Time series analysis by state space methods:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2012
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Oxford statistical science series
38 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. [326] - 339 |
| Beschreibung: | XXI, 346 S. graph. Darst. 24 cm |
| ISBN: | 019964117X 9780199641178 |
Internformat
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| 245 | 1 | 0 | |a Time series analysis by state space methods |c J. Durbin ; S. J. Koopman |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2012 | |
| 300 | |a XXI, 346 S. |b graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 500 | |a Literaturverz. S. [326] - 339 | ||
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| 653 | |a Time-series analysis | ||
| 653 | |a State-space methods | ||
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Datensatz im Suchindex
| _version_ | 1804149447149486080 |
|---|---|
| adam_text | Titel: Time series analysis by state space methods
Autor: Durbin, James
Jahr: 2012
Contents
1. Introduction 1
1.1 Basic ideas of state space analysis 1
1.2 Linear modeis 1
1.3 Non-Gaussian and nonlinear modeis 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 6
PART I THE LINEAR STATE SPACE MODEL
Local level model 9
2.1 Introduction 9
2.2 Filtering 11
2.2.1 The Kaiman filter 11
2.2.2 Regression lemma 13
2.2.3 Bayesian treatment 14
2.2.4 Minimum variance linear unbiased treatment 15
2.2.5 Illustration 16
2.3 Forecast errors 17
2.3.1 Cholesky decomposition 17
2.3.2 Error recursions 18
2.4 State smoothing 19
2.4.1 Smoothed state 19
2.4.2 Smoothed state variance 21
2.4.3 Illustration 23
2.5 Disturbance smoothing 23
2.5.1 Smoothed Observation disturbances 23
2.5.2 Smoothed state disturbances 24
2.5.3 Illustration 25
2.5.4 Cholesky decomposition and smoothing 25
2.6 Simulation 26
2.6.1 Illustration 27
2.7 Missing observations 28
2.7.1 Illustration 30
xiv Contents
2.8 Forecasting 30
2.8.1 Illustration 31
2.9 Initialisation 32
2.10 Parameter estimation 34
2.10.1 Loglikelihood evaluation 34
2.10.2 Concentration of loglikelihood 36
2.10.3 Illustration 37
2.11 Steady state 37
2.12 Diagnostic checking 38
2.12.1 Diagnostic tests for forecast errors 38
2.12.2 Detection of outliers and structural breaks 39
2.12.3 Illustration 40
2.13 Exercises 41
3. Linear state space modeis 43
3.1 Introduction 43
3.2 Univariate structural time series modeis 44
3.2.1 Trend component 44
3.2.2 Seasonal component 45
3.2.3 Basic structural time series model 46
3.2.4 Cycle component 48
3.2.5 Explanatory variables and intervention effects 49
3.2.6 STAMP 51
3.3 Multivariate structural time series modeis 51
3.3.1 Homogeneous modeis 51
3.3.2 Common levels 52
3.3.3 Latent risk model 52
3.4 ARMA modeis and ARIMA modeis 53
3.5 Exponential smoothing 57
3.6 Regression modeis 60
3.6.1 Regression with time-varying coefficients 60
3.6.2 Regression with ARMA errors 60
3.7 Dynamic factor modeis 61
3.8 State space modeis in continuous time 62
3.8.1 Local level model 63
3.8.2 Local linear trend model 64
3.9 Spline smoothing 66
3.9.1 Spline smoothing in discrete time 66
3.9.2 Spline smoothing in continuous time 68
3.10 Further comments on state space analysis 69
3.10.1 State space versus Box-Jenkins approaches 69
3.10.2 Benchmarking 71
3.10.3 Simultaneous modelling of series from different sources 73
3.11 Exercises 74
Contents xv
Filtering, smoothing and forecasting 76
4.1 Introduction 76
4.2 Basic results in multivariate regression theory 77
4.3 Filtering 82
4.3.1 Derivation of the Kaiman filter 82
4.3.2 Kaiman filter recursion 85
4.3.3 Kaiman filter for modeis with mean adjustments 85
4.3.4 Steady state 86
4.3.5 State estimation errors and forecast errors 86
4.4 State smoothing 87
4.4.1 Introduction 87
4.4.2 Smoothed state vector 88
4.4.3 Smoothed state variance matrix 90
4.4.4 State smoothing recursion 91
4.4.5 Updating smoothed estimates 91
4.4.6 Fixed-point and fixed-lag smoothers 92
4.5 Disturbance smoothing 93
4.5.1 Smoothed disturbances 93
4.5.2 Smoothed disturbance variance matrices 95
4.5.3 Disturbance smoothing recursion 96
4.6 Other state smoothing algorithms 96
4.6.1 Classical state smoothing 96
4.6.2 Fast state smoothing 97
4.6.3 The Whittle relation between smoothed estimates 98
4.6.4 Two filter formula for smoothing 98
4.7 Covariance matrices of smoothed estimators 100
4.8 Weight funetions 104
4.8.1 Introduction 104
4.8.2 Filtering weights 105
4.8.3 Smoothing weights 106
4.9 Simulation smoothing 107
4.9.1 Simulation smoothing by mean corrections 107
4.9.2 Simulation smoothing for the state vector 108
4.9.3 de Jong-Shephard method for Simulation of disturbances 109
4.10 Missing observations 110
4.11 Forecasting 112
4.12 Dimensionality of observational vector 113
4.13 Matrix formulations of basic results 114
4.13.1 State space model in matrix form 114
4.13.2 Matrix expression for densities 115
4.13.3 Filtering in matrix form: Cholesky decomposition 116
4.13.4 Smoothing in matrix form 118
4.13.5 Matrix expressions for signal 119
4.13.6 Simulation smoothing 120
4.14 Exercises 121
xvi Contents
5. Initialisation of filter and smoother 123
5.1 Introduction 123
5.2 The exact initial Kaiman filter 126
5.2.1 The basic recursions 126
5.2.2 Transition to the usual Kaiman filter 129
5.2.3 A convenient representation 130
5.3 Exact initial state smoothing 130
5.3.1 Smoothed mean of state vector 130
5.3.2 Smoothed variance of state vector 132
5.4 Exact initial disturbance smoothing 134
5.5 Exact initial Simulation smoothing 135
5.5.1 Modifications for diffuse initial conditions 135
5.5.2 Exact initial Simulation smoothing 136
5.6 Examples of initial conditions for some modeis 136
5.6.1 Structural time series modeis 136
5.6.2 Stationary ARMA modeis 137
5.6.3 Nonstationary ARIMA modeis 138
5.6.4 Regression model with ARMA errors 140
5.6.5 Spline smoothing 141
5.7 Augmented Kaiman filter and smoother 141
5.7.1 Introduction 141
5.7.2 Augmented Kaiman filter 141
5.7.3 Filtering based on the augmented Kaiman filter 142
5.7.4 Illustration: the local linear trend model 144
5.7.5 Comparisons of computational efficiency 145
5.7.6 Smoothing based on the augmented Kaiman filter 146
6. Further computational aspects 147
6.1 Introduction 147
6.2 Regression estimation 147
6.2.1 Introduction 147
6.2.2 Inclusion of coefficient vector in state vector 148
6.2.3 Regression estimation by augmentation 148
6.2.4 Least Squares and recursive residuals 150
6.3 Square root filter and smoother 150
6.3.1 Introduction 150
6.3.2 Square root form of variance updating 151
6.3.3 Givens rotations 152
6.3.4 Square root smoothing 153
6.3.5 Square root filtering and initialisation 154
6.3.6 Illustration: local linear trend model 154
6.4 Univariate treatment of multivariate series 155
6.4.1 Introduction 155
6.4.2 Details of univariate treatment 155
Contents xvii
6.4.3 Correlation between Observation equations 158
6.4.4 Computational efficiency 158
6.4.5 Illustration: vector splines 159
6.5 Collapsing large Observation vectors 161
6.5.1 Introduction 161
6.5.2 Collapse by transformation 162
6.5.3 A generalisation of collapsing by transformation 163
6.5.4 Computational efficiency 164
6.6 Filtering and smoothing under linear restrictions 164
6.7 Computer packages for state space methods 165
6.7.1 Introduction 165
6.7.2 SsfPack 165
6.7.3 The basic SsfPack funetions 166
6.7.4 The extended SsfPack funetions 166
6.7.5 Illustration: spline smoothing 167
7. Maximum likelihood estimation of parameters 170
7.1 Introduction 170
7.2 Likelihood evaluation 170
7.2.1 Loglikelihood when initial conditions are known 170
7.2.2 Diffuse loglikelihood 171
7.2.3 Diffuse loglikelihood via augmented Kaiman filter 173
7.2.4 Likelihood when elements of initial state vector are fixed
but unknown 174
7.2.5 Likelihood when a univariate treatment of multivariate
series is employed 174
7.2.6 Likelihood when the model contains regression effects 175
7.2.7 Likelihood when large Observation vector is collapsed 176
7.3 Parameter estimation 177
7.3.1 Introduction 177
7.3.2 Numerical maximisation algorithms 177
7.3.3 The score vector 179
7.3.4 The EM algorithm 182
7.3.5 Estimation when dealing with diffuse initial conditions 184
7.3.6 Large sample distribution of estimates 185
7.3.7 Effect of errors in parameter estimation 186
7.4 Goodness of fit 187
7.5 Diagnostic checking 188
8. Illustrations of the use of the linear model 190
8.1 Introduction 190
8.2 Structural time series modeis 190
8.3 Bivariate structural time series analysis 195
8.4 Box-Jenkins analysis 198
8.5 Spline smoothing 200
8.6 Dynamic factor analysis 202
xviii Contents
PART II NON-GAUSSIAN AND NONLINEAR STATE
SPACE MODELS
9. Special cases of nonlinear and non-Gaussian modeis 209
9.1 Introduction 209
9.2 Models with a linear Gaussian signal 209
9.3 Exponential family modeis 211
9.3.1 Poisson density 211
9.3.2 Binary density 212
9.3.3 Binomial density 212
9.3.4 Negative binomial density 213
9.3.5 Multinomial density 213
9.3.6 Multivariate extensions 214
9.4 Heavy-tailed distributions 215
9.4.1 t-distribution 215
9.4.2 Mixture of normals 215
9.4.3 General error distribution 215
9.5 Stochastic volatility modeis 216
9.5.1 Multiple volatility factors 217
9.5.2 Regression and fixed effects 217
9.5.3 Heavy-tailed disturbances 218
9.5.4 Additive noise 218
9.5.5 Leverage effects 219
9.5.6 Stochastic volatility in mean 220
9.5.7 Multivariate SV modeis 220
9.5.8 Generalised autoregressive conditional heteroscedasticity 221
9.6 Other financial modeis 222
9.6.1 Durations: exponential distribution 222
9.6.2 Trade frequencies: Poisson distribution 223
9.6.3 Credit risk modeis 223
9.7 Nonlinear modeis 224
10. Approximate filtering and smoothing 226
10.1 Introduction 226
10.2 The extended Kaiman filter 226
10.2.1 A multiplicative trend-cycle decomposition 228
10.2.2 Power growth model 229
10.3 The unscented Kaiman filter 230
10.3.1 The unscented transformation 230
10.3.2 Derivation of the unscented Kaiman filter 232
10.3.3 Further developments of the unscented transform 233
10.3.4 Comparisons between EKF and UKF 236
10.4 Nonlinear smoothing 237
10.4.1 Extended smoothing 237
10.4.2 Unscented smoothing 237
Contents xix
10.5 Approximation via data transformation 238
10.5.1 Partly multiplicative decompositions 239
10.5.2 Stochastic volatility model 239
10.6 Approximation via mode estimation 240
10.6.1 Mode estimation for the linear Gaussian model 240
10.6.2 Mode estimation for model with linear Gaussian signal 241
10.6.3 Mode estimation by linearisation 243
10.6.4 Mode estimation for exponential family modeis 245
10.6.5 Mode estimation for stochastic volatility model 245
10.7 Further advances in mode estimation 247
10.7.1 Linearisation based on the state vector 247
10.7.2 Linearisation for linear state equations 248
10.7.3 Linearisation for nonlinear modeis 250
10.7.4 Linearisation for multiplicative modeis 251
10.7.5 An optimal property for the mode 252
10.8 Treatments for heavy-tailed distributions 254
10.8.1 Mode estimation for modeis with heavy-tailed densities 254
10.8.2 Mode estimation for State errors with ^-distribution 255
10.8.3 A Simulation treatment for ^-distribution model 255
10.8.4 A Simulation treatment for mixture of normals model 258
11. Importance sampling for smoothing 260
11.1 Introduction 260
11.2 Basic ideas of importance sampling 261
11.3 Choice of an importance density 263
11.4 Implementation details of importance sampling 264
11.4.1 Introduction 264
11.4.2 Practical implementation of importance sampling 264
11.4.3 Antithetic variables 265
11.4.4 Diffuse Initialisation 266
11.5 Estimating funetions of the state vector 268
11.5.1 Estimating mean funetions 268
11.5.2 Estimating variance funetions 268
11.5.3 Estimating conditional densities 269
11.5.4 Estimating conditional distribution funetions 270
11.5.5 Forecasting and estimating with missing observations 270
11.6 Estimating loglikelihood and parameters 271
11.6.1 Estimation of likelihood 271
11.6.2 Maximisation of loglikelihood 272
11.6.3 Variance matrix of maximum likelihood estimate 273
11.6.4 Effect of errors in parameter estimation 273
11.6.5 Mean Square error matrix due to Simulation 273
11.7 Importance sampling weights and diagnostics 275
xx Contents
12. Particle filtering 276
12.1 Introduction 276
12.2 Filtering by importance sampling 276
12.3 Sequential importance sampling 278
12.3.1 Introduction 278
12.3.2 Recursions for particle filtering 279
12.3.3 Degeneracy and resampling 280
12.3.4 Algorithm for sequential importance sampling 282
12.4 The bootstrap particle filter 283
12.4.1 Introduction 283
12.4.2 The bootstrap filter 283
12.4.3 Algorithm for bootstrap filter 283
12.4.4 Illustration: local level model for Nile data 284
12.5 The auxiliary particle filter 287
12.5.1 Algorithm for auxiliary filter 287
12.5.2 Illustration: local level model for Nile data 288
12.6 Other implementations of particle filtering 288
12.6.1 Importance density from extended or
unscented filter 288
12.6.2 The local regression filter 291
12.6.3 The mode equalisation filter 294
12.7 Rao-Blackwellisation 296
12.7.1 Introduction 296
12.7.2 The Rao-Blackwellisation technique 297
13. Bayesian estimation of parameters 299
13.1 Introduction 299
13.2 Posterior analysis for linear Gaussian model 300
13.2.1 Posterior analysis based on importance
sampling 300
13.2.2 Non-informative priors 302
13.3 Posterior analysis for a nonlinear non-Gaussian
model 303
13.3.1 Posterior analysis of funetions of the
state vector 303
13.3.2 Computational aspects of Bayesian
analysis 305
13.3.3 Posterior analysis of parameter vector 307
13.4 Markov chain Monte Carlo methods 309
14. Non-Gaussian and nonlinear illustrations 312
14.1 Introduction 312
14.2 Nonlinear decomposition: UK visits abroad 312
14.3 Poisson density: van drivers killed in Great Britain 314
14.4 Heavy-tailed density: outlier in gas consumption 317
Contents xxi
14.5 Volatility: pound/dollar daily exchange rates 319
14.5.1 Data transformation analysis 319
14.5.2 Estimation via importance sampling 321
14.5.3 Particle filtering Illustration 322
14.6 Binary density: Oxford-Cambridge boat race 324
References 326
Author Index 340
Subject Index 343
|
| any_adam_object | 1 |
| author | Durbin, James 1923-2012 Koopman, Siem Jan |
| author_GND | (DE-588)170383393 (DE-588)171047141 |
| author_facet | Durbin, James 1923-2012 Koopman, Siem Jan |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV040398722 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:23:10Z |
| institution | BVB |
| isbn | 019964117X 9780199641178 |
| language | English |
| lccn | 2011945385 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025251954 |
| oclc_num | 794591362 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-824 DE-188 DE-384 DE-945 DE-355 DE-BY-UBR DE-11 DE-83 DE-N2 DE-521 DE-473 DE-BY-UBG DE-19 DE-BY-UBM DE-20 |
| owner_facet | DE-91G DE-BY-TUM DE-824 DE-188 DE-384 DE-945 DE-355 DE-BY-UBR DE-11 DE-83 DE-N2 DE-521 DE-473 DE-BY-UBG DE-19 DE-BY-UBM DE-20 |
| physical | XXI, 346 S. graph. Darst. 24 cm |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| 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 ; S. J. Koopman 2. ed. Oxford [u.a.] Oxford Univ. Press 2012 XXI, 346 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Oxford statistical science series 38 Literaturverz. S. [326] - 339 Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Zustandsraum (DE-588)4132647-7 gnd rswk-swf Time-series analysis State-space methods 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 38 (DE-604)BV001908661 38 DE-601 pdf/application http://www.gbv.de/dms/zbw/689557248.pdf Inhaltsverzeichnis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025251954&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 (DE-588)4067486-1 gnd Zustandsraum (DE-588)4132647-7 gnd |
| subject_GND | (DE-588)4067486-1 (DE-588)4132647-7 |
| 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 ; S. J. Koopman |
| title_fullStr | Time series analysis by state space methods J. Durbin ; S. J. Koopman |
| title_full_unstemmed | Time series analysis by state space methods J. Durbin ; S. J. Koopman |
| title_short | Time series analysis by state space methods |
| title_sort | time series analysis by state space methods |
| topic | Zeitreihenanalyse (DE-588)4067486-1 gnd Zustandsraum (DE-588)4132647-7 gnd |
| topic_facet | Zeitreihenanalyse Zustandsraum |
| url | http://www.gbv.de/dms/zbw/689557248.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025251954&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 |
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