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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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Initialisation of filter and smoother

Initialisation of filter and smoother

(p.123) 5 Initialisation of filter and smoother
Time Series Analysis by State Space Methods

J. Durbin

S.J. Koopman

Oxford University Press

Computational algorithms in state space analyses are mainly based on recursions, that is, formulae in which the value at time t + 1 is calculated from earlier values for t, t − 1, …, 1. This chapter deals with the question of how these recursions are started up at the beginning of the series, a process called initialisation. It provides a general treatment in which some elements of the initial state vector have known distributions while others are diffuse, that is, treated as random variables with infinite variance, or are treated as unknown constants to be estimated by maximum likelihood. The discussions cover the exact initial Kalman filter; exact initial state smoothing; exact initial disturbance smoothing; exact initial simulation smoothing; examples of initial conditions for some models; and augmented Kalman filter and smoother.

Keywords:   recursions, initialisation, state vector, maximum likelihood, Kalman filter, state smoothing, disturbance smoothing

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