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E-raamat: Dynamic Linear Models with R

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  • Formaat: PDF+DRM
  • Sari: Use R!
  • Ilmumisaeg: 12-Jun-2009
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9780387772387
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Dynamic Linear Models with RSuurem pilt
  • Formaat: PDF+DRM
  • Sari: Use R!
  • Ilmumisaeg: 12-Jun-2009
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9780387772387
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State space models have gained tremendous popularity in recent years in as disparate fields as engineering, economics, genetics and ecology. After a detailed introduction to general state space models, this book focuses on dynamic linear models, emphasizing their Bayesian analysis. Whenever possible it is shown how to compute estimates and forecasts in closed form; for more complex models, simulation techniques are used. A final chapter covers modern sequential Monte Carlo algorithms.

The book illustrates all the fundamental steps needed to use dynamic linear models in practice, using R. Many detailed examples based on real data sets are provided to show how to set up a specific model, estimate its parameters, and use it for forecasting. All the code used in the book is available online.

No prior knowledge of Bayesian statistics or time series analysis is required, although familiarity with basic statistics and R is assumed.



This text introduces general state space models in detail before focusing on dynamic linear models, emphasizing their Bayesian analysis. It illustrates all the fundamental steps needed to use dynamic linear models in practice, using R.

Arvustused

"This book is a welcome addition to the series Use R! The text is interspersed with snippets of R code to illustrate the techniques and models and provides the basis of an excellent text for private study." (International Statistical Review, 2010, 78, 1, 134-159) "Dynamic Linear models With R provides a friendly introduction to the world of dynamic linear models (DLMs)... . This book provides the reader with the minimal tools necessary for Bayesian analysis of time series data using DLMs. ...The main contribution...is the DLM package in R which provides functions for dynamic linear model creation as well as filtering, smoothing, and forecasting. Therefore, the book can be utilized as a descriptive manual that provides a hybrid practical-theoretical perspective on the purpose of the functions in this extremely useful R package. ...I'd like to thank these authors for a useful applied Bayesian time series handbook suitable to a graduate statistics course and also to thank the editors of the Use R! series for providing a valuable collection of books for a fantastic open-source software." (American Statistician, August 2010, Vol. 64, No. 3)

1 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
2 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 dlm
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
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 y1:T: 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
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
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