a novel definition for quantification of mode shape complexity abstract complex mode shapes are quite often encountered in structural dynamics however there is no universally accepted parameter for the quantification of mode shape complexity after reviewing the existing methods a novel approach is proposed in this paper in order to quantify mode shape complexity for general structures the new parameter proposed in this paper is based on conservation of energy principle when a structure is vibrating at a specific mode during a period of vibration the levels of complexity of the individual mode shapes of a sample structure are then quantified using the proposed new parameter and the other parameters available in the literature the corresponding results are compared the validity and the generality of the new parameter are demonstrated for various damping scenarios

estimation of stochastic volatility models via monte carlo maximum likelihood this paper discusses the monte carlo maximum likelihood method of estimating stochastic volatility sv models the basic sv model can be expressed as a linear state space model with log chi square disturbances the likelihood function can be approximated arbitrarily accurately by decomposing it into a gaussian part constructed by the kalman filter and a remainder function whose expectation is evaluated by simulation no modifications of this estimation procedure are required when the basic sv model is extended in a number of directions likely to arise in applied empirical research this compares favorably with alternative approaches the finite sample performance of the new estimator is shown to be comparable to the monte carlo markov chain mcmc method

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

estimation of stable distributions by indirect inference this article deals with the estimation of the parameters of an stable distribution by the indirect inference method with the skewed t distribution as an auxiliary model the latter distribution appears as a good candidate for an auxiliary model since it has the same number of parameters as the stable distribution with each parameter playing a similar role to improve the properties of the estimator in finite sample we use a variant of the method called constrained indirect inference in a monte carlo study we show that this method delivers estimators with good properties in finite sample in particular they are much more efficient than two other prevalent methods based on the characteristic function and the empirical quantiles we provide an empirical application to hedge fund returns

fisher s information for discretely sampled levy processes this paper studies the asymptotic behavior of the fisher information for a levy process discretely sampled at an increasing frequency we show that it is possible to distinguish not only the continuous part of the process from its jumps part but also different types of jumps and derive the rates of convergence of efficient estimators

the decoupling of damped linear systems in free or forced vibration abstract the purpose of this paper is to extend classical modal analysis to decouple any viscously damped linear system in non oscillatory free vibration or in forced vibration based upon an exposition of how exponential decay in a system can be regarded as imaginary oscillations the concept of damped modes of imaginary vibration is introduced by phase synchronization of these real and physically excitable modes a time varying transformation is constructed to decouple non oscillatory free vibration when time drifts caused by viscous damping and by external excitation are both accounted for a time varying decoupling transformation for forced vibration is derived the decoupling procedure devised herein reduces to classical modal analysis for systems that are undamped or classically damped this paper constitutes the second and final part of a solution to the classical decoupling problem together with an earlier paper a general methodology that requires only the solution of a quadratic eigenvalue problem is developed to decouple any damped linear system

a test of separate families of distributions based on the empirical moment generating function summary in testing an hypothesis that a population has a specified distribution against the alternative that its distribution belongs to a separate family it is well known that the likelihood ratio test does not apply we propose a test based on the difference between the sample moment generating function and its theoretical counterpart under ho the argument of the moment generating function is chosen to maximize the test s largesample power small sample properties of the test in two applications are studied by simulation

estimates of errors in the frequency response of non classically damped systems abstract this paper examines the vibration behaviour of non classically damped systems in the frequency domain errors in the frequency response incurred by neglecting off diagonal entries of a diagonally dominant modal damping matrix are assessed the exact response is shown to be equivalent to an infinite taylor s series and it is demonstrated that the commonly employed approximation of ignoring off diagonal entries of the modal damping matrix is equivalent to retaining one term of the series the frequency dependence of coupling of the non classical modes is obtained

on some fourier methods for inference abstract common statistical procedures such as maximum likelihood and m estimation admit generalized representations in the fourier domain the fourier domain provides fertile ground for approaching a number of difficult problems in inference in particular the empirical characteristic function and its extension for stationary time series are shown to be fundamental tools which support numerically simple inference procedures having arbitrarily high asymptotic efficiency and certain robustness features as well a numerical illustration involving the symmetric stable laws is given

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

the transformation of second order linear systems into independent equations the class of second order linear dynamical systems is considered a method and algorithm are presented to transform any system with n degrees of freedom into n independent second order equations the conversion utilizes a real invertible but nonlinear mapping and is applicable to practically every linear system two examples from earthquake engineering are provided to indicate the utility of this approach

density approximations for multivariate affine jump diffusion processes we introduce closed form transition density expansions for multivariate affine jump diffusion processes the expansions rely on a general approximation theory which we develop in weighted hilbert spaces for random variables which possess all polynomial moments we establish parametric conditions which guarantee existence and differentiability of transition densities of affine models and show how they naturally fit into the approximation framework empirical applications in option pricing credit risk and likelihood inference highlight the usefulness of our expansions the approximations are extremely fast to evaluate and they perform very accurately and numerically stable

a note on new stability and stabilization conditions for t s fuzzy systems with time delay fuzzy sets syst 263 2015 82 91 in a recent paper zhang et al 2015 2 a new lyapunov krasovskii functional containing the fuzzy line integral lyapunov function lilf has been introduced to deal with the problem of the stability analysis and stabilization for takagi sugeno t s fuzzy systems with time delay and less conservative stability and stabilization conditions are achieved however the special structural information about the line integral lyapunov matrices is overlooked in 2 which is harmful to the validity of the main results

diagonal dominance of damping and the decoupling approximation in linear vibratory systems a common approximation in the analysis of non classically damped systems is to ignore the off diagonal elements of the modal damping matrix this procedure is termed the decoupling approximation it is generally believed that errors due to the decoupling approximation should be negligible if the modal damping matrix is diagonally dominant in addition the errors are expected to decrease as the modal damping matrix becomes more diagonally dominant it is shown numerically in this paper that over a finite range errors due to the decoupling approximation can increase monotonically at any specified rate while the modal damping matrix becomes more diagonally dominant with its off diagonal elements decreasing continuously in magnitude an explanation for these unexpected drifts of decoupling errors is provided with the use of complex coupling coefficients small off diagonal elements in the modal damping matrix are not sufficient to ensure small errors due to the decoupling approximation any error criterion based solely upon the diagonal dominance of the modal damping matrix would not be accurate

new stability and stabilization conditions for t s fuzzy systems with time delay this paper is concerned with the problem of the stability analysis and stabilization for takagi sugeno t s fuzzy systems with time delay a new lyapunov krasovskii functional containing the fuzzy line integral lyapunov function and the simple functional is chosen by using a recently developed wirtinger based integral inequality and introducing slack variables less conservative conditions in terms of linear matrix inequalities lmis are derived several examples are given to show the advantages of the proposed results

an improved version of the quandt ramsey mgf estimator for mixtures of normal distributions and switching regressions quandt and ramsey have suggested an estimator for normal mixtures and switching regressions which minimizes a sum of squared differences between empirical and theoretical values of the moment generating function this paper demonstrates how their estimator can be improved by minimizing a generalized sum of squares rather than an ordinary sum of squares when this is done more points of evaluation moments are unambiguously better than less most of the results presented are also applicable to method of moments estimators in general

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

instrumental variable estimation of nonlinear errors in variables models this paper establishes that instruments enable the identification of nonparametric regression models in the presence of measurement error by providing a closed form solution for the regression function in terms of fourier transforms of conditional expectations of observable variables for parametrically specified regression functions we propose a root n consistent and asymptotically normal estimator that takes the familiar form of a generalized method of moments estimator with a plugged in nonparametric kernel density estimate both the identification and the estimation methodologies rely on fourier analysis and on the theory of generalized functions the finite sample properties of the estimator are investigated through monte carlo simulations

a new fuzzy lyapunov function approach for a takagi sugeno fuzzy control system design in this paper a new fuzzy lyapunov function approach is presented for a class of continuous time takagi sugeno fuzzy control system the proposed fuzzy lyapunov function is formulated as a line integral of a fuzzy vector which is a function of the state and it can be regarded as the work done from the origin to the current state in the fuzzy vector field unlike the approaches using a fuzzy blending of multiple quadratic lyapunov functions the time derivatives of membership functions do not appear in the proposed approach the effectiveness of the proposed approach is shown through numerical examples

the decoupling of defective linear dynamical systems in free motion abstract it was demonstrated in two earlier papers that there exists a real linear time varying transformation that decouples any non defective linear dynamical system in free vibration in the configuration space as an extension of this work the present paper represents the first systematic effort to decouple defective systems it is shown that the decoupling of defective systems is a rather delicate procedure that depends on the multiplicities of the system eigenvalues while any defective system can be decoupled with the eigenvalues kept invariant the geometric multiplicities of these eigenvalues may not be preserved several numerical examples are provided to illustrate the theoretical developments

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

on the efficiency of empirical characteristic function procedures summary the asymptotic normality and arbitrarily high efficiency of some new statistical procedures based on the empirical characteristic function is established under general conditions

validating forecasts of the joint probability density of bond yields can affine models beat random walk most existing empirical studies on affine term structure models atsms have mainly focused on in sample goodness of fit of historical bond yields and ignored out of sample forecast of future bond yields using an omnibus nonparametric procedure for density forecast evaluation in a continuous time framework we provide probably the first comprehensive empirical analysis of the out of sample performance of atsms in forecasting the joint conditional probability density of bond yields we find that although the random walk models tend to have better forecasts for the conditional mean dynamics of bond yields some atsms provide better forecasts for the joint probability density of bond yields however all atsms considered are still overwhelmingly rejected by our tests and fail to provide satisfactory density forecasts there exists room for further improving density forecasts for bond yields by extending atsms