Dynamic linear models with R:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Springer
2009
|
| Series: | Use R!
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIII, 251 S. graph. Darst. |
| ISBN: | 9780387772370 |
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Record in the Search Index
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| adam_text |
Titel: Dynamic linear models with R
Autor: Petris, Giovanni
Jahr: 2009
Contents
Introduction: basic notions about Bayesian inference . 1
1.1 Basic notions. 2
1.2 Simple dependence structures. 5
1.3 Synthesis of conditional distributions. 11
1.4 Choice of the prior distribution. 14
1.5 Bayesian inference in the linear regression model. 18
1.6 Markov chain Monte Carlo methods. 22
1.6.1 Gibbs sampler. 24
1.6.2 Metropolis-Hastings algorithm. 24
1.6.3 Adaptive rejection Metropolis sampling. 25
Problems. 29
Dynamic linear models. 31
2.1 Introduction. 31
2.2 A simple example . 35
2.3 State space models . 39
2.4 Dynamic linear models. 41
2.5 Dynamic linear models in package dim . 43
2.6 Examples of nonlinear and non-Gaussian state space models . 48
2.7 State estimation and forecasting. 49
2.7.1 Filtering . 51
2.7.2 Kalman filter for dynamic linear models. 53
2.7.3 Filtering with missing observations. 59
2.7.4 Smoothing. 60
2.8 Forecasting. 66
2.9 The innovation process and model checking. 73
2.10 Controllability and observability of time-invariant DLMs. 77
2.11 Filter stability. 80
Problems. 83
XII Contents
3 Model specification. 85
3.1 Classical tools for time series analysis. 85
3.1.1 Empirical methods . 85
3.1.2 ARIMA models. 87
3.2 Univariate DLMs for time series analysis. 88
3.2.1 Trend models. 89
3.2.2 Seasonal factor models.100
3.2.3 Fourier form seasonal models.102
3.2.4 General periodic components .109
3.2.5 DLM representation of ARIMA models.112
3.2.6 Example: estimating the output gap.115
3.2.7 Regression models.121
3.3 Models for multivariate time series.125
3.3.1 DLMs for longitudinal data.126
3.3.2 Seemingly unrelated time series equations.127
3.3.3 Seemingly unrelated regression models.132
3.3.4 Hierarchical DLMs .134
3.3.5 Dynamic regression.136
3.3.6 Common factors .138
3.3.7 Multivariate ARMA models.139
Problems.142
4 Models with unknown parameters.143
4.1 Maximum likelihood estimation.144
4.2 Bayesian inference.148
4.3 Conjugate Bayesian inference.149
4.3.1 Unknown covariance matrices: conjugate inference.150
4.3.2 Specification of Wt by discount factors.152
4.3.3 A discount factor model for time-varying Vt.158
4.4 Simulation-based Bayesian inference.160
4.4.1 Drawing the states given yx.r'- forward filtering
backward sampling.161
4.4.2 General strategies for MCMC.162
4.4.3 Illustration: Gibbs sampling for a local level model . 165
4.5 Unknown variances.167
4.5.1 Constant unknown variances: d Inverse Gamma prior . 167
4.5.2 Multivariate extensions .171
4.5.3 A model for outliers and structural breaks.177
4.6 Further examples.186
4.6.1 Estimating the output gap: Bayesian inference.186
4.6.2 Dynamic regression.192
4.6.3 Factor models.200
Problems.206
Contents XIII
5 Sequential Monte Carlo methods.207
5.1 The basic particle filter.208
5.1.1 A simple example.213
5.2 Auxiliary particle filter.216
5.3 Sequential Monte Carlo with unknown parameters.219
5.3.1 A simple example with unknown parameters.226
5.4 Concluding remarks .228
A Useful distributions.231
B Matrix algebra: Singular Value Decomposition.237
Index.241
References.245 |
| any_adam_object | 1 |
| author | Petris, Giovanni Petrone, Sonia Campagnoli, Patrizia |
| author_facet | Petris, Giovanni Petrone, Sonia Campagnoli, Patrizia |
| author_role | aut aut aut |
| author_sort | Petris, Giovanni |
| author_variant | g p gp s p sp p c pc |
| building | Verbundindex |
| bvnumber | BV035725789 |
| callnumber-first | Q - Science |
| callnumber-label | QA276 |
| callnumber-raw | QA276.45.R3 |
| callnumber-search | QA276.45.R3 |
| callnumber-sort | QA 3276.45 R3 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | MR 2100 SK 840 ST 601 |
| ctrlnum | (OCoLC)310400804 (DE-599)DNB992520916 |
| dewey-full | 519.502855369 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.502855369 |
| dewey-search | 519.502855369 |
| dewey-sort | 3519.502855369 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Soziologie Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-20T10:19:11Z |
| institution | BVB |
| isbn | 9780387772370 |
| language | English |
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| physical | XIII, 251 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series2 | Use R! |
| spelling | Petris, Giovanni Verfasser aut Dynamic linear models with R Giovanni Petris ; Sonia Petrone ; Patrizia Campagnoli Dordrecht [u.a.] Springer 2009 XIII, 251 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Use R! Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf R Programm (DE-588)4705956-4 gnd rswk-swf Lineares dynamisches System (DE-588)4167727-4 gnd rswk-swf Lineares dynamisches System (DE-588)4167727-4 s Bayes-Verfahren (DE-588)4204326-8 s R Programm (DE-588)4705956-4 s b DE-604 Petrone, Sonia Verfasser aut Campagnoli, Patrizia Verfasser aut Erscheint auch als Online-Ausgabe 978-0-387-77238-7 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3239931&prov=M&dok%5Fvar=1&dok%5Fext=htm Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018002486&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Petris, Giovanni Petrone, Sonia Campagnoli, Patrizia Dynamic linear models with R Bayes-Verfahren (DE-588)4204326-8 gnd R Programm (DE-588)4705956-4 gnd Lineares dynamisches System (DE-588)4167727-4 gnd |
| subject_GND | (DE-588)4204326-8 (DE-588)4705956-4 (DE-588)4167727-4 |
| title | Dynamic linear models with R |
| title_auth | Dynamic linear models with R |
| title_exact_search | Dynamic linear models with R |
| title_full | Dynamic linear models with R Giovanni Petris ; Sonia Petrone ; Patrizia Campagnoli |
| title_fullStr | Dynamic linear models with R Giovanni Petris ; Sonia Petrone ; Patrizia Campagnoli |
| title_full_unstemmed | Dynamic linear models with R Giovanni Petris ; Sonia Petrone ; Patrizia Campagnoli |
| title_short | Dynamic linear models with R |
| title_sort | dynamic linear models with r |
| topic | Bayes-Verfahren (DE-588)4204326-8 gnd R Programm (DE-588)4705956-4 gnd Lineares dynamisches System (DE-588)4167727-4 gnd |
| topic_facet | Bayes-Verfahren R Programm Lineares dynamisches System |
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