a one factor multivariate time series model of metropolitan wage rates abstract the paper formulates and estimates a single factor multivariate time series model the model is a dynamic generalization of the multiple indicator or factor analysis model it is shown to be a special case of the general state space model and can be estimated by maximum likelihood methods using the kalman filter algorithm the model is used to obtain estimates of the unobserved metropolitan wage rate for los angeles based on observations of sectoral wages within the standard metropolitan statistical area hypothesis tests model diagnostics and out of sample forecasts are used to evaluate the model

fitting nonlinear ordinary differential equation models with random effects and unknown initial conditions using the stochastic approximation expectation maximization saem algorithm the past decade has evidenced the increased prevalence of irregularly spaced longitudinal data in social sciences clearly lacking however are modeling tools that allow researchers to fit dynamic models to irregularly spaced data particularly data that show nonlinearity and heterogeneity in dynamical structures we consider the issue of fitting multivariate nonlinear differential equation models with random effects and unknown initial conditions to irregularly spaced data a stochastic approximation expectation maximization algorithm is proposed and its performance is evaluated using a benchmark nonlinear dynamical systems model namely the van der pol oscillator equations the empirical utility of the proposed technique is illustrated using a set of 24 h ambulatory cardiovascular data from 168 men and women pertinent methodological challenges and unresolved issues are discussed

kalman filtering estimation of unobserved rational expectations with an application to the german hyperinflation abstract the assumption that rational expectations always lie on a convergent path is subject to an empirical test using the german hyperinflation data the estimation technique employs a kalman filtering algorithm after presenting a brief background for the convergent expectations problem and a derivation of the various model specifications a generalized expectations model and its attendant kalman filtering estimation technique are discussed additional estimation details and empirical results are then presented based on an assumption of normally distributed errors the null hypothesis of convergent paths is rejected in all situations involving a deterministic specification of the evolution of the unobserved parameter which characterizes the convergent path the same null hypothesis is rejected in four of the six cases corresponding to a stochastic specification of the evolution of the unobserved parameter which characterizes the convergent path a discussion of these findings their economic significance and suggestions for further research concludes the paper

brief algebraic solution to the robust spr problem for two polynomials in this paper we provide an algebraic method for the design of an appropriate transfer function making simultaneously two polynomials strictly positive real spr in the so called robust spr problem for two polynomials this problem arises in the design of recursive estimation algorithms used for identification purposes and in active noise control anc applications in the former a given transfer function involving the poles of the unknown transfer function must be made spr in the latter the phase of a transfer function must be matched within a range of email protected 2 p 2 robust spr design methods try to fulfill the phase requirements for all possible transfer functions belonging to a given uncertainty description here we focus on uncertainties described by two polynomials

bias in estimating multivariate and univariate diffusions a b s t r a c t multivariate continuous time models are now widely used in economics and finance empirical applications typically rely on some process of discretization so that the system may be estimated with discrete data this paper introduces a framework for discretizing linear multivariate continuous time systems that includes the commonly used euler and trapezoidal approximations as special cases and leads to a general class of estimators for the mean reversion matrix asymptotic distributions and bias formulae are obtained for estimates of the mean reversion parameter explicit expressions are given for the discretization bias and its relationship to estimation bias in both multivariate and in univariate settings in the univariate context we compare the performance of the two approximation methods relative to exact maximum likelihood ml in terms of bias and variance for the vasicek process the bias and the variance of the euler method are found to be smaller than the trapezoidal method which are in turn smaller than those of exact ml simulations suggest that when the mean reversion is slow the approximation methods work better than ml the bias formulae are accurate and for scalar models the estimates obtained from the two approximate methods have smaller bias and variance than exact ml for the square root process the euler method outperforms the nowman method in terms of both bias and variance simulation evidence indicates that the euler method has smaller bias and variance than exact ml nowman s method and the milstein method

frequency domain estimation of temporally aggregated gaussian cointegrated systems this paper considers joint estimation of long run equilibrium coefficients and parameters governing the short run dynamics of a fully parametric gaussian cointegrated system formulated in continuous time the model allows the stationary disturbances to be generated by a stochastic differential equation system and for the variables to be a mixture of stocks and flows we derive a precise form for the exact discrete analogue of the continuous time model in triangular error correction form which acts as the basis for frequency domain estimation of the unknown parameters using discrete time data we formally establish the order of consistency and the asymptotic sampling properties of such an estimator the estimator of the cointegrating parameters is shown to converge at the rate of the sample size to a mixed normal distribution while that of the short run parameters converges at the rate of the square root of the sample size to a limiting normal distribution

extending the state space model to accommodate missing values in responses and covariates this article proposes an extended state space model for accommodating multivariate panel data the novel aspect of this contribution is an adjustment to the classical model for multiple subjects that allows missingness in the covariates in addition to the responses missing covariate data are handled by a second state space model nested inside the first to represent unobserved exogenous information relevant kalman filter equations are derived and explicit expressions are provided for both the e and m steps of an expectation maximization em algorithm to obtain maximum gaussian likelihood estimates of all model parameters in the presence of missing data the resulting em algorithm becomes computationally intractable but a simplification of the m step leads to a new procedure that is shown to be an expectation conditional maximization ecm algorithm under exogeneity of the covariates simulation studies reveal that the approach appears to be relatively robust to moderate percentages of missing dat

orthogonal designs with maximal rates orthogonal designs have been used as space time block codes for wireless communications with multiple transmit antennas which can achieve full transmit diversity and have a very simple decoupled maximum likelihood decoding algorithm the rate of an orthogonal design is defined as the ratio of the number of transmitted information symbols in a block of channel uses to the length of the given block which reflects the bandwidth efficiency of the employed space time block code constructed from the orthogonal design this paper focuses on the analysis and synthesis of orthogonal designs with the maximum possible rates which may be real or complex and square or rectangular matrices we first provide several representations of orthogonal designs and their characterizations in terms of hurwitz radon matrix equations next we observe that the real orthogonal designs square or rectangular and the complex square orthogonal designs with maximal rates have been well understood from the existing results in the mathematics literature which can be dated back to 1890s however unfortunately it is not the case for the complex rectangular orthogonal designs with rates as high as possible we then construct a class of complex orthogonal designs for any number of transmit antennas the proposed complex orthogonal designs for the number of transmit antennas n 2m 1 and 2m have the same rate m 1 and 2m where m is any natural number finally we demonstrate that for n 2m 1 and 2m with any given natural number m the value m 1 and 2m is the maximum possible rate that the complex orthogonal designs square or rectangular with n transmit antennas can achieve

longitudinal data with serial correlation a state space approach a general linear mixed model first order autoregressive errors state space representations the laird ware model in state space form autoregressive moving average errors nonlinear models multivariate models appendix fortran subroutines

a new delta expansion for multivariate diffusions via the ito taylor expansion abstract in this paper we develop a new delta expansion approach to deriving analytical approximation to the transition densities of multivariate diffusions using the ito taylor expansion of the conditional expectation of the dirac delta function our approach yields an explicit recursive formulas for the expansion coefficients and is universally applicable for a wide spectrum of models particularly the time inhomogeneous non affine irreducible multivariate diffusions we show that this new approach can be viewed as an extension of ait sahalia 2002 and lee et al 2014 to the case of multivariate models the derived expansions are proved to converge to the true probability density as the observational time interval shrinks the obtained approximations can thereby be used to carry out the maximum likelihood estimation for the diffusions with discretely observed data extensive numerical experiments demonstrate the accuracy and effectiveness of our approach

bayesian versus frequentist measures of error in small area estimation summary this paper compares analytically and empirically the frequentist and bayesian measures of error in small area estimation the model postulated is the nested error regression model which allows for random small area effects to represent the joint effect of small area characteristics that are not accounted for by the fixed regressor variables when the variance components are known then under a uniform prior for the regression coefficients and normality of the error terms the frequentist and the bayesian approaches yield the same predictors and prediction mean squared errors mses defined accordingly when the variance components are unknown it is common practice to replace the unknown variances by sample estimates in the expressions for the optimal predictors so that the resulting empirical predictors remain the same under the two approaches the use of this paradigm requires however modifications to the expressions of the prediction mse to account for the extra variability induced by the need to estimate the variance components the main focus of this paper is to review and compare the modifications to prediction mses proposed in the literature under the two approaches with special emphasis on the orders of the bias of the resulting approximations to the true mses some new approximations based on monte carlo simulation are also proposed and compared with the existing methods the advantage of these approximations is their simplicity and generality finite sample frequentist properties of the various methods are explored by a simulation study the main conclusions of this study are that the use of second order bias corrections generally yields better results in terms of the bias of the mse approximations and the coverage properties of confidence intervals for the small area means the bayesian methods are found to have good frequentist properties but they can be inferior to the frequentist methods the second order approximations under both approaches have however larger variances than the corresponding first order approximations which in most cases result in higher mses of the mse approximations

the estimation of systems of joint differential difference equations this paper considers estimation of the parameters of systems of joint differential difference equations the existence and uniqueness of the solution to the model are demonstrated and the properties of the continuous time and discretely sampled processes are derived the focus is on frequency domain methods throughout one of the main technical achievements being the derivation of a computable expression for the spectral density function of the discretely observed data which are allowed to be mixtures of stock and flow variables a frequency domain gaussian estimator is proposed and its consistency and asymptotic normality are established without requiring the assumption that the data are gaussian the finite sample properties of the estimator are assessed in a small simulation exercise

explicit form of approximate transition probability density functions of diffusion processes abstract a continuous time diffusion process is very popular in modeling and provides useful tools to analyze particularly but not restricted to a variety of economic and financial variables the transition probability density function tpdf of a diffusion process plays an important role in understanding and explaining the dynamics of the process a new way to find closed form approximate tpdfs for multivariate diffusions is proposed in this paper this method can be applied to general multivariate time inhomogeneous diffusion processes as long as roughly speaking they have smooth drift and volatility functions a diffusion process is said to be reducible if it can be converted into a unit diffusion process where the volatility is the identity matrix we have established how to obtain the approximate tpdf of a reducible diffusion explicitly when a diffusion process is not reducible an explicit form of approximate tpdf can be obtained by using the results in ait sahalia 2008 and choi 2013 the tpdf expansion suggested here enables us to obtain a recursive formula for the coefficient of the approximate tpdf for a multivariate jump diffusion monte carlo simulation studies of conducting maximum likelihood estimation mle using our approximations provide convincing evidence that our tpdf expansion can be used for the mle when the true tpdf is unavailable we also applied our approximate tpdfs to option pricing the differences between our option prices and those from the extended black scholes formula are shown to be quite small this implies that our methods can be employed to price assets whose underlying state variables follow general diffusion models

continuous time state space modeling of panel data by means of sem maximum likelihood parameter estimation of the continuous time linear stochastic state space model is considered on the basis of largen discrete time data using a structural equation modeling sem program random subject effects are allowed to be part of the model the exact discrete model edm is employed which links the discrete time model parameters to the underlying continuous time model parameters by means of nonlinear restrictions the edm is generalized to cover not only time invariant parameters but also the cases of stepwise time varying piecewise time invariant parameters and parameters varying continuously over time according to a general polynomial scheme the identification of the continuous time parameters is discussed and an educational example is presented

the dimensionality of the aliasing problem in models with rational spectral densities this paper reconsiders the aliasing problem of identifying the parameters of a continuous time stochastic process from discrete time data it analyzes the extent to which restricting attention to processes with rational spectral density matrices reduces the number of observationally equivalent models it focuses on rational specifications of spectral density matrices since rational parameterizations are commonly employed in the analysis of the time series data this abstract was borrowed from another version of this item

technical communique on the strengthened robust spr problem for discrete time systems the well known necessary and sufficient condition to find a solution to the robust strictly positive real spr problem namely that the phase difference of the polynomials involved must be less than p was found to be also necessary and sufficient in the strengthened robust spr problem by anderson and landau in a recent work only for the continuous time case in this brief communication we derive a necessary condition in the discrete time case which cannot be formulated in phase terms and which is more stringent than the condition of the robust spr problem thereby establishing a fundamental difference between both continuous time and discrete time domains

closed form likelihood expansions for multivariate time inhomogeneous diffusions the aim of this paper is to find approximate log transition density functions for multivariate timeinhomogeneous diffusions in closed form there are many empirical evidences that the underlying data generating processes for many economic variables might change over time one possible way to explain the time dependent behavior of state variables is to model the drift or volatility terms as functions of time as well as state variables closed form likelihood expansions for multivariate time homogeneous diffusions have been obtained by ait sahalia 2008 this research is built on his work and extends his results to time inhomogeneous cases simulation study reveals that our method yields a very accurate approximate likelihood function that can be a good candidate when the true likelihood function is unavailable

systems of seemingly unrelated regression equations with time varying coefficients an interplay of kalman filtering scoring em and minque method abstract this paper gives a detailed description of the implementation of ml estimation using scoring and em for the hyperparameters of a particular econometric state space we also show how the em method can be turned into an on line estimation method and how this procedure relates to an adaptive method of variance component estimation based on minque theory a small simulation study for a single equation model indicates how much can be gained in terms of computer time by using a combination of scoring and em

zero inflated regime switching stochastic differential equation models for highly unbalanced multivariate multi subject time series data in the study of human dynamics the behavior under study is often operationalized by tallying the frequencies and intensities of a collection of lower order processes for instance the higher order construct of negative affect may be indicated by the occurrence of crying frowning and other verbal and nonverbal expressions of distress fear anger and other negative feelings however because of idiosyncratic differences in how negative affect is expressed some of the lower order processes may be characterized by sparse occurrences in some individuals to aid the recovery of the true dynamics of a system in cases where there may be an inflation of such zero responses we propose adding a regime unobserved phase of non occurrence to a bivariate ornstein uhlenbeck ou model to account for the high instances of non occurrence in some individuals while simultaneously allowing for multivariate dynamic representation of the processes of interest under nonzero responses the transition between the occurrence i e active and non occurrence i e inactive regimes is represented using a novel latent markovian transition model with dependencies on latent variables and person specific covariates to account for inter individual heterogeneity of the processes bayesian estimation and inference are based on markov chain monte carlo algorithms implemented using the jags software we demonstrate the utility of the proposed zero inflated regime switching ou model to a study of young children s self regulation at 36 and 48 months

alternative algorithms for the estimation of dynamic factor mimic and varying coefficient regression models this paper provides a general approach to the formulation and estimation of dynamic unobserved component models after introducing the general model two methods for estimating the unknown parameters are presented both are algorithms for maximizing the likelihood function the first is based on the method of scoring the second is the em algorithm a derivative free method each iteration of em requires a kalman filter and smoother followed by straightforward regression calculations the paper suggests using the em methods to quickly locate a neighborhood of the maximum scoring can then be used to pinpoint the maximum and calculate the information matrix

a standard error for the estimated state vector of a state space model abstract this paper motivates an estimate of the variance of the estimated state vector x t in a state space model when the vector of parameters characterizing system dynamics must be estimated from the data

frequency domain gaussian estimation of temporally aggregated cointegrated systems this paper discusses the joint estimation of the long run equilibrium coe cients and the parameters governing the short run dynamics of a fully parametric cointegrated system formulated in continuous time the model allows the stationary disturbances to be generated by a stochastic di erential equation system and for the variables to be a mixture of stocks and flows we derive a precise form for the exact discrete analogue of the continuous time model in triangular error correction form which acts as the basis for frequency domain gaussian estimation of the unknown parameters using discrete time data we formally establish the order of consistency and the asymptotic sampling properties of such an estimator the function of the data that estimates the cointegrating parameters is shown to converge at the rate of the sample size to a mixed normal distribution while that estimating the short run parameters converges at the rate of the square root of the sample size to a limiting normal distribution

fully nonparametric estimation of scalar diffusion models we propose a functional estimation procedure for homogeneous stochastic differential equations based on a discrete sample of observations and with minimal requirements on the data generating process we show how to identify the drift and diffusion function in situations where one or the other function is considered a nuisance parameter the asymptotic behavior of the estimators is examined as the observation frequency increases and as the time span lengthens we prove almost sure consistency and weak convergence to mixtures of normal laws where the mixing variates depend on the chronological local time of the underlying diffusion process that is the random time spent by the process in the vicinity of a generic spatial point the estimation method and asymptotic results apply to both stationary and nonstationary recurrent processes

time delay embedding increases estimation precision of models of intraindividual variability this paper investigates the precision of parameters estimated from local samples of time dependent functions we find that time delay embedding i e structuring data prior to analysis by constructing a data matrix of overlapping samples increases the precision of parameter estimates and in turn statistical power compared to standard independent rows of panel data we show that the reason for this effect is that the sign of estimation bias depends on the position of a misplaced data point if there is no a priori knowledge about initial conditions of the time dependent function hence we reason that the advantage of time delayed embedding is likely to hold true for a wide variety of functions we support these conclusions both by mathematical analysis and two simulations