Dynamic Linear Models with R

By: Giovanni Petris, Sonia Petrone, Patrizia Campagnoli

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Paperback | 3 June 2009

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268 Pages

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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.

Industry Reviews

"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)

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Introduction: basic notions about Bayesian inference	p. 1
Basic notions	p. 2
Simple dependence structures	p. 5
Synthesis of conditional distributions	p. 11
Choice of the prior distribution	p. 14
Bayesian inference in the linear regression model	p. 18
Markov chain Monte Carlo methods	p. 22
Gibbs sampler	p. 24
Metropolis-Hastings algorithm	p. 24
Adaptive rejection Metropolis sampling	p. 25
Problems	p. 29
Dynamic linear models	p. 31
Introduction	p. 31
A simple example	p. 35
State space models	p. 39
Dynamic linear models	p. 41
Dynamic linear models in package dlm	p. 43
Examples of nonlinear and non-Gaussian state space models	p. 48
State estimation and forecasting	p. 49
Filtering	p. 51
Kalman filter for dynamic linear models	p. 53
Filtering with missing observations	p. 59
Smoothing	p. 60
Forecasting	p. 66
The innovation process and model checking	p. 73
Controllability and observability of time-invariant DLMs	p. 77
Filter stability	p. 80
Problems	p. 83
Model specification	p. 85
Classical tools for time series analysis	p. 85
Empirical methods	p. 85
ARIMA models	p. 87
Univariate DLMs for time series analysis	p. 88
Trend models	p. 89
Seasonal factor models	p. 100
Fourier form seasonal models	p. 102
General periodic components	p. 109
DLM representation of ARIMA models	p. 112
Example: estimating the output gap	p. 115
Regression models	p. 121
Models for multivariate time series	p. 125
DLMs for longitudinal data	p. 126
Seemingly unrelated time series equations	p. 127
Seemingly unrelated regression models	p. 132
Hierarchical DLMs	p. 134
Dynamic regression	p. 136
Common factors	p. 138
Multivariate ARMA models	p. 139
Problems	p. 142
Models with unknown parameters	p. 143
Maximum likelihood estimation	p. 144
Bayesian inference	p. 148
Conjugate Bayesian inference	p. 149
Unknown covariance matrices: conjugate inference	p. 150
Specification of Wt by discount factors	p. 152
A discount factor model for time-varying Vt	p. 158
Simulation-based Bayesian inference	p. 160
Drawing the states given y1:T: forward filtering backward sampling	p. 161
General strategies for MCMC	p. 162
Illustration: Gibbs sampling for a local level model	p. 165
Unknown variances	p. 167
Constant unknown variances: d Inverse Gamma Prior	p. 167
Multivariate extensions	p. 171
A model for outliers and structural breaks	p. 177
Further examples	p. 186
Estimating the output gap: Bayesian inference	p. 186
Dynamic regression	p. 192
Factor models	p. 200
Problems	p. 206
Sequential Monte Carlo methods	p. 207
The basic particle filter	p. 208
A simple example	p. 213
Auxiliary particle filter	p. 216
Sequential Monte Carlo with unknown parameters	p. 219
A simple example with unknown parameters	p. 226
Concluding remarks	p. 228
Useful distributions	p. 231
Matrix algebra: Singular Value Decomposition	p. 237
Index	p. 241
References	p. 245
Table of Contents provided by Ingram. All Rights Reserved.

Dynamic Linear Models with R

At a Glance

Paperback

Industry Reviews

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