end conditions are obtained using the analysis of symmetric and antisymmetric modes fourth the orthogonality conditions of the eigenfunctions or mode shape and the procedure to obtain the forced response using the method of eigenfunction expansion is presented finally a numerical example is shown for a non slender beam to signify the differences among the four beam models

jackknife bootstrap and other resampling methods in regression analysis motivated by a representation for the least squares estimator we propose a class of weighted jackknife variance estimators for the least squares estimator by deleting any fixed number of observations at a time they are unbiased for homoscedastic errors and a special case the delete one jackknife is almost unbiased for heteroscedastic errors the method is extended to cover nonlinear parameters regression m estimators nonlinear regression and generalized linear models interval estimators can be constructed from the jackknife histogram three bootstrap methods are considered two are shown to give biased variance estimators and one does not have the bias robustness property enjoyed by the weighted delete one jackknife a general method for resampling residuals is proposed it gives variance estimators that are bias robust several bias reducing estimators are proposed some simulation results are reported

active boundary control of an euler bernoulli beam for generating vibration free state abstract this paper presents active boundary control abc of an euler bernoulli beam which enables one to generate a desired boundary condition at any designated position of a target beam structure thereby permitting the structure to possess desired properties characterized by the boundary condition furthermore abc has potential to create a completely vibration free state in the designated area of a beam this paper begins by presenting the principle of abc using a transfer matrix method the optimal control law of the abc system being derived it is found that in addition to conventional four classical boundary conditions free pinned clamped and sliding support abc can generate two more boundary conditions that may not be observed in real systems but realized by abc it is also found that as a result of applying abc to a specific location including a current conventional boundary of a beam a completely vibration free state in the target region of a beam can be realized finally an experiment using an adaptive feedforward control was conducted demonstrating that abc enables the generation of a desired boundary condition at the designated location of a target beam and of a completely vibration free state of a beam

on integrable doebner goldin equations we integrate sub families of a family of nonlinear schrodinger equations proposed by doebner and goldin in the 1 1 dimensional case which have exceptional lie symmetries since the method of integration involves non local transformations of dependent and independent variables general solutions obtained include implicitly determined functions by properly specifying one of the arbitrary functions contained in these solutions we obtain broad classes of explicit square integrable solutions the physical significance and some analytical properties of the solutions obtained are briefly discussed

ultra high frequency volatility estimation with dependent microstructure noise we analyze the impact of time series dependence in market microstructure noise on the properties of estimators of the integrated volatility of an asset price based on data sampled at frequencies high enough for that noise to be a dominant consideration we show that combining two time scales for that purpose will work even when the noise exhibits time series dependence analyze in that context a refinement of this approach is based on multiple time scales and compare empirically our different estimators to the standard realized volatility

dynamic boundary control of a euler bernoulli beam a flexible beam clamped to a rigid base at one end and free at the other end is considered to stabilize the beam vibrations a dynamic boundary force control and a dynamic boundary torque control applied at the free end of the beam are proposed it is proved that with the proposed controls the beam vibrations decay exponentially the proof uses a lyapunov functional based on the energy functional of the system

backstepping approach to the arbitrary decay rate for euler bernoulli beam under boundary feedback in this article we are concerned with the boundary stabilisation of the euler bernoulli beam equation for which all eigenvalues of the control free system are located on the imaginary axis of the complex plane the fourth order system in spacial variable is transformed into a coupled heat like system this enables us to make a natural backstepping transformation in vector form to transform the system into a target system which has arbitrary decay rate the state feedback is thus designed it is shown that the original closed loop system is exponentially stable with the given arbitrary decay rate

boundary controllers and observers for the linearized schrodinger equation we consider a problem of stabilization of the linearized schrodinger equation using boundary actuation and measurements we propose two different control designs first a simple proportional collocated boundary controller is shown to exponentially stabilize the system how ever the decay rate of the closed loop system cannot be prescribed the second full state feedback boundary control design achieves an arbitrary decay rate we formally view the schrodinger equa tion as a heat equation in complex variables and apply the backstepping method recently developed for boundary control of reaction advection diffusion equations the resulting controller is then sup plied with the backstepping observer to obtain an output feedback compensator the designs are illustrated with simulations

asymptotic equivalence for inference on the volatility from noisy observations we consider discrete time observations of a continuous martingale under measurement error this serves as a fundamental model for high frequency data in finance where an efficient price process is observed under microstructure noise it is shown that this nonparametric model is in le cam s sense asymptotically equivalent to a gaussian shift experiment in terms of the square root of the volatility function and a nonstandard noise level as an application new rate optimal estimators of the volatility function and simple efficient estimators of the integrated volatility are constructed

limit theorems for moving averages of discretized processes plus noise this paper presents some limit theorems for certain functionals of moving averages of semimartingales plus noise which are observed at high frequency our method generalizes the pre averaging approach see bernoulli15 2009 634 658 stochastic process appl 119 2009 2249 2276 and provides consistent estimates for various characteristics of general semimartingales furthermore we prove the associated multidimensional stable central limit theorems as expected we find central limit theorems with a convergence rate n 1 4 if n is the number of observations

testing for jumps in a discretely observed process we propose a new test to determine whether jumps are present in asset returns or other discretely sampled processes as the sampling interval tends to 0 our test statistic converges to 1 if there are jumps and to another deterministic and known value such as 2 if there are no jumps the test is valid for all ito semimartingales depends neither on the law of the process nor on the coefficients of the equation which it solves does not require a preliminary estimation of these coefficients and when there are jumps the test is applicable whether jumps have finite or infinite activity and for an arbitrary blumenthal getoor index we finally implement the test on simulations and asset returns data

high frequency covariance estimates with noisy and asynchronous financial data this article proposes a consistent and efficient estimator of the high frequency covariance quadratic covariation of two arbitrary assets observed asynchronously with market microstructure noise this estimator is built on the marriage of the quasi maximum likelihood estimator of the quadratic variation and the proposed generalized synchronization scheme and thus is not influenced by the epps effect moreover the estimation procedure is free of tuning parameters or bandwidths and is readily implementable monte carlo simulations show the advantage of this estimator by comparing it with a variety of estimators with specific synchronization methods the empirical studies of six foreign exchange future contracts illustrate the time varying correlations of the currencies during the 2008 global financial crisis demonstrating the similarities and differences in their roles as key currencies in the global market

risk jumps and diversification we test for price discontinuities or jumps in a panel of high frequency intraday stock returns and an equiweighted index constructed from the same stocks using a new test for common jumps that explicitly utilizes the cross covariance structure in the returns to identify non diversifiable jumps we find strong evidence for many modest sized yet highly significant cojumps that simply pass through standard jump detection statistics when applied on a stock by stock basis our results are further corroborated by a striking within day pattern in the significant cojumps with a sharp peak at the time of regularly scheduled macroeconomic news announcements r 2008 published by elsevier b v

a tale of two time scales it is a common practice in finance to estimate volatility from the sum of frequently sampled squared returns however market microstructure poses challenges to this estimation approach as evidenced by recent empirical studies in finance the present work attempts to lay out theoretical grounds that reconcile continuous time modeling and discrete time samples we propose an estimation approach that takes advantage of the rich sources in tick by tick data while preserving the continuous time assumption on the underlying returns under our framework it becomes clear why and where the usual volatility estimator fails when the returns are sampled at the highest frequencies if the noise is asymptotically small our work provides a way of finding the optimal sampling frequency a better approach the two scales estimator works for any size of the noise

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

modeling stabilization and control of serially connected beams many flexible structures consist of a large number of components coupled end to end in the form of a chain in this paper we consider the simplest type of such structures which is formed by n seri

an efficient feedback control algorithm for beams experimental investigations an experimental implementation of a rapid active control strategy for flexible structures combined with a modal filter for state reconstruction is presented the control law which builds upon komornik s original idea is designed so as to achieve an arbitrarily large decay rate of the energy of the system at the price of solving once and for all a well conditioned small size linear system instead of a riccati equation it is applied to a slender beam the fundamental ideas and properties of this simple but efficient strategy are explained the emphasis is put on the practical implementation and on the experimental results which show an important increase of the apparent modal damping even for values of the resulting gain that do not generate spill over the proposed feedback outperforms the standard lq control the actual behaviour of the closed loop system is accurately predicted by a complete electro mechanical model that accounts for the identified dynamics of the shaker

sliding mode boundary control of an euler bernoulli beam subject to disturbances in this paper a control technique is presented for an undamped pinned pinned euler bernoulli beam with control inputs and bounded disturbances on one boundary the control strategy drives the system to its origin at an arbitrary exponential rate in the presence of the disturbances this is achieved in two main steps first a backstepping transformation is used to convert the marginally stable euler bernoulli beam system to a new form that has an exponentially stable homogeneous form control inputs are needed to fully convert the system to this form however since they are distorted by unknown bounded disturbances the next step implements a sliding mode controller to account for them the proposed sliding manifolds require a combination of classical and second order techniques in order to avoid discontinuous chattering on the physical system therefore the continuous sliding mode controllers developed return the beam to its origin at an arbitrary exponential rate and do so in the presence of unknown bounded disturbances on the boundary the main contributions of this paper with respect to previous backstepping designs for the euler bernoulli beam are that all three of the following goals are accomplished together i steady state position is the origin ii decay rate has no theoretical restrictions and iii is robust to bounded disturbances

testing for common arrivals of jumps for discretely observed multidimensional processes we consider a bivariate process xt x 1 t x 2 t which is observed on a flnite time interval 0 t at discrete times 0 n 2 n assuming that its two components x 1 and x 2 have jumps on 0 t we derive tests to decide whether they have at least one jump occurring at the same time common jumps or not disjoint jumps there are two difierent tests for the two possible null hypotheses common jumps or disjoint jumps those tests have a prescribed asymptotic level as the mesh n goes to 0 we show on some simulations that these tests perform reasonably well even in the flnite sample case and we also put them in use for some exchange rates data

modeling and boundary control of translational and rotational motions of nonlinear slender beams in three dimensional space abstract equations of motion of extensible and shearable slender beams with large translational and rotational motions under external loads in three dimensional space are first derived in a vector form boundary feedback controllers are then designed to ensure that the beams are practically k exponentially stable at the equilibrium the control design well posedness and stability analysis are based on two lyapunov type theorems developed for a class of evolution systems in hilbert space numerical simulations on a slender beam immersed in sea water are included to illustrate the effectiveness of the proposed control design