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## Theory and Econometrics

*Lars Peter Hansen and Thomas J. Sargent*

### in Recursive Models of Dynamic Linear Economies

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691042770
- eISBN:
- 9781400848188
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691042770.003.0001
- Subject:
- Economics and Finance, History of Economic Thought

This chapter sets out the book's focus, namely constructing and applying competitive equilibria for a class of linear-quadratic-Gaussian dynamic economies with complete markets. Here, an economy will ... More

## 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

## 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

## 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

## A Crash Course in Bayesian Inference

*Edward P. Herbst and Frank Schorfheide*

### in Bayesian Estimation of DSGE Models

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691161082
- eISBN:
- 9781400873739
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691161082.003.0003
- Subject:
- Economics and Finance, Econometrics

This chapter provides a self-contained review of Bayesian inference and decision making. It begins with a discussion of Bayesian inference for a simple autoregressive (AR) model, which takes the form ... 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

## Smoothers

*E. Cosme*

### in Advanced Data Assimilation for Geosciences: Lecture Notes of the Les Houches School of Physics: Special Issue, June 2012

- Published in print:
- 2014
- Published Online:
- March 2015
- ISBN:
- 9780198723844
- eISBN:
- 9780191791185
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198723844.003.0004
- Subject:
- Physics, Geophysics, Atmospheric and Environmental Physics

This chapter describes the use of smoothers in data assimilation. The filtering problem in data assimilation consists in estimating the state of a system based on past and present observations. In ... More

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