zbMATH — the first resource for mathematics

Hidden Markov models for time series. An introduction using R. (English) Zbl 1180.62130
Monographs on Statistics and Applied Probability 110. Boca Raton, FL: CRC Press (ISBN 978-1-58488-573-3/hbk; 978-1-4200-1089-3/ebook). xxii, 275 p. (2009).
This text is written for readers who wish to acquire a general understanding of the models and their uses, and who wish to apply them. Because of that, there is a lack of generality of the treatment and some dearth of material on specific issues such as identifiability, hypothesis testing, properties of estimators and reversible jump Markov chain Monte Carlo methods. Only a modest level of knowledge of probability and statistics is assumed.
The authors present most of the ideas by using a single running example and a simple model, the Poisson-hidden Markov model. In Chapter 8, Extensions of the basic hidden Markov model, and in Part Two of the book, it is illustrated how this basic model can be extended and generalized. The authors have attempted to make the models more accessible by illustrating how the computing environment R can be used to carry out the computations. Exercises are included for all chapters. Some exercises are of a theoretical nature, both to fill in the details and to illustrate some of the concepts introduced in the text. The programming exercises are intended to encourage readers to develop expertise in R.
A short overview of the contents of the book is as follows: Part I: Model structure, properties and methods; Preliminaries: mixtures and Markov chains; Hidden Markov models: definition and properties; Estimation by direct maximation of the likelihood; Estimation by the EM algorithm; Forecasting, decoding and state prediction; Model selection and checking; Bayesian inference for Poisson-HMs; Extensions of the basic hidden Markov models.
Part II is entirely devoted to applications. Eight case studies are presented, each in a separate chapter. They illustrate how the basic Poisson hidden Markov models can be progressively and variously extended and generalized. Examples of the R code are presented in the Appendix.

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62-04 Software, source code, etc. for problems pertaining to statistics
65C40 Numerical analysis or methods applied to Markov chains
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62F15 Bayesian inference
65C60 Computational problems in statistics (MSC2010)
EM algorithm
Full Text: DOI