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Dynamic Linear Models with R

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ISBN-10: 0387772375

ISBN-13: 9780387772370

Edition: 2009

Authors: Giovanni Petris, Sonia Petrone, Patrizia Campagnoli

List price: $79.99
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Description:

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,…    
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Book details

List price: $79.99
Copyright year: 2009
Publisher: Springer New York
Publication date: 6/2/2009
Binding: Paperback
Pages: 252
Size: 6.10" wide x 9.25" long x 0.50" tall
Weight: 1.100

Introduction: basic notions about Bayesian inference
Basic notions
Simple dependence structures
Synthesis of conditional distributions
Choice of the prior distribution
Bayesian inference in the linear regression model
Markov chain Monte Carlo methods
Gibbs sampler
Metropolis-Hastings algorithm
Adaptive rejection Metropolis sampling
Problems
Dynamic linear models
Introduction
A simple example
State space models
Dynamic linear models
Dynamic linear models in package dlm
Examples of nonlinear and non-Gaussian state space models
State estimation and forecasting
Filtering
Kalman filter for dynamic linear models
Filtering with missing observations
Smoothing
Forecasting
The innovation process and model checking
Controllability and observability of time-invariant DLMs
Filter stability
Problems
Model specification
Classical tools for time series analysis
Empirical methods
ARIMA models
Univariate DLMs for time series analysis
Trend models
Seasonal factor models
Fourier form seasonal models
General periodic components
DLM representation of ARIMA models
Example: estimating the output gap
Regression models
Models for multivariate time series
DLMs for longitudinal data
Seemingly unrelated time series equations
Seemingly unrelated regression models
Hierarchical DLMs
Dynamic regression
Common factors
Multivariate ARMA models
Problems
Models with unknown parameters
Maximum likelihood estimation
Bayesian inference
Conjugate Bayesian inference
Unknown covariance matrices: conjugate inference
Specification of Wt by discount factors
A discount factor model for time-varying Vt
Simulation-based Bayesian inference
Drawing the states given y1:T: forward filtering backward sampling
General strategies for MCMC
Illustration: Gibbs sampling for a local level model
Unknown variances
Constant unknown variances: d Inverse Gamma Prior
Multivariate extensions
A model for outliers and structural breaks
Further examples
Estimating the output gap: Bayesian inference
Dynamic regression
Factor models
Problems
Sequential Monte Carlo methods
The basic particle filter
A simple example
Auxiliary particle filter
Sequential Monte Carlo with unknown parameters
A simple example with unknown parameters
Concluding remarks
Useful distributions
Matrix algebra: Singular Value Decomposition
Index
References