dlm
dlm: Bayesian and Likelihood Analysis of Dynamic Linear Models Maximum likelihood, Kalman filtering and smoothing, and Bayesian analysis of Normal linear State Space models, also known as Dynamic Linear Models. This book gives an introduction to statistical time series analysis by dynamic linear models. It covers the basic notions of dynamic linear models and state space models, the Kalman filter for estimation and forecasting in dynamic linear models with known parameters, and maximum likelihood estimation. It also presents many specific dynamic linear models particularly suited for time series analysis, both for univariate and multivariate data. The main methods and models are illustrated with examples based on real data. For this, the authors have developed an R package, DIM, for inference and forecasting with dynamic linear models. The code to run all the examples in the book and the data sets not included in the package can be downloaded from the web site of the book, definetti.uark.edu/gpetris/dlm. The text is organized as follows. Chapter 1 gives an introduction, presenting basic notions in Bayesian inference. The basic elements of Bayesian analysis for linear regression models are reminded, and Markov chain Monte Carlo methods are presented. Chapter 2 is on dynamic linear models. State space models, dynamic linear models, state estimation and forecasting, filtering and the Kalman filter, and some specialized topics are dealt with. Chapter 3 discusses model specifications. The first paragraph deals with classical tools for time series analysis. Then, dynamic linear models for time series analysis are investigated, both univariate and multivariate. Chapter 4 covers models with unknown parameters. It presents a discussion of maximum likelihood estimation and a much more elaborated one on Bayesian inference. The last chapter is on sequential Monte Carlo methods.
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References in zbMATH (referenced in 11 articles , 1 standard article )
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Sorted by year (- Nicholas Michaud, Perry de Valpine, Daniel Turek, Christopher J. Paciorek: Sequential Monte Carlo Methods in the nimble R Package (2017) arXiv
- Neale, Michael C.; Hunter, Michael D.; Pritikin, Joshua N.; Zahery, Mahsa; Brick, Timothy R.; Kirkpatrick, Robert M.; Estabrook, Ryne; Bates, Timothy C.; Maes, Hermine H.; Boker, Steven M.: OpenMX 2.0: extended structural equation and statistical modeling (2016)
- Colombi, R.; Giordano, S.: Multiple hidden Markov models for categorical time series (2015)
- Fúquene, Jairo; Pérez, María-Eglée; Pericchi, Luis R.: An alternative to the inverted gamma for the variances to modelling outliers and structural breaks in dynamic models (2014)
- Sheinson, Daniel M.; Niemi, Jarad; Meiring, Wendy: Comparison of the performance of particle filter algorithms applied to tracking of a disease epidemic (2014)
- Triantafyllopoulos, K.: Multivariate stochastic volatility estimation using particle filters (2014)
- Ruiz-Cárdenas, Ramiro; Krainski, Elias T.; Rue, Håvard: Direct fitting of dynamic models using integrated nested Laplace approximations -- INLA (2012)
- Lodewyckx, Tom; Tuerlinckx, Francis; Kuppens, Peter; Allen, Nicholas B.; Sheeber, Lisa: A hierarchical state space approach to affective dynamics (2011)
- Lopes, Hedibert F.; Tsay, Ruey S.: Particle filters and Bayesian inference in financial econometrics (2011)
- Salcedo, Gladys E.; Morettin, Pedro A.: A test for comparing two discrete stochastic dynamical systems under heteroskedasticity (2011)
- Petris, Giovanni; Petrone, Sonia; Campagnoli, Patrizia: Dynamic linear models with R (2009)