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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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Approximate filtering and smoothing

Approximate filtering and smoothing

(p.226) 10 Approximate filtering and smoothing
Time Series Analysis by State Space Methods

J. Durbin

S.J. Koopman

Oxford University Press

This chapter discusses approximate filtering and smoothing methods for the analysis of non-Gaussian and nonlinear models. The chapter is organized as follows. Sections 10.2 and 10.3 consider two approximate filters, the extended Kalman filter and the unscented Kalman filter, respectively. Section 10.4 considers nonlinear smoothing and shows how approximate smoothing recursions can be derived for the two approximate filters. Section 10.5 argues that approximate solutions for filtering and smoothing can also be obtained when the data are transformed in an appropriate way. Sections 10.6 and 10.7 discuss methods for computing the mode estimate of the state and signal vectors. Different treatments for models with heavy-tailed errors are collected and presented in Section 10.8.

Keywords:   non-Gaussian models, nonlinear models, kalman filter, smoothing, mode estimation

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