efficient high dimensional importance sampling the paper describes a simple generic and yet highly accurate efficient importance sampling eis monte carlo mc procedure for the evaluation of high dimensional numerical integrals eis is based upon a sequence of auxiliary weighted regressions which actually are linear under appropriate conditions it can be used to evaluate likelihood functions and byproducts thereof such as ml estimators for models which depend upon unobservable variables a dynamic stochastic volatility model and a logit panel data model with unobserved heterogeneity random effects in both dimensions are used to provide illustrations of eis high numerical accuracy even under small number of mc draws mc simulations are used to characterize the finite sample numerical and statistical properties of eis based ml estimators

an analogue of the torus decomposition theorem for certain poincare duality groups it is shown that poincare duality groups which satisfy the maximal condition on centralisers have a canonical decomposition as the fundamental group of a finite graph of groups in which the edge groups are polycyclic by finite the results give useful information only when there are large polycyclic subgroups since 3 manifolds groups satisfy max c the results provide a purely group theoretic proof of the torus decomposion theorem in general fundamental groups of closed aspherical manifolds satisfy poincare duality and in fact many of the known examples satisfy max c thus the results provide a new approach to aspherical manifolds of higher dimensions

a kalman filtering derivation of simultaneous input and state estimation abstract simultaneous input and state estimation algorithms are studied as particular limits of kalman filtering problems this admits interpretation of the algorithm properties and critical analysis of their claims to being partly model free and to providing unbiased estimates a disturbance model white noise of unbounded variance is provided and the bias feature is shown to be a geometric projection property rather than probabilistic in nature as a consequence of this analysis the algorithm is connected in the stationary case to algebraic riccati equation computations for the gains estimate covariances and filter frequency response

simultaneous input and state estimation for nonlinear systems with applications to flow field estimation this paper studies the problem of simultaneous input and state estimation sise for nonlinear dynamical systems with and without direct input output feedthrough we take a bayesian perspective to develop a sequential joint input and state estimation approach our scheme gives rise to a nonlinear maximum a posteriori optimization problem which we solve using the classical gauss newton method the proposed approach generalizes a number of sise methods presented in the literature we illustrate the effectiveness of the proposed scheme for nonlinear systems with direct feedthrough in an oceanographic flow field estimation problem involving submersible drogues that measure position intermittently and acceleration continuously

monte carlo maximum likelihood estimation for non gaussian state space models state space models are considered for observations which have non gaussian distributions we obtain accurate approximations to the loglikelihood for such models by monte carlo simulation devices are introduced which improve the accuracy of the approximations and which increase computational efficiency the loglikelihood function is maximised numerically to obtain estimates of the unknown hyperparameters standard errors of the estimates due to simulation are calculated details are given for the important special cases where the observations come from an exponential family distribution and where the observation equation is linear but the observation errors are non gaussian the techniques are illustrated with a series for which the observations have a poisson distribution and a series for which the observation errors have a t distribution

finite sets of data compatible with multidimensional inequality measures by using a general solution to the problem of extending a preorder conditional on a list of ex ante comparisons between pairs we ellucidate when a finite set of predetermined comparisons can be incorporated to a multidimensional inequality measure even if the population size is variable

asymptotic filtering theory for univariate arch models this paper builds on this earlier work by deriving the asymptotic distribution of the measurement error this allows us to approximate the measurement accuracy of arch conditional variance estimates and compare the efficiency achieved by different arch models we are also able to characterize the relative importance of different kinds of misspecification for example we show that misspecifying conditional means adds only trivially at least asymptotically to measurement error while other factors for example capturing the leverage effect accommodating thick tailed residuals and correctly modelling the variability of the conditional variance process are potentially much more important third we are able to characterize a class of asymptotically optimal arch conditional variance estimates

observation driven models for poisson counts summary this paper is concerned with a general class of observation driven models for time series of counts whose conditional distributions given past observations and explanatory variables follow a poisson distribution these models provide a flexible framework for modelling a wide range of dependence structures conditions for stationarity and ergodicity of these processes are established from which the large sample properties of the maximum likelihood estimators can be derived simulations are provided to give additional insight into the finite sample behaviour of the estimators finally an application to a regression model for daily counts of asthma presentations at a sydney hospital is described

accelerating score driven time series models abstract we propose a new class of score driven time series models that allows for a more flexible weighting of score innovations for the filtering of time varying parameters the parameter for the score innovation is made time varying by means of an updating equation that accounts for the autocorrelations of past innovations we provide the theoretical foundations for this acceleration method by showing optimality in terms of reducing kullback leibler divergence the empirical relevance of this accelerated score driven updating method is illustrated in two empirical studies first we include acceleration in the generalized autoregressive conditional heteroskedasticity model we adopt the new model to extract volatility from exchange rates and to analyze daily density forecasts of volatilities from all individual stock return series in the standard poor s 500 index second we consider a score driven acceleration for the time varying mean and use this new model in a forecasting study for us inflation

brief paper unbiased minimum variance input and state estimation for linear discrete time systems this paper addresses the problem of simultaneously estimating the state and the input of a linear discrete time system a recursive filter optimal in the minimum variance unbiased sense is developed where the estimation of the state and the input are interconnected the input estimate is obtained from the innovation by least squares estimation and the state estimation problem is transformed into a standard kalman filtering problem necessary and sufficient conditions for the existence of the filter are given and relations to earlier results are discussed

autoregressive conditional duration a new model for irregularly spaced transaction data this paper proposes a new statistical model for the analysis of data which arrive at irregular intervals the model treats the time between events as a stochastic process and proposes a new class of point processes with dependent arrival rates the conditional intensity is developed and compared with other self exciting processes because the model focuses on the expected duration between events it is called the autoregressive conditional duration acd model asymptotic properties of the quasi maximum likelihood estimator are developed as a corollary to arch model results strong evidence is provided for duration clustering for the financial transaction data analyzed both deterministic time of day effects and stochastic effects are important the model is applied to the arrival times of trades and therefore is a model of transaction volume and also to the arrival of other events such as price changes models for the volatility of prices are estimated with price based durations and examined from a market microstructure point of view

a unified filter for simultaneous input and state estimation of linear discrete time stochastic systems in this paper we present a unified optimal and exponentially stable filter for linear discrete time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum variance sense without making any assumptions on the direct feedthrough matrix we also provide the connection between the stability of the estimator and a system property known as strong detectability and discuss the global optimality of the proposed filter finally an illustrative example is given to demonstrate the performance of the unified unbiased minimum variance filter

locally parametric nonparametric density estimation this paper develops a nonparametric density estimator with parametric overtones suppose f x is some family of densities indexed by a vector of parameters we define a local kernel smoothed likelihood function which for each x can be used to estimate the best local parametric approximant to the true density this leads to a new density estimator of the form f x o x thus inserting the best local parameter estimate for each new value of x when the bandwidth used is large this amounts to ordinary full likelihood parametric density estimation while for moderate and small bandwidths the method is essentially nonparametric using only local properties of data and the model alternative ways more general than via the local likelihood are also described the methods can be seen as ways of nonparametrically smoothing the parameter within a parametric class properties of this new semiparametric estimator are investigated our preferred version has approximately the same variance as the ordinary kernel method but potentially a smaller bias the new method is seen to perform better than the traditional kernel method in a broad nonparametric vicinity of the parametric model employed while at the same time being capable of not losing much in precision to full likelihood methods when the model is correct other versions of the method are approximately equivalent to using particular higher order kernels in a semiparametric framework the methodology we develop can be seen as the density estimation parallel to local likelihood and local weighted least squares theory in nonparametric regression

unbiased minimum variance linear state estimation abstract a method is developed for linear estimation in the presence of unknown or highly non gaussian system inputs the state update is determined so that it is unaffected by the unknown inputs the filter may not be globally optimum in the mean square error sense however it performs well when the unknown inputs take extreme or unexpected values in many geophysical and environmental applications it is performance during these periods which counts the most the application of the filter is illustrated in the real time estimation of mean areal precipitation

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

technical communique unbiased minimum variance input and state estimation for linear discrete time systems with direct feedthrough this paper extends previous work on joint input and state estimation to systems with direct feedthrough of the unknown input to the output using linear minimum variance unbiased estimation a recursive filter is derived where the estimation of the state and the input are interconnected the derivation is based on the assumption that no prior knowledge about the dynamical evolution of the unknown input is available the resulting filter has the structure of the kalman filter except that the true value of the input is replaced by an optimal estimate

on the convexity of some divergence measures based on entropy functions three measures of divergence between vectors in a convex set of a n dimensional real vector space are defined in terms of certain types of entropy functions and their convexity property is studied among other results a classification of the entropies of degree alpha is obtained by the convexity of these measures these results have applications in information theory and biological studies

information theoretic optimality of observation driven time series models for continuous responses we investigate information theoretic optimality properties of the score function of the predictive likelihood as a device for updating a real valued time varying parameter in a univariate observation driven model with continuous responses we restrict our attention to models with updates of one lag order the results provide theoretical justification for a class of score driven models which includes the generalized autoregressive conditional heteroskedasticity model as a special case ourmain contribution is to show that only parameter updates based on the score will always reduce the local kullback leibler divergence between the true conditional density and themodel implied conditional density this result holds irrespective of the severity of modelmisspecification we also show that use of the score leads to a considerably smaller global kullback leibler divergence in empirically relevant settings we illustrate the theory with an application to time varying volatility models we show that the reduction in kullback leibler divergence across a range of different settings can be substantial compared to updates based on for example squared lagged observations

uses of entropy and divergence measures for evaluating econometric approximations and inference this paper provides the uses of the kullback and leibler divergence measure in two directions first a new result on the asymptotic expansion of the kullback and leibler divergence is provided which can be used for comparing two distributions an application to compare two alternative approximate distributions from the unknown true exact distribution of a student t statistic in a dynamic regression is given second we explore the application of the kullback and leibler divergence measure to non parametric estimation and specification testing in regression models a non parametric specification test is proposed

technical communique on the optimality of recursive unbiased state estimation with unknown inputs for system models with unknown inputs state estimates may be obtained using linear minimum variance unbiased estimation here a proof is presented showing that the optimal solution over the class of all linear unbiased estimates may be written in the form of a linear recursive filter thereby validating previous work in this area