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Hidden Markov and other models for discrete-valued time series. (English) Zbl 0868.60036

Monographs on Statistics and Applied Probability. 70. London: Chapman & Hall. xvi, 236 p. (1997).
Discrete-valued time series occur quite frequently but methods for their statistical analysis are scattered in statistical literature. The monograph gives a review of published models and also contains new material. The first part of the book presents an account of the models other than hidden Markov, e.g. DARMA models of Jacobs and Lewis, models based on thinning, Markov regression models, parameter-driven models and others. Part two is devoted to hidden Markov models. The authors describe correlation properties, likelihood function, distributional properties, parameter estimation and other topics. Some extensions and modifications concern multinomial-hidden Markov models, multivariate models, models with non-stationary or non-homogeneous Markov chain etc. Applications include a detailed statistical analysis of several interesting data sets (eruptions of the Old Faithful geyser, epileptic seizure counts, births at a hospital, wind direction, evapotranspiration, shares on a stock exchange, daily rainfall, homicides and suicides,...).
The book is well written. It gives a nice description of methods proposed for analysis of discrete-valued time series, their theoretical background and examples of applications. The book can be recommended to statisticians who analyze data as well as to students and teachers. It can be used as very good material for seminars and special lectures.
Reviewer: J.Anděl (Praha)

MSC:

60G10 Stationary stochastic processes
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
62-02 Research exposition (monographs, survey articles) pertaining to statistics

Software:

AS 183; NPSOL
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