J. Durbin and S.J. Koopman
- 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 ...
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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 Bayesian standpoint. The four lemmas lead to derivations of the Kalman filter and smoothing recursions for the estimation of the state vector and its conditional variance matrix given the data. The chapter also derives recursions for estimating the observation and state disturbances, and derives the simulation smoother, which is an important tool in the simulation methods employed later in the book. It shows that allowance for missing observations and forecasting are easily dealt with in the state space framework.Less
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 Bayesian standpoint. The four lemmas lead to derivations of the Kalman filter and smoothing recursions for the estimation of the state vector and its conditional variance matrix given the data. The chapter also derives recursions for estimating the observation and state disturbances, and derives the simulation smoother, which is an important tool in the simulation methods employed later in the book. It shows that allowance for missing observations and forecasting are easily dealt with in the state space framework.
J. Durbin and S.J. Koopman
- 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
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 describes the notations used and other books on state space methods.Less
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 describes the notations used and other books on state space methods.
J. Durbin and S.J. Koopman
- 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
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 state space model by constructing importance samples of additional parameters. It then shows how to combine these with Kalman filter and smoother outputs to obtain the estimates of state parameters required. A brief description is also given of the alternative simulation technique, Markov chain Monte Carlo methods.Less
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 state space model by constructing importance samples of additional parameters. It then shows how to combine these with Kalman filter and smoother outputs to obtain the estimates of state parameters required. A brief description is also given of the alternative simulation technique, Markov chain Monte Carlo methods.
