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Full Description
Hidden Markov Models for Time Series: An Introduction Using R, Second Edition illustrates the great flexibility of hidden Markov models (HMMs) as general-purpose models for time series data. The book provides a broad understanding of the models and their uses.
After presenting the basic model formulation, the book covers estimation, forecasting, decoding, prediction, model selection, and Bayesian inference for HMMs. Through examples and applications, the authors describe how to extend and generalize the basic model so that it can be applied in a rich variety of situations.
The book demonstrates how HMMs can be applied to a wide range of types of time series: continuous-valued, circular, multivariate, binary, bounded and unbounded counts, and categorical observations. It also discusses how to employ the freely available computing environment R to carry out the computations.
Features
Presents an accessible overview of HMMs
Explores a variety of applications in ecology, finance, epidemiology, climatology, and sociology
Includes numerous theoretical and programming exercises
Provides most of the analysed data sets online
New to the second edition
A total of five chapters on extensions, including HMMs for longitudinal data, hidden semi-Markov models and models with continuous-valued state process
New case studies on animal movement, rainfall occurrence and capture-recapture data
Contents
Model structure, properties and methods, Preliminaries: mixtures and Markov chains, Hidden Markov models: definition and properties, Direct maximization of the likelihood, Estimation by the EM algorithm, Forecasting, decoding and state prediction, Model selection and checking, Bayesian inference for Poisson-HMMs, R packages, Extensions, Covariates and other extra dependencies, Continuous-valued state processes, Hidden semi-Markov models as HMMs, HMMs for longitudinal data, Applications , Epileptic seizures, Daily rainfall occurrence, Eruptions of the Old Faithful geyser, HMMs for animal movement, Wind direction at Koeberg, Models for financial series, Births at Edendale Hospital, Homicides and suicides in Cape Town, Animal behaviour model with feedback, Survival rates of Soay sheep, Examples of R code, The functions, Examples of code using the above functions, Some proofs Factorization needed for forward probabilities, Two results for backward probabilities, Conditional independence of Xt1 and XTt+1, References
