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17
On Sequential Monte Carlo Sampling Methods for Bayesian Filtering
 STATISTICS AND COMPUTING
, 2000
"... In this article, we present an overview of methods for sequential simulation from posterior distributions. These methods are of particular interest in Bayesian filtering for discrete time dynamic models that are typically nonlinear and nonGaussian. A general importance sampling framework is develop ..."
Abstract

Cited by 976 (75 self)
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In this article, we present an overview of methods for sequential simulation from posterior distributions. These methods are of particular interest in Bayesian filtering for discrete time dynamic models that are typically nonlinear and nonGaussian. A general importance sampling framework is developed that unifies many of the methods which have been proposed over the last few decades in several different scientific disciplines. Novel extensions to the existing methods are also proposed. We show in particular how to incorporate local linearisation methods similar to those which have previously been employed in the deterministic filtering literature; these lead to very effective importance distributions. Furthermore we describe a method which uses RaoBlackwellisation in order to take advantage of the analytic structure present in some important classes of statespace models. In a final section we develop algorithms for prediction, smoothing and evaluation of the likelihood in dynamic models.
Data revisions are not wellbehaved
 Journal of Money, Credit and Banking
, 2008
"... We document the empirical properties of revisions to major macroeconomic variables in the United States. Our
ndings suggest that they do not satisfy simple desirable statistical properties. In particular, we
nd that these revisions do not have a zero mean, which indicates that the initial announ ..."
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Cited by 40 (4 self)
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We document the empirical properties of revisions to major macroeconomic variables in the United States. Our
ndings suggest that they do not satisfy simple desirable statistical properties. In particular, we
nd that these revisions do not have a zero mean, which indicates that the initial announcements by statistical agencies are biased. We also
nd that the revisions are quite large compared to the original variables and they are predictable using the information set at the time of the initial announcement, which means that the initial announcements of statistical agencies are not rational forecasts. We also provide evidence that professional forecasters ignore this predictability.
A survey of sequential Monte Carlo methods for economics and finance
, 2009
"... This paper serves as an introduction and survey for economists to the field of sequential Monte Carlo methods which are also known as particle filters. Sequential Monte Carlo methods are simulation based algorithms used to compute the highdimensional and/or complex integrals that arise regularly in ..."
Abstract

Cited by 31 (7 self)
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This paper serves as an introduction and survey for economists to the field of sequential Monte Carlo methods which are also known as particle filters. Sequential Monte Carlo methods are simulation based algorithms used to compute the highdimensional and/or complex integrals that arise regularly in applied work. These methods are becoming increasingly popular in economics and finance; from dynamic stochastic general equilibrium models in macroeconomics to option pricing. The objective of this paper is to explain the basics of the methodology, provide references to the literature, and cover some of the theoretical results that justify the methods in practice.
Nonlinear and NonGaussian StateSpace Modeling with Monte Carlo Techniques: A Survey and Comparative Study
 In Rao, C., & Shanbhag, D. (Eds.), Handbook of Statistics
, 2000
"... Since Kitagawa (1987) and Kramer and Sorenson (1988) proposed the filter and smoother using numerical integration, nonlinear and/or nonGaussian state estimation problems have been developed. Numerical integration becomes extremely computerintensive in the higher dimensional cases of the state vect ..."
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Cited by 19 (4 self)
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Since Kitagawa (1987) and Kramer and Sorenson (1988) proposed the filter and smoother using numerical integration, nonlinear and/or nonGaussian state estimation problems have been developed. Numerical integration becomes extremely computerintensive in the higher dimensional cases of the state vector. Therefore, to improve the above problem, the sampling techniques such as Monte Carlo integration with importance sampling, resampling, rejection sampling, Markov chain Monte Carlo and so on are utilized, which can be easily applied to multidimensional cases. Thus, in the last decade, several kinds of nonlinear and nonGaussian filters and smoothers have been proposed using various computational techniques. The objective of this paper is to introduce the nonlinear and nonGaussian filters and smoothers which can be applied to any nonlinear and/or nonGaussian cases. Moreover, by Monte Carlo studies, each procedure is compared by the root mean square error criterion.
Prediction Of Final Data With Use Of Preliminary And/or Revised Data
 Journal of Forecasting
, 1995
"... : In the case of U.S. national accounts, the data are revised for the first few years and every decade, which implies that we do not really have the final data. In this paper, we aim to predict the final data, using the preliminary data and/or the revised data. The following predictors are introduce ..."
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Cited by 13 (4 self)
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: In the case of U.S. national accounts, the data are revised for the first few years and every decade, which implies that we do not really have the final data. In this paper, we aim to predict the final data, using the preliminary data and/or the revised data. The following predictors are introduced and derived from a context of the nonlinear filtering or smoothing problem, which are: (i) prediction of the final data of time t given the preliminary data up to time t
Continuousdiscrete unscented Kalman filtering,” http://www.fernunihagen.de/FBWIWI/forschung/beitraege
"... The unscented Kalman filter (UKF) is formulated for the continuousdiscrete state space model. The exact moment equations are solved approximately by using the unscented transform (UT) and the measurement update is obtained by computing the normal correlation, again using the UT. In contrast to the ..."
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Cited by 11 (3 self)
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The unscented Kalman filter (UKF) is formulated for the continuousdiscrete state space model. The exact moment equations are solved approximately by using the unscented transform (UT) and the measurement update is obtained by computing the normal correlation, again using the UT. In contrast to the usual treatment, the system and measurement noise sequences are included from the start and are not treated later by extension of the state vector. The performance of the UKF is compared to Taylor expansions (extended Kalman filter EKF, second and higher order nonlinear filter SNF, HNF), the Gaussian filter, and simulated Monte Carlo filters using a bimodal GinzburgLandau model and the chaotic Lorenz model.
On Markov Chain Monte Carlo Methods For Nonlinear And NonGaussian StateSpace Models
 Communications in Statistics, Simulation and Computation, Vol.28, No.4, pp.867
, 1999
"... In this paper, a nonlinear and/or nonGaussian smoother utilizing Markov chain Monte Carlo Methods is proposed, where the measurement and transition equations are specified in any general formulation and the error terms in the statespace model are not necessarily normal. The random draws are direct ..."
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Cited by 9 (2 self)
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In this paper, a nonlinear and/or nonGaussian smoother utilizing Markov chain Monte Carlo Methods is proposed, where the measurement and transition equations are specified in any general formulation and the error terms in the statespace model are not necessarily normal. The random draws are directly generated from the smoothing densities. For random number generation, the MetropolisHastings algorithm and the Gibbs sampling technique are utilized. The proposed procedure is very simple and easy for programming, compared with the existing nonlinear and nonGaussian smoothing techniques. Moreover, taking several candidates of the proposal density function, we examine precision of the proposed estimator.
On Nonlinear and Nonnormal Filter Using Rejection Sampling
, 1999
"... In this paper, a nonlinear and/or nonnormal filter is proposed using rejection sampling. Generating random draws of the statevector directly from the filtering density, the filtering estimate is simply obtained as the arithmetic average of the random draws. In the proposed filter, the random draws ..."
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Cited by 6 (5 self)
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In this paper, a nonlinear and/or nonnormal filter is proposed using rejection sampling. Generating random draws of the statevector directly from the filtering density, the filtering estimate is simply obtained as the arithmetic average of the random draws. In the proposed filter, the random draws are recursively generated at each time. The MonteCarlo experiments indicate that the proposed nonlinear and nonnormal filter shows a good performance. Keywords Nonlinear, Nonnormal, Filtering, Rejection Sampling, Proposal Density. I. Introduction Nonlinear filters have been investigated for a long time (e.g., Alspach and Sorenson [1], Sorenson and Alspach [18] and Wishner, Tabaczynski and Athans [23]) and we still have numerous densitybased nonlinear filtering algorithms. Kitagawa [13] and Kramer and Sorenson [16] proposed the numerical integration procedure. Tanizaki [20] and Tanizaki and Mariano [22] utilized the MonteCarlo integration with importance sampling for nonlinear and no...
Nonlinear and Nonnormal Filter Using Importance Sampling: Antithetic Monte Carlo Integration
"... In this paper, the importance sampling filter proposed by Mariano and Tanizaki (1995), Tanizaki (1996), Tanizaki and Mariano (1994) is extended using the antithetic Monte Carlo method to reduce the simulation errors. By Monte Carlo studies, the importance sampling filter with the antithetic Monte Ca ..."
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Cited by 3 (2 self)
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In this paper, the importance sampling filter proposed by Mariano and Tanizaki (1995), Tanizaki (1996), Tanizaki and Mariano (1994) is extended using the antithetic Monte Carlo method to reduce the simulation errors. By Monte Carlo studies, the importance sampling filter with the antithetic Monte Carlo method is compared with the importance sampling filter without the antithetic Monte Carlo method. It is shown that for all the simulation studies the former is clearly superior to the latter especially when number of random draws is small.
Estimation Of Unknown Parameters In Nonlinear And NonGaussian State Space Models
"... For the last decade, various simulationbased nonlinear ..."
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Cited by 2 (1 self)
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For the last decade, various simulationbased nonlinear