Time Series Analysis by State Space Methods (2nd edn)
Time Series Analysis by State Space Methods (2nd edn)
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Abstract
This book presents a comprehensive treatment of the state space approach to time series analysis. The distinguishing feature of state space time series models is that observations are regarded as being made up of distinct components such as trend, seasonal, regression elements and disturbance elements, each of which is modelled separately. The techniques that emerge from this approach are very flexible. Part I presents a full treatment of the construction and analysis of linear Gaussian state space models. The methods are based on the Kalman filter and are appropriate for a wide range of problems in practical time series analysis. The analysis can be carried out from both classical and Bayesian perspectives. Part I then presents illustrations to real series and exercises are provided for a selection of chapters. Part II discusses approximate and exact approaches for handling broad classes of non-Gaussian and nonlinear state space models. Approximate methods include the extended Kalman filter and the more recently developed unscented Kalman filter. The book shows that exact treatments become feasible when simulation-based methods such as importance sampling and particle filtering are adopted. Bayesian treatments based on simulation methods are also explored.
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Front Matter
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1
Introduction
J. Durbin andS.J. Koopman
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Part I
The linear state space model-
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Local level model
J. Durbin andS.J. Koopman
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3
Linear state space models
J. Durbin andS.J. Koopman
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4
Filtering, smoothing and forecasting
J. Durbin andS.J. Koopman
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5
Initialisation of filter and smoother
J. Durbin andS.J. Koopman
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6
Further computational aspects
J. Durbin andS.J. Koopman
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7
Maximum likelihood estimation of parameters
J. Durbin andS.J. Koopman
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8
Illustrations of the use of the linear model
J. Durbin andS.J. Koopman
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2
Local level model
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Part II
Non-Gaussian and nonlinear state space models-
9
Special cases of nonlinear and non-Gaussian models
J. Durbin andS.J. Koopman
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10
Approximate filtering and smoothing
J. Durbin andS.J. Koopman
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11
Importance sampling for smoothing
J. Durbin andS.J. Koopman
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12
Particle filtering
J. Durbin andS.J. Koopman
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13
Bayesian estimation of parameters
J. Durbin andS.J. Koopman
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14
Non-Gaussian and nonlinear illustrations
J. Durbin andS.J. Koopman
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9
Special cases of nonlinear and non-Gaussian models
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End Matter
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