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

a note on interval estimation with fuzzy data abstract in this note we formulate the problem of interval estimation when the experimental outcomes cannot be exactly perceived but they may be assimilated with fuzzy information then we suggest a method to derive crude confidence intervals but always possible to apply

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

nonparametric specification tests for stochastic volatility models based on volatility density this paper develops a specification test for stochastic volatility models by comparing the nonparametric kernel deconvolution density estimator of an integrated volatility density with its parametric counterpart l2 distance is used to measure the discrepancy the asymptotic null distributions of the test statistics are established and the asymptotic power functions are computed through monte carlo simulations the size and power properties of the test statistics are studied the tests are applied to an empirical example

mcmc maximum likelihood for latent state models abstract this paper develops a pure simulation based approach for computing maximum likelihood estimates in latent state variable models using markov chain monte carlo methods mcmc our mcmc algorithm simultaneously evaluates and optimizes the likelihood function without resorting to gradient methods the approach relies on data augmentation with insights similar to simulated annealing and evolutionary monte carlo algorithms we prove a limit theorem in the degree of data augmentation and use this to provide standard errors and convergence diagnostics the resulting estimator inherits the sampling asymptotic properties of maximum likelihood we demonstrate the approach on two latent state models central to financial econometrics a stochastic volatility and a multivariate jump diffusion models we find that convergence to the mle is fast requiring only a small degree of augmentation

likelihood analysis of non gaussian measurement time series summary in this paper we provide methods for estimating non gaussian time series models these techniques rely on markov chain monte carlo to carry out simulation smoothing and bayesian posterior analysis of parameters and on importance sampling to estimate the likelihood function for classical inference the time series structure of the models is used to ensure that our simulation algorithms are efficient

some properties of fuzzy groups on definit des sous groupes flous normaux des sous groupes flous normaux de niveau et leurs homomorphismes et on donne certaines de leurs proprietes

the scan sampler for time series models summary an algorithm called the scan sampler is developed and discussed the scan sampler has a variety of uses for time series analysis based on the state space model with nongaussian observations the algorithm is based on the kalman filter smoothing algorithm it can be used for bayesian inference using markov chain monte carlo and to find posterior modes

monte carlo methods for estimating smoothing and filtering one and two factor stochastic volatility models one and two factor stochastic volatility models are assessed over three sets of stock returns data sp the problem is to get the shape of the conditional returns distribution right none of the models come close to matching the tails of this distribution including a second factor provides only a relatively small improvement over the single factor models fitting this aspect of the data is important for option pricing and risk management

particle efficient importance sampling abstract the efficient importance sampling eis method is a general principle for the numerical evaluation of high dimensional integrals that uses the sequential structure of target integrands to build variance minimising importance samplers despite a number of successful applications in high dimensions it is well known that importance sampling strategies are subject to an exponential growth in variance as the dimension of the integration increases we solve this problem by recognising that the eis framework has an offline sequential monte carlo interpretation the particle eis method is based on non standard resampling weights that take into account the construction of the importance sampler as a sequential approximation to the state smoothing density we apply the method for a range of univariate and bivariate stochastic volatility specifications we also develop a new application of the eis approach to state space models with student s t state innovations our results show that the particle eis method strongly outperforms both the standard eis method and particle filters for likelihood evaluation in high dimensions we illustrate the efficiency of the method for bayesian inference using the particle marginal metropolis hastings and importance sampling squared algorithms

filtering and smoothing algorithms for state space models abstract the paper reviews and generalizes recent filtering and smoothing algorithms for observations generated by a state model in particular the paper discusses the modified kalman filter derived by ansley and kohn 1985 and kohn and ansley 1986 to deal with state space models having partially diffuse initial conditions and shows how to compute the limiting normalized likelihood of the observations for such models the paper also discusses and generalizes the new smoothing algorithm presented by kohn and ansley 1987c 1989 and extends it to state space models with partially diffuse initial conditions

generalized autoregressive moving average models a class of generalized autoregressive moving average garma models is developed that extends the univariate gaussian arma time series model to a flexible observation driven model for non gaussian time series data the dependent variable is assumed to have a conditional exponential family distribution given the past history of the process the model estimation is carried out using an iteratively reweighted least squares algorithm properties of the model including stationarity and marginal moments are either derived explicitly or investigated using monte carlo simulation the relationship of the garma model to other models is shown including the autoregressive models of zeger and qaqish the moving average models of li and the reparameterized generalized autoregressive conditional heteroscedastic garch model providing the formula for its fourth marginal moment not previously derived the model is demonstrated by the application of the garma model with a negative binomial conditional distribution to

join reducibility of fuzzy subgroups abstract we show that the lattice of all normal fuzzy subgroups of a group g is a sublattice of the lattice of all fuzzy subgroups of g and discuss join ir reductibility of fuzzy subgroups and representations of fuzzy subgroups as joins of join irreducible fuzzy subgroups

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

time series analysis of non gaussian observations based on state space models from both classical and bayesian perspectives the analysis of non gaussian time series by using state space models is considered from both classical and bayesian perspectives the treatment in both cases is based on simulation using importance sampling and antithetic variables markov chain monte carlo methods are not employed non gaussian disturbances for the state equation as well as for the observation equation are considered methods for estimating conditional and posterior means of functions of the state vector given the observations and the mean square errors of their estimates are developed these methods are extended to cover the estimation of conditional and posterior densities and distribution functions the choice of importance sampling densities and antithetic variables is discussed the techniques work well in practice and are computationally efficient their use is illustrated by applying them to a univariate discrete time series a series with outliers and a volatility series

a powerful portmanteau test of lack of fit for time series a new portmanteau test for time series more powerful than the tests of ljung and box and monti is proposed the test is based on the mth root of the determinant of the mth autocorrelation matrix it is shown that the proposed statistic is a function of all of the squared multiple correlation coefficients of the regressions of the residuals on their lags when the number of lags goes from 1 to m it can also be written as a function of the first m partial autocorrelation coefficients the asymptotic distribution of the test statistic is a linear combination of chi squared distributions and can be approximated by a gamma distribution it is shown depending on the model and sample size that this test can be up to 50 more powerful than the ljung and box and monti tests the test is applied to the detection of several types of nonlinearity by using the autocorrelation matrix of the squared residuals and it is shown that in general the new test is more powerful than the test of mcleod and li an example

diagnosing shocks in time series abstract efficient means of modeling aberrant behavior in times series are developed our methods are based on state space forms and allow test statistics for various interventions to be computed from a single run of the kalman filter smoother the approach encompasses existing detection methodologies departures commonly observed in practice such as outlying values level shifts and switches are readily dealt with new diagnostic statistics are proposed implications for structural models autoregressive integrated moving average models and models with explanatory variables are given

fuzzy subgroups as union of two fuzzy subgroups abstract the problem of writing a fuzzy subgroup of a group g as a union of two fuzzy subgroups has been discussed by dixit et al in this paper an attempt has been made to study this problem further in a broader framework of nontrivial decomposition of a fuzzy subgroup thus something more than the settlement of the question of the possibility of having nonequivalent fuzzy subgroups in this union raised by the author at the end of the section 3 of their paper has been proved

the hessian method highly efficient simulation smoothing in a nutshell abstract i introduce the hessian highly efficient simulation smoothing in a nutshell method for numerically efficient simulation smoothing in state space models with univariate states given a vector of parameters the vector of states 1 n is gaussian and the observed vector y y 1 y n need not be i describe a procedure to construct a close approximation q y to the target density p y it requires code to compute five derivatives of log p y t t with respect to t t 1 n and is not otherwise model specific since q y is proper fully normalised and simulable it can be used as an importance density for importance sampling is or as a proposal density for markov chain monte carlo mcmc hessian is an acronym but it also refers to the sparse hessian matrix of log p y with respect to the hessian method is based on sparse matrix operations rather than the kalman filter i construct q y and a related approximation q y of p y for two stochastic volatility models two stochastic count models and a stochastic duration model i illustrate their use for numerical approximation of likelihood function values and marginal likelihoods using is and for posterior inference using is and mcmc compared with other simulation smoothing methods the hessian method is highly numerically efficient in an is application featuring a student s t stochastic volatility model and n 8851 daily log returns the efficiency of is for numerical approximation of the elements of the posterior mean e y is between 80 and 100

testing the assumptions behind importance sampling importance sampling is used in many areas of modern econometrics to approximate unsolvable integrals its reliable use requires the sampler to possess a variance for this guarantees a square root speed of convergence and asymptotic normality of the estimator of the integral however this assumption is seldom checked in this paper we use extreme value theory to empirically assess the appropriateness of this assumption our main application is the stochastic volatility model where importance sampling is commonly used for maximum likelihood estimation of the parameters of the model

time series with additive noise summary we put forward a state space model where the unobservable state variable can be any gaussian stochastic process we discuss both maximum likelihood estimation and bayesian inference for this generalised model the methodology developed in this paper is particularly important for the class of long memory plus noise models armed with the simulation smoother introduced in this paper we can estimate a class of non gaussian measurement time series models with long memory in the state equation

the structure of dynamic correlations in multivariate stochastic volatility models this paper proposes two types of stochastic correlation structures for multivariate stochastic volatility msv models namely the constant correlation cc msv and dynamic correlation dc msv models from which the stochastic covariance structures can easily be obtained both structures can be used for purposes of determining optimal portfolio and risk management strategies through the use of correlation matrices and for calculating value at risk var forecasts and optimal capital charges under the basel accord through the use of covariance matrices a technique is developed to estimate the dc msv model using the markov chain monte carlo mcmc procedure and simulated data show that the estimation method works well various multivariate conditional volatility and msv models are compared via simulation including an evaluation of alternative var estimators the dc msv model is also estimated using three sets of empirical data namely nikkei 225 index hang seng index and straits times index returns and significant dynamic correlations are found the dynamic conditional correlation dcc model is also estimated and is found to be far less sensitive to the covariation in the shocks to the indexes the correlation process for the dcc model also appears to have a unit root and hence constant conditional correlations in the long run in contrast the estimates arising from the dc msv model indicate that the dynamic correlation process is stationary

the simulation smoother for time series models summary recently suggested procedures for simulating from the posterior density of states given a gaussian state space time series are refined and extended we introduce and study the simulation smoother which draws from the multivariate posterior distribution of the disturbances of the model so avoiding the degeneracies inherent in state samplers the technique is important in gibbs sampling with non gaussian time series models and for performing bayesian analysis of gaussian time series

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

efficient sequential monte carlo with multiple proposals and control variates sequential monte carlo is a useful simulation based method for online filtering of state space models for certain complex state space models a single proposal distribution is usually not satisfactory and using multiple proposal distributions is a general approach to address various aspects of the filtering problem this article proposes an efficient method of using multiple proposals in combination with control variates the likelihood approach of tan 2004 is used in both resampling and estimation the new algorithm is shown to be asymptotically more efficient than the direct use of multiple proposals and control variates the guidance for selecting multiple proposals and control variates is also given numerical examples are used to demonstrate that the new algorithm can significantly improve over the bootstrap filter and auxiliary particle filter

particle filters for continuous likelihood evaluation and maximisation in this paper a method is introduced for approximating the likelihood for the unknown parameters of a state space model the approximation converges to the true likelihood as the simulation size goes to infinity in addition the approximating likelihood is continuous as a function of the unknown parameters under rather general conditions the approach advocated is fast and robust and it avoids many of the pitfalls associated with current techniques based upon importance sampling we assess the performance of the method by considering a linear state space model comparing the results with the kalman filter which delivers the true likelihood we also apply the method to a non gaussian state space model the stochastic volatility model finding that the approach is efficient and effective applications to continuous time finance models and latent panel data models are considered two different multivariate approaches are proposed the neoclassical growth model is considered as an application

constructing stationary time series models using auxiliary variables with applications here we present a novel method for modeling stationary time series our approach is to construct the model with a specified marginal family and build the dependence structure around it we show that the resulting time series is linear with a simple autocorrelation structure we construct models that parallel existing structures namely state space models autoregressive conditional heteroscedasticity arch models and generalized arch models we use bayesian techniques to estimate the resulting models we also demonstrate that the models perform well compared with competing methods for the applications considered count models and volatility models

independent particle filters sequential monte carlo methods especially the particle filter pf and its various modifications have been used effectively in dealing with stochastic dynamic systems the standard pf samples the current state through the underlying state dynamics then uses the current observation to evaluate the sample s importance weight however there is a set of problems in which the current observation provides significant information about the current state but the state dynamics are weak and thus sampling using the current observation often produces more efficient samples than sampling using the state dynamics in this article we propose a new variant of the pf the independent particle filter ipf to deal with these problems the ipf generates exchangeable samples of the current state from a sampling distribution that is conditionally independent of the previous states a special case of which uses only the current observation each sample can then be matched with multiple samples of the previous states in

markov chain monte carlo methods for stochastic volatility models this paper is concerned with simulation based inference in generalized models of stochastic volatility defined by heavy tailed student t distributions with unknown degrees of freedom and exogenous variables in the observation and volatility equations and a jump component in the observation equation by building on the work of kim shephard and chib rev econom stud 65 1998 361 we develop efficient markov chain monte carlo algorithms for estimating these models the paper also discusses how the likelihood function of these models can be computed by appropriate particle filter methods computation of the marginal likelihood by the method of chib j amer statist assoc 90 1995 1313 is also considered the methodology is extensively tested and validated on simulated data and then applied in detail to daily returns data on the s p 500 index where several stochastic volatility models are formally compared under different priors on the parameters

smoothing and interpolation with the state space model abstract a new result dealing with smoothing and interpolation in the state space model is developed and explored the result simplifies the derivation of existing smoothing algorithms and provides alternate forms that have analytic and practical computing advantages the connection to signal extraction and interpolation is explored and diffuse specifications are considered

approximating hidden gaussian markov random fields summary gaussian markov random field gmrf models are frequently used in a wide variety of applications in most cases parts of the gmrf are observed through mutually independent data hence the full conditional of the gmrf a hidden gmrf hgmrf is of interest we are concerned with the case where the likelihood is non gaussian leading to non gaussian hgmrf models several researchers have constructed block sampling markov chain monte carlo schemes based on approximations of the hgmrf by a gmrf using a second order expansion of the log density at or near the mode this is possible as the gmrf approximation can be sampled exactly with a known normalizing constant the markov property of the gmrf approximation yields computational efficiency the main contribution in the paper is to go beyond the gmrf approximation and to construct a class of non gaussian approximations which adapt automatically to the particular hgmrf that is under study the accuracy can be tuned by intuitive parameters to nearly any precision these non gaussian approximations share the same computational complexity as those which are based on gmrfs and can be sampled exactly with computable normalizing constants we apply our approximations in spatial disease mapping and model based geostatistical models with different likelihoods obtain procedures for block updating and construct metropolized independence samplers

a semiparametric stochastic volatility model abstract in this paper the correlation structure in the classical leverage stochastic volatility sv model is generalized based on a linear spline in the new model the correlation between the return and volatility innovations is time varying and depends nonparametrically on the type of news arrived to the market theoretical properties of the proposed model are examined the model estimation and comparison are conducted by bayesian methods the performance of the estimates are examined in simulations the new model is fitted to daily and weekly us data and compared with the classical sv and garch models in terms of their in sample and out of sample performances empirical results suggest evidence in favor of the proposed model in particular the new model finds strong evidence of time varying leverage effect in individual stocks when the classical model fails to identify the leverage effect

posterior mode estimation by extended kalman filtering for multivariate dynamic generalized linear models abstract a family of multivariate dynamic generalized linear models is introduced as a general framework for the analysis of time series with observations from the exponential family besides common conditionally gaussian models this article deals with univariate models for counted and binary data and as the most interesting multivariate case models for nonstationary multicategorical time series for univariate responses a related yet different class of models has been introduced in a bayesian setting by west harrison and migon assuming conjugate prior posterior distributions for the natural parameter of the exponential family they derive an approximate filter for estimation of time varying states or parameters however their method raises some problems in particular in extending it to the multivariate case a different approach to filtering and smoothing is chosen in this article to avoid a full bayesian analysis based on numerical integration which becomes computationally critical for higher

an ell _ 1 laplace robust kalman smoother robustness is a major problem in kalman filtering and smoothing that can be solved using heavy tailed distributions e g l1 laplace this paper describes an algorithm for finding the maximum a posteriori map estimate of the kalman smoother for a nonlinear model with gaussian process noise and l1 laplace observation noise the algorithm uses the convex composite extension of the gauss newton method this yields convex programming subproblems to which an interior point path following method is applied the number of arithmetic operations required by the algorithm grows linearly with the number of time points because the algorithm preserves the underlying block tridiagonal structure of the kalman smoother problem excellent fits are obtained with and without outliers even though the outliers are simulated from distributions that are not l1 laplace it is also tested on actual data with a nonlinear measurement model for an underwater tracking experiment the l1 laplace smoother is able to construct a smoothed fit without data removal from data with very large outliers

maximization by parts in likelihood inference this article presents and examines a new algorithm for solving a score equation for the maximum likelihood estimate in certain problems of practical interest the method circumvents the need to compute second order derivatives of the full likelihood function it exploits the structure of certain models that yield a natural decomposition of a very complicated likelihood function in this decomposition the first part is a log likelihood from a simply analyzed model and the second part is used to update estimates from the first part convergence properties of this iterative fixed point algorithm are examined and asymptotics are derived for estimators obtained using only a finite number of iterations illustrative examples considered in the article include multivariate gaussian copula models nonnormal random effects models generalized linear mixed models and state space models properties of the algorithm and of estimators are evaluated in simulation studies on a bivariate copula model and a nonnormal

maximum likelihood estimation of partially observed diffusion models this paper develops a maximum likelihood ml method to estimate partially observed diffusion models based on data sampled at discrete times the method combines two techniques recently proposed in the literature in two separate steps in the first step the closed form approach of ait sahalia 2008 is used to obtain a highly accurate approximation to the joint transition probability density of the latent and the observed states in the second step the efficient importance sampling technique of richard and zhang 2007 is used to integrate out the latent states thereby yielding the likelihood function using both simulated and real data we show that the proposed ml method works better than alternative methods the new method does not require the underlying diffusion to have an affine structure and does not involve infill simulations therefore the method has a wide range of applicability and its computational cost is moderate

particle based adaptive lag online marginal smoothing in general state space models we present a novel algorithm an adaptive lag smoother approximating efficiently in an online fashion sequences of expectations under the marginal smoothing distributions in general state space models the algorithm evolves recursively a bank of estimators one for each marginal in resemblance with the so called particle based rapid incremental smoother paris each estimator is propagated until a stopping criterion measuring the fluctuations of the estimates is met the presented algorithm is furnished with theoretical results describing its asymptotic limit and memory usage

the multi state latent factor intensity model for credit rating transitions a new empirical reduced form model for credit rating transitions is introduced it is a parametric intensity based duration model with multiple states and driven by exogenous covariates and latent dynamic factors the model has a generalized semi markov structure designed to accommodate many of the stylized facts of credit rating migrations parameter estimation is based on monte carlo maximum likelihood methods for which the details are discussed in this paper a simulation experiment is carried out to show the effectiveness of the estimation procedure an empirical application is presented for transitions in a 7 grade rating system the model includes a common dynamic component that can be interpreted as the credit cycle asymmetric effects of this cycle across rating grades and additional semi markov dynamics are found to be statistically significant finally we investigate whether the common factor model suffices to capture systematic risk in rating transition data by introducing multiple factors in the model

the fuzzy decision problem an approach to the point estimation problem with fuzzy information abstract this paper is devoted to the extension of the bayesian method for the point estimation when the available information is vague in the nonfuzzy case the parametric estimation can be approached as a particularization in the statistical decision problem this motivates us to accomplish the mentioned extension by looking at the parametric estimation in the fuzzy case as a special situation in the fuzzy decision problem defined by tanaka okuda and asia in this way concepts in the fuzzy decision problem are first expressed in the estimation terminology then on the basis of these concepts we shall introduce some notions and state some interesting results finally several illustrative examples will be exposed

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

representation of lattices by fuzzy sets abstract we prove that every lattice l of finite length can be represented by a fuzzy set on the collection x of meet irreducible elements of l a decomposition of this fuzzy set gives a family of isotone functions from x to 2 0 1 the lattice of which is isomorphic to l more generally conditions under which any collection of isotone functions from a finite set into 2 corresponds to a decomposition of a fuzzy set are given as a consequence the representation theorem for a finite distributive lattice by the lattice of all isotone functions is obtained the collection of all lattices characterized by the same fuzzy set turns out to be a lattice with the above mentioned distributive lattice as the greatest element

on the asymptotic efficiency of approximate bayesian computation estimators many statistical applications involve models for which it is difficult to evaluate the likelihood but from which it is relatively easy to sample approximate bayesian computation is a likelihood free method for implementing bayesian inference in such cases we present results on the asymptotic variance of estimators obtained using approximate bayesian computation in a large data limit our key assumption is that the data is summarized by a fixed dimensional summary statistic that obeys a central limit theorem we prove asymptotic normality of the mean of the approximate bayesian computation posterior this result also shows that in terms of asymptotic variance we should use a summary statistic that is the same dimension as the parameter vector p and that any summary statistic of higher dimension can be reduced through a linear transformation to dimension p in a way that can only reduce the asymptotic variance of the posterior mean we look at how the monte carlo error of an importance sampling algorithm that samples from the approximate bayesian computation posterior affects the accuracy of estimators we give conditions on the importance sampling proposal distribution such that the variance of the estimator will be the same order as that of the maximum likelihood estimator based on the summary statistics used this suggests an iterative importance sampling algorithm which we evaluate empirically on a stochastic volatility model

level subgroups and union of fuzzy subgroups abstract in this paper we investigate the conditions under which a given fuzzy subgroup of a given group can or can not be realized as a union of two proper fuzzy subgroups moreover we formulate the notion of fuzzy subgroup generated by a given fuzzy subset by level subgroups we also give characterizations of fuzzy conjugate subgroups and fuzzy characteristic subgroups by their level subgroups also we discuss the relationship between level subgroups of a given fuzzy subgroup and the level subgroups of its homomorphic image

exact initial kalman filtering and smoothing for nonstationary time series models abstract this article presents a new exact solution for the initialization of the kalman filter for state space models with diffuse initial conditions for example the regression model with stochastic trend seasonal and other nonstationary autoregressive integrated moving average components requires a partially diffuse initial state vector the proposed analytical solution is easy to implement and computationally efficient the exact solution for smoothing is also given missing observations are handled in a straightforward manner all proofs rely on elementary results

dynamic generalized linear models and bayesian forecasting abstract dynamic bayesian models are developed for application in nonlinear non normal time series and regression problems providing dynamic extensions of standard generalized linear models a key feature of the analysis is the use of conjugate prior and posterior distributions for the exponential family parameters this leads to the calculation of closed standard form predictive distributions for forecasting and model criticism the structure of the models depends on the time evolution of underlying state variables and the feedback of observational information to these variables is achieved using linear bayesian prediction methods data analytic aspects of the models concerning scale parameters and outliers are discussed and some applications are provided dynamic bayesian models are developed for application in nonlinear non normal time series and regression problems providing dynamic extensions of standard generalized linear models a key feature of the analysis is the use of conjugate prior and

polar generation of random variates with the t distribution the polar method of box and muller uses two independent uniform variates in order to generate two independent normal variates it can be adapted so that two variates from student s t distribution with parameter v are generated though the two variates are now not independent an algorithm based on the polar method is exact inexpensive and valid for all v 0 box and muller s 1 polar method for generating random normal variates relies on two convenient properties of the normal distribution which we may formulate as follows i let x n o 1 then x can be regarded as the real part of a complex random variable z which has a radial distribution the contours of the density function of z form circles centered at the origin ii write z x iy reie9 then the distribution function fr 1gr of r is a simple algebraic expression so simple that it is invertible that is given g gr r we can write down a closed expression for r in term of g the aim of this article is to show that properties i and ii are shared by the student t distribution with parameter v the tv distribution defined by the density 1 ft x b v 2 1 2 i v 1 2 1 x2 v v l 2 thus we are asserting that the tv distribution like the normal has a tractable radial parent if t has the density 1 we shall write t tv many methods have been proposed for the generation of tv variates the most important ones are described in devroye 2 pp 445 450 whose masterly survey we shall not attempt to emulate the faster algorithms may require either a comparatively great programming effort or the expensive recalculation of certain quantities required by the algorithm whenever v is changed as devroye notes problems arise when v is small and the departure from normality is greatest particularly in the region 0 0 we now show how the polar method may be applied to the tv distribution to yield such an algorithm received by the editor december 23 1992 and in revised form may 12 1993 1991 mathematics subject classification primary 65c10 secondary 62e15

stochastic volatility in asset prices estimation with simulated maximum likelihood abstract the stochastic volatility model is used to estimate daily asset price dynamics the model is estimated by integrating latent volatility out of the joint density of prices and volatility to obtain the marginal density of prices due to high number of dimensions of the integral no conventional integration technique is applicable a monte carlo method called simulated maximum likelihood is used to obtain the marginal density where the latent variable is simulated conditional on available information the model is estimated by 2022 observations from the s p 500 index for comparison arch type models are estimated with the same data

a negative binomial model for time series of counts we study generalized linear models for time series of counts where serial dependence is introduced through a dependent latent process in the link function conditional on the covariates and the latent process the observation is modelled by a negative binomial distribution to estimate the regression coefficients we maximize the pseudolikelihood that is based on a generalized linear model with the latent process suppressed we show the consistency and asymptotic normality of the generalized linear model estimator when the latent process is a stationary strongly mixing process we extend the asymptotic results to generalized linear models for time series where the observation variable conditional on covariates and a latent process is assumed to have a distribution from a one parameter exponential family thus we unify in a common framework the results for poisson log linear regression models of davis et al 2000 negative binomial logit regression models and other similarly specified generalized linear models language en

the stochastic conditional duration model a latent variable model for the analysis of financial durations we introduce a class of models for the analysis of durations which we call stochastic conditional duration scd models these models are based on the assumption that the durations are generated by a dynamic stochastic latent variable the model yields a wide range of shapes of hazard functions the estimation of the parameters is performed by quasi maximum likelihood and using the kalman filter the model is applied to trade price and volume durations of stocks traded at nyse we also investigate the relation between price durations spread trade intensity and volume c 2003 elsevier b v all rights reserved

disturbance smoother for state space models summary this paper develops a method to evaluate the smoothed estimator of the disturbance vector in a state space model together with its mean squared error matrix this disturbance smoother also leads to an efficient smoother for the state vector applications include a method to calculate auxiliary residuals for unobserved components time series models and an em algorithm for estimating covariance parameters in a state space model

state space modeling of animal movement and mortality with application to salmon a stochastic model for the movement and eventual mortality of an individual animal is formulated as a combination of three components initial spatial location survival status at any point in time and spatial translation between points in time alternative theories about survival and migration can be expressed in terms of different models for any of the three components the model can be extended to groups of animals spatially and or temporally aggregated by appropriate integration when information about animal counts is partial or inexact as from mark recapture or harvest data state space models are a natural framework for estimating both unknown parameters and animal abundance as an example a multivariate linear normal state space model that explicitly incorporates each of the three individual animal components is formulated for the migration and harvest of pacific coho salmon oncorhynchus kisutch using recoveries of tagged coho salmon caught in ocean fisheries and associated measures of fishing effort the kalman filter and maximum likelihood are used to estimate parameters of the processes and the kalman smooth is used to estimate abundances given estimated parameters and current harvest and effort data real time management of exploited populations could be improved by using the kalman prediction algorithm

efficient estimation and prediction in time series regression models summary for a time series regression model with correlated residuals we show how to compute efficiently the likelihood predict future values and interpolate missing values as an illustration we consider a regression model with autoregressive moving average residuals

approximate bayesian inference for latent gaussian models by using integrated nested laplace approximations summary structured additive regression models are perhaps the most commonly used class of models in statistical applications it includes among others generalized linear models generalized additive models smoothing spline models state space models semiparametric regression spatial and spatiotemporal models log gaussian cox processes and geostatistical and geoadditive models we consider approximate bayesian inference in a popular subset of structured additive regression models latent gaussian models where the latent field is gaussian controlled by a few hyperparameters and with non gaussian response variables the posterior marginals are not available in closed form owing to the non gaussian response variables for such models markov chain monte carlo methods can be implemented but they are not without problems in terms of both convergence and computational time in some practical applications the extent of these problems is such that markov chain monte carlo sampling is simply not an appropriate tool for routine analysis we show that by using an integrated nested laplace approximation and its simplified version we can directly compute very accurate approximations to the posterior marginals the main benefit of these approximations is computational where markov chain monte carlo algorithms need hours or days to run our approximations provide more precise estimates in seconds or minutes another advantage with our approach is its generality which makes it possible to perform bayesian analysis in an automatic streamlined way and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged

monte carlo state space likelihoods by weighted posterior kernel density estimation maximum likelihood estimation and likelihood ratio tests for nonlinear non gaussian state space models require numerical integration for likelihood calculations several methods including monte carlo mc expectation maximization mc likelihood ratios direct mc integration and particle filter likelihoods are inefficient for the motivating problem of stage structured population dynamics models in experimental settings an mc kernel likelihood mckl method is presented that estimates classical likelihoods up to a constant by weighted kernel density estimates of bayesian posteriors mckl is derived by using bayesian posteriors as importance sampling densities for unnormalized kernel smoothing integrals mc error and mode bias due to kernel smoothing are discussed and two methods for reducing mode bias are proposed zooming in on the maximum likelihood parameters using a focused prior based on an initial estimate and using a posterior cumulant based approximation of mode bias a simulated example show

assessing the predictive influence of cases in a state space process an important inferential objective in state space modelling is to recover unobserved states using fixed interval smoothing thus the identification of cases which have a substantial influence on the smoothers is a relevant practical problem to facilitate this identification we propose a case deletion diagnostic which can be easily computed using the outputs of the standard filtering and smoothing algorithms our diagnostic is defined as the kullback leibler directed divergence between two versions of the conditional density which determines the smoothers one based on all the data the other based on all the data except for the case or cases in question we investigate the detection performance of the diagnostic in a practical application

monte carlo estimation for nonlinear non gaussian state space models we develop a proposal or importance density for state space models with a nonlinear non gaussian observation vector y p y and an unobserved linear gaussian signal vector p the proposal density is obtained from the laplace approximation of the smoothing density p y we present efficient algorithms to calculate the mode of p y and to sample from the proposal density the samples can be used for importance sampling and markov chain monte carlo methods the new results allow the application of these methods to state space models where the observation density p y is not log concave additional results are presented that lead to computationally efficient implementations we illustrate the methods for the stochastic volatility model with leverage

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

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

generalized dynamic panel data models with random effects for cross section and time abstract an exact maximum likelihood method is developed for the estimation of parameters in a nonlinear non gaussian dynamic panel data model with unobserved random individual specific and time varying effects we propose an estimation procedure based on the importance sampling technique in particular a sequence of conditional importance densities is derived which integrates out all random effects from the joint distribution of endogenous variables we disentangle the integration over both the cross section and the time series dimensions the estimation method facilitates the modeling of large panels in both dimensions we evaluate the method in an extended monte carlo study for dynamic panel data models with observations from different non gaussian distributions we finally present three empirical illustrations for i union choice of young males using a binary panel ii crime rates of families using a binomial panel and iii economic growth modeling using a student s t panel

homomorphism of fuzzy groups correspondence theorem and fuzzy quotient groups abstract we define a notion of containment of an ordinary kernel of a group homomorphism in a fuzzy subgroup using this idea we provide the long awaited solution of the problem of showing a one to one correspondence between the family of fuzzy subgroups of a group containing the kernel of a given homomorphism and the family of fuzzy subgroups of the homomorphic image of the given group it is shown that an ordinary kernel gives rise to the notion of fuzzy quotient group in a natural way consequently the fundamental theorem of homomorphisms is established for fuzzy subgroups moreover we provide new proofs for the facts that the homomorphic image of a fuzzy subgroup is always a fuzzy subgroup and fuzzy normality is invariant under surjective homomorphism