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Time Series Analysis by State Space MethodsSecond Edition$
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James Durbin and Siem Jan Koopman

Print publication date: 2012

Print ISBN-13: 9780199641178

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199641178.001.0001

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Filtering, smoothing and forecasting

Filtering, smoothing and forecasting

(p.76) 4 Filtering, smoothing and forecasting
Time Series Analysis by State Space Methods

J. Durbin

S.J. Koopman

Oxford University Press

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.

Keywords:   linear Gaussian state space model, multivariate regression, Kalman filter, recursions, disturbance smoothing, state smoothing

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