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Importance sampling for smoothing

J. Durbin and S.J. Koopman

in Time Series Analysis by State Space Methods: Second Edition

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199641178
eISBN:
9780191774881
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641178.003.0011
Subject:
Mathematics, Probability / Statistics

This chapter develops the methodology of importance sampling based on simulation for the analysis of observations from the non-Gaussian and nonlinear models that were specified in Chapter 9. It shows ... More


Filtering, smoothing and forecasting

J. Durbin and S.J. Koopman

in Time Series Analysis by State Space Methods: Second Edition

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199641178
eISBN:
9780191774881
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641178.003.0004
Subject:
Mathematics, Probability / Statistics

This chapter begins with a set of four lemmas from elementary multivariate regression which provides the essentials of the theory for the general linear state space model from both a classical and a ... More


Introduction

J. Durbin and S.J. Koopman

in Time Series Analysis by State Space Methods: Second Edition

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199641178
eISBN:
9780191774881
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641178.003.0001
Subject:
Mathematics, Probability / Statistics

This introductory chapter provides an overview of the main themes covered in the present book, namely linear Gaussian state space models and non-Gaussian and nonlinear state space models. It also ... More


Martingale unobserved component models

Neil Shephard

in Unobserved Components and Time Series Econometrics

Published in print:
2015
Published Online:
January 2016
ISBN:
9780199683666
eISBN:
9780191763298
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199683666.003.0010
Subject:
Economics and Finance, Econometrics

This chapter generalizes the familiar linear Gaussian unobserved component models or structural time series models to martingale unobserved component models. This generates forecasts whose rate of ... More


Online Bayesian learning in dynamic models: an illustrative introduction to particle methods

Hedibert F Lopes and Carlos M Carvalho

in Bayesian Theory and Applications

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199695607
eISBN:
9780191744167
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199695607.003.0011
Subject:
Mathematics, Probability / Statistics

This chapter provides a step-by-step review of Monte Carlo (MC) methods for filtering in general nonlinear and non-Gaussian dynamic models, also known as state-space models or hidden Markov models. ... More


Bayesian estimation of parameters

J. Durbin and S.J. Koopman

in Time Series Analysis by State Space Methods: Second Edition

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199641178
eISBN:
9780191774881
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641178.003.0013
Subject:
Mathematics, Probability / Statistics

This chapter discusses the use of importance sampling for the estimation of parameters in Bayesian analysis for models of Part I and Part II. It first develops the analysis of the linear Gaussian ... More


Maximum likelihood estimation of parameters

J. Durbin and S.J. Koopman

in Time Series Analysis by State Space Methods: Second Edition

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199641178
eISBN:
9780191774881
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641178.003.0007
Subject:
Mathematics, Probability / Statistics

This chapter discusses maximum likelihood estimation of parameters both for the case where the distribution of the initial state vector is known and for the case where at least some elements of the ... More


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