Time Series Analysis by State Space Methods

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Clarendon Press, Jun 21, 2001 - Business & Economics - 253 pages
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This excellent text provides 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 made up of distinct components such as trend, seasonal, regression elements and disturbence terms, each of which is modelled separately. The techniques that emerge from this approach are very flexible and are capable of handling a much wider range of problems than the main analytical system currently in use for time series analysis, the Box-Jenkins ARIMA system. The book provides an excellent source for the development of practical courses on time series analysis.
 

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Contents

Chapter 1 Introduction
1
13 NonGaussian and nonlinear models
3
14 Prior knowledge
4
16 Other books on state space methods
5
The linear Gaussian state space model
7
Chapter 2 Local level model
9
22 Filtering
11
23 Forecast errors
13
Chapter 6 Further computational aspects
121
63 Square root filter and smoother
124
64 Univariate treatment of multivariate series
128
65 Filtering and smoothing under linear restrictions
134
Chapter 7 Maximum likelihood estimation
138
73 Parameter estimation
142
74 Goodness of fit
152
Chapter 8 Bayesian analysis
155

24 State smoothing
16
25 Disturbance smoothing
19
26 Simulation
22
27 Missing observations
23
28 Forecasting
25
29 Initialisation
27
210 Parameter estimation
30
211 Steady state
32
212 Diagnostic checking
33
Lemma in multivariate normal regression
37
Chapter 3 Linear Gaussian state space models
38
32 Structural time series models
39
33 ARMA models and ARIMA models
46
34 Exponential smoothing
49
35 State space versus BoxJenkins approaches
51
36 Regression with timevarying coefficients
54
39 Simultaneous modelling of series from different sources
56
310 State space models in continuous time
57
311 Spline smoothing
61
Chapter 4 Filtering smoothing and forecasting
64
42 Filtering
65
43 State smoothing
70
44 Disturbance smoothing
73
45 Covariance matrices of smoothed estimators
77
46 Weight functions
81
47 Simulation smoothing
83
48 Missing observations
92
49 Forecasting
93
410 Dimensionality of observational vector
94
411 General matrix form for filtering and smoothing
95
52 The exact initial Kalman filter
101
53 Exact initial state smoothing
106
54 Exact initial disturbance smoothing
109
55 Exact initial simulation smoothing
110
57 Augmented Kalman filter and smoother
115
83 Markov chain Monte Carlo methods
159
Chapter 9 Illustrations of the use of the linear Gaussian model
161
93 Bivariate structural time series analysis
167
94 BoxJenkins analysis
169
95 Spline smoothing
172
96 Approximate methods for modelling volatility
175
NonGaussian and nonlinear state space models
177
Chapter 10 NonGaussian and nonlinear state space models
179
103 Exponential family models
180
104 Heavytailed distributions
183
105 Nonlinear models
184
106 Financial models
185
Chapter 11 Importance sampling
189
112 Basic ideas of importance sampling
190
113 Linear Gaussian approximating models
191
114 Linearisation based on first two derivatives
193
115 Linearisation based on the first derivative
195
116 Linearisation for nonGaussian state components
198
1 17 Linearisation for nonlinear models
199
118 Estimating the conditional mode
202
119 Computational aspects of importance sampling
204
Chapter 12 Analysis from a classical standpoint
212
123 Estimating conditional densities and distribution functions
213
124 Forecasting and estimating with missing observations
214
125 Parameter estimation
215
Chapter 13 Analysis from a Bayesian standpoint
222
133 Computational aspects of Bayesian analysis
225
134 Posterior analysis of parameter vector
226
135 Markov chain Monte Carlo methods
228
Chapter 14 NonGaussian and nonlinear illustrations
230
outlier in gas consumption in UK
233
pounddollar daily exchange rates
236
OxfordCambridge boat race
237
146 NonGaussian and nonlinear analysis using SsfPack
238
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About the author (2001)

James Durbin is at London School of Economics and Political Science. Siem Jan Koopman is at Department of Econometrics, Free University, Amsterdam, The Netherlands.

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