Time series analysis by state space methods:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Oxford Univ. Press
2008
|
| Ausgabe: | reprinted |
| Schriftenreihe: | Oxford statistical science series
24 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. [241] - 247 |
| Beschreibung: | XVII, 253 S. graph. Darst. |
| ISBN: | 9780198523543 0198523548 |
Internformat
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| 100 | 1 | |a Durbin, James |d 1923-2012 |e Verfasser |0 (DE-588)170383393 |4 aut | |
| 245 | 1 | 0 | |a Time series analysis by state space methods |c J. Durbin and S. J. Koopman |
| 250 | |a reprinted | ||
| 264 | 1 | |a Oxford |b Oxford Univ. Press |c 2008 | |
| 300 | |a XVII, 253 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Oxford statistical science series |v 24 | |
| 500 | |a Literaturverz. S. [241] - 247 | ||
| 650 | 4 | |a Zeitreihenanalyse - Zustandsraum | |
| 650 | 4 | |a Time-series analysis | |
| 650 | 4 | |a State-space methods | |
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| 689 | 0 | 1 | |a Zustandsraum |0 (DE-588)4132647-7 |D s |
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| 700 | 1 | |a Koopman, Siem Jan |e Verfasser |0 (DE-588)171047141 |4 aut | |
| 830 | 0 | |a Oxford statistical science series |v 24 |w (DE-604)BV001908661 |9 24 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017154365 | ||
Datensatz im Suchindex
| _version_ | 1804138670536523776 |
|---|---|
| adam_text | Contents
Introduction
1
1.1 Basic
ideas of state space analysis
1
1.2
Linear Gaussian model
1
1.3
Non-Gaussian and nonlinear models
3
1.4
Prior knowledge
4
1.5
Notation
4
1.6
Other books on state space methods
5
1.7
Website for the book
5
I THE LINEAR GAUSSIAN STATE SPACE MODEL
Local level model
9
2.1
Introduction
9
2.2
Filtering
11
2.2.1
The
Kalman
Filter
11
2.2.2
Illustration
12
2.3
Forecast errors
13
2.3.1
Cholesky decomposition
14
2.3.2
Error recursions
15
2.4
State smoothing
16
2.4.1
Smoothed state
16
2.4.2
Smoothed state variance
17
2.4.3
Illustration
18
2.5
Disturbance smoothing
19
2.5.1
Smoothed observation disturbances
20
2.5.2
Smoothed state disturbances
20
2.5.3
Illustration
21
2.5.4
Cholesky decomposition and smoothing
22
2.6
Simulation
22
2.6.1
Illustration
23
2.7
Missing observations
23
2.7.1
Illustration
25
2.8
Forecasting
25
2.8.1
Illustration
27
CONTENTS
2.9
Initialisation
27
2.10
Parameter estimation
30
2.10.1
Loglikelihood evaluation
30
2.10.2
Concentration of loglikelihood
31
2.10.3
Illustration
32
2.11
Steady state
32
2.12
Diagnostic checking
33
2.12.1
Diagnostic tests for forecast errors
33
2.12.2
Detection of outliers and structural breaks
35
2.12.3
Illustration
35
2.13
Appendix: Lemma in multivariate normal regression
37
Linear
Gaussian
state space models
38
3.1
Introduction
38
3.2
Structural time series models
39
3.2.1
Univariate models
39
3.2.2
Multivariate models
44
3.2.3
STAMP
45
3.3
ARMA
models and
АШМА
models
46
3.4
Exponential smoothing
49
3.5
State space versus Box-Jenkins approaches
51
3.6
Regression with time-varying coefficients
54
3.7
Regression with
ARMA
errors
54
3.8
Benchmarking
54
3.9
Simultaneous modelling of series from different sources
56
ЗЛО
State space models in continuous time
57
3.10.1
Local level model
57
3.10.2
Local linear trend model
59
3.11
Spline smoothing
61
3.11.1
Spline smoothing in discrete time
61
3.11.2
Spline smoothing in continuous time
62
Filtering, smoothing and forecasting
64
4.1
Introduction
64
4.2
Filtering
65
4.2.1
Derivation of
Kalman
filter
65
4.2.2
Kalman
filter recursion
67
4.2.3
Steady state
68
4.2.4
State estimation errors and forecast errors
68
4.3
State smoothing
70
4.3.1
Smoothed state vector
70
4.3.2
Smoothed state variance matrix
72
4.3.3
State smoothing recursion
73
4.4
Disturbance smoothing
73
CONTENTS xüi
4.4.1
Smoothed disturbances
73
4.4.2 Fast
state smoothing
75
4.4.3
Smoothed disturbance variance matrices
75
4.4.4
Disturbance smoothing recursion
76
4.5
Covariance matrices of smoothed estimators
77
4.6
Weight functions
81
4.6.1
Introduction
81
4.6.2
Filtering weights
81
4.6.3
Smoothing weights
82
4.7
Simulation smoothing
83
4.7.1
Simulating observation disturbances
84
4.7.2
Derivation of simulation smoother for observation
disturbances
87
4.7.3
Simulation smoothing recursion
89
4.7.4
Simulating state disturbances
90
4.7.5
Simulating state vectors
91
4.7.6
Simulating multiple samples
92
4.8
Missing observations
92
4.9
Forecasting
93
4.10
Dimensionality of observational vector
94
4.11
General matrix form for filtering and smoothing
95
Initialisation of filter and smoother
99
5.1
Introduction
99
5.2
The exact initial
Kalman
filter
101
5.2.1
The basic recursions
101
5.2.2
Transition to the usual
Kalman
filter
104
5.2.3
A convenient representation
105
5.3
Exact initial state smoothing
106
5.3.1
Smoothed mean of state vector
106
5.3.2
Smoothed variance of state vector
107
5.4
Exact initial disturbance smoothing
109
5.5
Exact initial simulation smoothing
110
5.6
Examples of initial conditions for some models
110
5.6.1
Structural time series models
110
5.6.2
Stationary
ARMA
models
Ш
5.6.3
Nonstationary ARIMA models
112
5.6.4
Regression model with
ARMA
errors
114
5.6.5
Spline smoothing
115
5.7
Augmented
Kalman
filter and smoother
115
5.7.1
Introduction
П5
5.7.2
Augmented
Kalman
filter
115
5.7.3
Filtering based on the augmented
Kalman
filter
116
CONTENTS
5.7.4 Illustration:
the local
linear
trend model
118
5.7.5
Comparisons of computational efficiency
119
5.7.6
Smoothing based on the augmented
Kalman
filter
120
Farther computational aspects
121
6.1
Introduction
121
6.2
Regression estimation
121
6.2.1
Introduction
121
6.2.2
Inclusion of coefficient vector in state vector
122
6.2.3
Regression estimation by augmentation
122
6.2.4
Least squares and recursive residuals
123
6.3
Square root filter and smoother
124
6.3.1
Introduction
124
6.3.2
Square root form of variance updating
125
6.3.3
Givens
rotations
126
6.3.4
Square root smoothing
127
6.3.5
Square root filtering and initialisation
127
6.3.6
¡lustration: local linear trend model
128
6.4
Univariale treatment of
multi
variate
series
128
6.4.1
Introduction
128
6.4.2
Details of univariate treatment
129
6.4.3
Correlation between observation equations
131
6.4.4
Computational efficiency
132
6.4.5
Illustration: vector splines
133
6.5
Filtering and smoothing under linear restrictions
134
6.6
The algorithms of SsfPack
134
6.6.1
Introduction
134
6.6.2
The SsfPack function
135
6.6.3
Illustration: spline smoothing
136
Maximum
likelihood estimation
138
7.1
Introduction
138
7.2
Likelihood evaluation
138
7.2.1
Loglikelihood when initial conditions are known
138
7.2.2
Diffuse loglikelihood
139
7.2.3
Diffuse loglikelihood evaluated via augmented
Kalman
filter
140
7.2.4
Likelihood when elements of initial state vector are
fixed but unknown
141
7.3
Parameter estimation
142
7.3.1
Introduction
142
7.3.2
Numerical maximisation algorithms
142
7.3.3
The score vector
144
7.3.4
The EM algorithm
147
CONTENTS xv
7.3.5 Parameter
estimation
when dealing with diffuse
initial conditions
149
7.3.6
Large sample distribution of maximum likelihood
estimates
150
7.3.7
Effect of errors in parameter estimation
150
7.4
Goodness of fit
152
7.5
Diagnostic checking
152
8
Bayesian analysis
155
8.1
Introduction
155
8.2
Posterior analysis of state vector
155
8.2.1
Posterior analysis conditional on parameter vector
155
8.2.2
Posterior analysis when parameter vector is
unknown
155
8.2.3
Non-informative priors
158
8.3
Markov chain Monte Carlo methods
159
9
Illustrations of the use of the linear Gaussian model
161
9.1
Introduction
161
9.2
Structural time series models
161
9.3
Bivariate structural time series analysis
167
9.4
Box-Jenkins analysis
169
9.5
Spline smoothing
172
9.6
Approximate methods for modelling volatility
175
Π
NON-GAUSSIAN AND NONLINEAR STATE SPACE MODELS
10
Non-Gaussian and nonlinear state space models
179
10.1
Introduction
179
10.2
The general non-Gaussian model
179
10.3
Exponential family models
180
10.3.1
Poisson
density
181
10.3.2
Binary density
181
10.3.3
Binomial density
181
10.3.4
Negative binomial density
182
10.3.5
Multinomial density
182
10.4
Heavy-tailed distributions
183
10.4.1
/-Distribution
183
10.4.2
Mixture of normals
184
10.4.3
General error distribution
184
10.5
Nonlinear models
184
10.6
Financial models
185
10.6.1
Stochastic volatility models
185
xvi CONTENTS
10.6.2 General autoregressive
conditional
heteroscedasticity 187
10.6.3
Durations: exponential distribution
188
10.6.4
Trade frequencies:
Poisson
distribution
188
11
Importance sampling
189
11.1
Introduction
189
11.2
Basic ideas of importance sampling
190
11.3
Linear Gaussian approximating models
191
11.4
Linearisation based on first two derivatives
193
11.4.1
Exponentional family models
195
11.4.2
Stochastic volatility model
195
11.5
Linearisation based on the first derivative
195
11.5.1
ř-distribution
197
11.5.2
Mixture of normals
197
11.5.3
General error distribution
197
11.6
Linearisation for non-Gaussian state components
198
11.6.1
ř-distribution
for state errors
199
11.7
Linearisation for nonlinear models
199
11.7.1
Multiplicative models
201
11.8
Estimating the conditional mode
202
11.9
Computational aspects of importance sampling
204
11.9.1
Introduction
204
11.9.2
Practical implementation of importance sampling
204
11.9.3
Antithetic variables
205
11.9.4
Diffuse initialisation
206
11.9.5
Treatment of
ř-distribution
without importance
sampling
208
11.9.6
Treatment of Gaussian mixture distributions without
importance sampling
210
12
Analysis
f
rom
a classical standpoint
212
12.1
Introduction
212
12.2
Estimating conditional means and variances
212
12.3
Estimating conditional densities and distribution
functions
213
12.4
Forecasting and estimating with missing observations
214
12.5
Parameter estimation
215
12.5.1
Introduction
215
12.5.2
Estimation of likelihood
215
12.5.3
Maximisation of loglikelihood
216
12.5.4
Variance matrix of maximum likelihood estimate
217
12.5.5
Effect of errors in parameter estimation
217
CONTENTS xvü
12.5.6
Mean
square
error
matrix
due to simulation
217
12.5.7
Estimation when the state disturbances are Gaussian
219
12.5.8
Control variables
219
13
Analysis from a Bayesian standpoint
222
13.1
Introduction
222
13.2
Posterior analysis of functions of the state vector
222
13.3
Computational aspects of Bayesian analysis
225
13.4
Posterior analysis of parameter vector
226
13.5
Markov chain Monte Carlo methods
228
14
Non-Gaussian and nonlinear illustrations
230
14.1
Introduction
230
14.2
Poisson
density: van drivers killed in Great Britain
230
14.3
Heavy-tailed density: outlier in gas consumption in UK
233
14.4
Volatility: pound/dollar daily exchange rates
236
14.5
Binary density: Oxford-Cambridge boat race
237
14.6
Non-Gaussian and nonlinear analysis using SsfPack
238
References
241
Author index
249
Subject index
251
|
| any_adam_object | 1 |
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| ctrlnum | (OCoLC)554886150 (DE-599)BVBBV035350208 |
| dewey-full | 519.5/521 519.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/5 21 519.55 |
| dewey-search | 519.5/5 21 519.55 |
| dewey-sort | 3519.5 15 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | reprinted |
| format | Book |
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| id | DE-604.BV035350208 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:31:53Z |
| institution | BVB |
| isbn | 9780198523543 0198523548 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017154365 |
| oclc_num | 554886150 |
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| owner | DE-355 DE-BY-UBR DE-91G DE-BY-TUM |
| owner_facet | DE-355 DE-BY-UBR DE-91G DE-BY-TUM |
| physical | XVII, 253 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series | Oxford statistical science series |
| series2 | Oxford statistical science series |
| spelling | Durbin, James 1923-2012 Verfasser (DE-588)170383393 aut Time series analysis by state space methods J. Durbin and S. J. Koopman reprinted Oxford Oxford Univ. Press 2008 XVII, 253 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford statistical science series 24 Literaturverz. S. [241] - 247 Zeitreihenanalyse - Zustandsraum Time-series analysis State-space methods Zustandsraum (DE-588)4132647-7 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 s Zustandsraum (DE-588)4132647-7 s DE-604 Koopman, Siem Jan Verfasser (DE-588)171047141 aut Oxford statistical science series 24 (DE-604)BV001908661 24 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017154365&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Durbin, James 1923-2012 Koopman, Siem Jan Time series analysis by state space methods Oxford statistical science series Zeitreihenanalyse - Zustandsraum Time-series analysis State-space methods Zustandsraum (DE-588)4132647-7 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| subject_GND | (DE-588)4132647-7 (DE-588)4067486-1 |
| title | Time series analysis by state space methods |
| title_auth | Time series analysis by state space methods |
| title_exact_search | Time series analysis by state space methods |
| title_full | Time series analysis by state space methods J. Durbin and S. J. Koopman |
| title_fullStr | Time series analysis by state space methods J. Durbin and S. J. Koopman |
| title_full_unstemmed | Time series analysis by state space methods J. Durbin and S. J. Koopman |
| title_short | Time series analysis by state space methods |
| title_sort | time series analysis by state space methods |
| topic | Zeitreihenanalyse - Zustandsraum Time-series analysis State-space methods Zustandsraum (DE-588)4132647-7 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| topic_facet | Zeitreihenanalyse - Zustandsraum Time-series analysis State-space methods Zustandsraum Zeitreihenanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017154365&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001908661 |
| work_keys_str_mv | AT durbinjames timeseriesanalysisbystatespacemethods AT koopmansiemjan timeseriesanalysisbystatespacemethods |