the ensemble statistics of the vibrational energy density of a random system subjected to single point harmonic excitation this paper is concerned with the ensemble statistics of the energy density of a random system subjected to a harmonic point load both the mean and variance of the reverberant energy density i e the total response minus the direct field are investigated it is shown that the ensemble average of the reverberant energy density is not spatially homogeneous but rather the value at the drive point is between two and three times the spatially averaged value depending on the modal overlap factor this result is closely analogous to established results regarding the case of transient excitation expressions are also derived for the relative variance of the reverberant energy density both remote from the drive point and at the drive point and a number of anomalies are found in existing results a comparison is made with simulation results for a randomized plate and this comparison highlights the importance of the ensemble size considered in the simulations the present analysis is based on a random point process model of the system natural frequencies and both gaussian orthogonal ensemble goe statistics and poisson statistics are considered

subsampling high frequency data the main contribution of this paper is to propose a novel way of conducting inference for an important general class of estimators that includes many estimators of integrated volatility a subsampling scheme is introduced that consistently estimates the asymptotic variance for an estimator thereby facilitating inference and the construction of valid confidence intervals the new method does not rely on the exact form of the asymptotic variance which is useful when the latter is of complicated form the method is applied to the volatility estimator of ait sahalia et al 2011 in the presence of autocorrelated and heteroscedastic market microstructure noise

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

transient response of structures with uncertain properties to nonlinear shock loading abstract a method is presented to predict the transient response of a structure at the driving point following an impact or a shock loading the displacement and the contact force are calculated solving the discrete convolution between the impulse response and the contact force itself expressed in terms of a nonlinear hertzian contact stiffness application of random point process theory allows the calculation of the impulse response function from knowledge of the modal density and the geometric characteristics of the structure only the theory is applied to a wide range of structures and results are experimentally verified for the case of a rigid object hitting a beam a plate a thin and a thick cylinder and for the impact between two cylinders the modal density of the flexural modes for a thick slender cylinder is derived analytically good agreement is found between experimental simulated and published results showing the reliability of the method for a wide range of situations including impacts and pyroshock applications

constrained source coding with side information the source coding problem with side information at the decoder is studied subject to a constraint that the encoder to whom the side information is unavailable be able to compute the decoder s reconstruction sequence to within some distortion for discrete memoryless sources and finite single letter distortion measures an expression is given for the minimal description rate as a function of the joint law of the source and side information and of the allowed distortions at the encoder and at the decoder the minimal description rate is also computed for a memoryless gaussian source with squared error distortion measures a solution is also provided to a more general problem where there are more than two distortion constraints and each distortion measure may be a function of three arguments the source symbol the encoder s reconstruction symbol and the decoder s reconstruction symbol

volatility estimators for discretely sampled levy processes this paper studies the estimation of the volatility parameter in a model where the driving process is a brownian motion or a more general symmetric stable process that is perturbed by another levy process we distinguish between a parametric case where the law of the perturbing process is known and a semiparametric case where it is not in the parametric case we construct estimators which are asymptotically efficient in the semiparametric case we can obtain asymptotically efficient estimators by sampling at a sufficiently high frequency and these estimators are efficient uniformly in the law of the perturbing process

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

a simple method for the adjustment of profile likelihoods summary we propose a simple adjustment for profile likelihoods the aim of the adjustment is to alleviate some of the problems inherent in the use of profile likelihoods such as bias inconsistency and overoptimistic variance estimates the adjustment is applied to the profile loglikelihood score function at each parameter value so that its mean is zero and its variance is the negative expected derivative matrix of the adjusted score function for cases in which explicit calculation of the adjustments is difficult we give two methods to simplify their computation an automatic simulation method that requires as input only the profile loglikelihood and its first few derivatives first order asymptotic expressions some examples are provided and a comparison is made with the conditional profile log likelihood of cox and reid

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

assessment of uncertainty in high frequency data the observed asymptotic variance the availability of high frequency financial data has generated a series of estimators based on intra day data improving the quality of large areas of financial econometrics however estimating the standard error of these estimators is often challenging the root of the problem is that traditionally standard errors rely on estimating a theoretically derived asymptotic variance and often this asymptotic variance involves substantially more complex quantities than the original parameter to be estimated standard errors are important they are used to assess the precision of estimators in the form of confidence intervals to create feasible statistics for testing to build forecasting models based on say daily estimates and also to optimize the tuning parameters the contribution of this paper is to provide an alternative and general solution to this problem which we call observed asymptotic variance it is a general nonparametric method for assessing asymptotic variance avar it provides consistent estimators of avar for a broad class of integrated parameters t dt where the spot parameter process can be a general semimartingale with continuous and jump components the observed avar is implemented with the help of a two scales method its construction works well in the presence of microstructure noise and when the observation times are irregular or asynchronous in the multivariate case the methodology is valid for a wide variety of estimators including the standard ones for variance and covariance and also for more complex estimators such as of leverage effects high frequency betas and semivariance

martingale approximations for sums of stationary processes approximations to sums of stationary and ergodic sequences by martingales are investigated necessary and sufficient conditions for such sums to be asymptotically normal conditionally given the past up to time 0 are obtained it is first shown that a martingale approximation is necessary for such normality and then that the sums are asymptotically normal if and only if the approximating martingales satisfy a lindeberg feller condition using the explicit construction of the approximating martingales a central limit theorem is derived for the sample means of linear processes the conditions are not sufficient for the functional version of the central limit theorem this is shown by an example and a slightly stronger sufficient condition is given

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

a test for the rank of the volatility process the random perturbation approach in this paper we present a test for the maximal rank of the matrix valued volatility process in the continuous it o semimartingale framework our idea is based upon a random perturbation of the original high frequency observations of an it o semimartingale which opens the way for rank testing we develop the complete limit theory for the test statistic and apply it to various null and alternative hypotheses finally we demonstrate a homoscedasticity test for the rank process

on adjustments based on the signed root of the empirical likelihood ratio statistic summary the standard multivariate normal approximation to the distribution of the signed root of the empirical likelihood ratio statistic is considered in cases where inference is required for a smooth function of the mean of the distribution from which the sample is drawn the error in this approximation is of order o n 2 where n is the sample size and it is shown that the error can be reduced to order o n 1 by using a mean adjustment when a scalar parameter is of interest use of the mean adjustment produces confidence intervals whose endpoints each have coverage error of order o n 1 this is in contrast to use of the unadjusted signed root or equivalently use of the chi squared approximation for the empirical likelihood ratio statistic which produces one sided limits having coverage error of order 0 n 2 for a vector parameter of interest a procedure asymptotically equivalent to the mean adjustment is developed that avoids explicit calculation of the signed square root it is argued for the scalar parameter case that the coverage error of one sided limits can be further reduced to o n 312 by use of both mean and variance adjustments the variance adjustment is given in the case when a scalar mean is of interest the coverage accuracy of confidence limits obtained by the various methods is illustrated by simulation

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

on the reciprocity relationship between direct field radiation and diffuse reverberant loading this analysis is concerned with the derivation of a diffuse field reciprocity relationship between the diffuse field excitation of a connection to a structural or acoustic subsystem and the radiation impedance of the connection such a relationship has been derived previously for connections described by a single degree of freedom in the present work it is shown that the diffuse field reciprocity relationship also arises when describing the ensemble average response of connections to structural or acoustic subsystems with uncertain boundaries furthermore it is shown that the existing diffuse field reciprocity relationship can be extended to encompass connections that possess an arbitrary number of degrees of freedom the present work has application to i the calculation of the diffuse field response of structural acoustic systems modeled by finite elements boundary elements and infinite elements ii the general calculation of the coupling loss factors employed in statistical energy analysis sea and iii the derivation of an alternative analysis method for describing the dynamic interactions of coupled subsystems with uncertain boundaries a generalized boundary approach to sea

the modified signed likelihood statistic and saddlepoint approximations summary for a number of tests in exponential families we show that the use of a normal approximation to the modified signed likelihood ratio statistic r is equivalent to the use of a saddlepoint approximation this is also true in a large deviation region where the signed likelihood ratio statistic r is of order in

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

on the jump activity index for semimartingales hk rgc hkust6011 07p hkust6015 08p hkust6019 10p national nature science foundation of china 71071155 fundamental research funds for the central universities renmin university of china 10xnl007 nsfc 71071155

anova for diffusions and ito processes ito processes are the most common form of continuous semimartingales and include diffusion processes this paper is concerned with the nonparametric regression relationship between two such ito processes we are interested in the quadratic variation integrated volatility of the residual in this regression over a unit of time such as a day a main conceptual finding is that this quadratic variation can be estimated almost as if the residual process were observed the difference being that there is also a bias which is of the same asymptotic order as the mixed normal error term the proposed methodology anova for diffusions and ito processes can be used to measure the statistical quality of a parametric model and non parametrically the appropriateness of a one regressor model in general on the other hand it also helps quantify and characterize the trading hedging error in the case of financial applications

continuous record asymptotics for rolling sample variance estimators it is widely known that conditional covariances of asset returns change over time researchers doing empirical work have adopted many strategies for accommodating conditional heteroskedasticity among the popular strategies are a chopping the available data into short blocks of time and assuming homoskedasticity within the blocks b performing one sided rolling regressions in which only data from say the preceding five year period is used to estimate the conditional covariance of returns at a given date and c performing two sided rolling regressions in which covariances are estimated for each date using say five years of lags and five years of leads another model garch amounts to a one sided weighted rolling regression we develop continuous record asymptotic approximations for the measurement error in conditional variances and covariances when using these methods we derive asymptotically optimal window lengths for standard rolling regressions and optimal weights for weighted rolling regressions as an empirical example we estimate volatility on the s p 500 stock index using daily data from 1928 to 1990

infereni on full or partial parameters based on the standardized signed log likelihood ratio on etudie des tests et des limites de confiance bases sur la statistique du rapport de log vraisemblance signee en ajustant cette statistique de telle sorte qu a un ordre superieur d approximation la distribution normale standard soit valable