Hidden Markov Models for Time Series (2^nd Ed.) An Introduction Using R, Second Edition Chapman & Hall/CRC Monographs on Statistics and Applied Probability Series

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

1. Presents an accessible overview of HMMs



2. Explores a variety of applications in ecology, finance, epidemiology, climatology, and sociology



3. Includes numerous theoretical and programming exercises



4. Provides most of the analysed data sets online

New to the second edition

1. A total of five chapters on extensions, including HMMs for longitudinal data, hidden semi-Markov models and models with continuous-valued state process



2. New case studies on animal movement, rainfall occurrence and capture-recapture data

Model structure, properties and methods
Preliminaries: mixtures and Markov chainsIntroduction
Independent mixture models
Markov chains
Exercises

Hidden Markov models: definition and properties
A simple hidden Markov model
The basics
The likelihood
Exercises

Direct maximization of the likelihood
Introduction
Scaling the likelihood computation
Maximization subject to constraints
Other problems
Example: earthquakes
Standard errors and confidence intervals
Example: parametric bootstrap
Exercises

Estimation by the EM algorithmForward and backward probabilities
The EM algorithm
Examples of EM applied to Poisson-HMMs
Discussion
Exercises

Forecasting, decoding and state predictionConditional distributions
Forecast distributions
Decoding
State prediction
HMMs for classification
Exercises

Model selection and checkingModel selection by AIC and BIC
Model checking with pseudo-residuals
Examples
Discussion
Exercises

Bayesian inference for Poisson-HMMsApplying the Gibbs sampler to Poisson-HMMs
Bayesian estimation of the number of states
Example: earthquakes
Discussion
Exercises

R packagesThe package depmixS4The package HiddenMarkovThe package msmThe package R20penBUGS
Discussion

Extensions
General state-dependent distributionsIntroduction
Univariate state-dependent distribution
Multinomial and categorical HMMs
Multivariate state-dependent distribution
Exercises

Covariates and other extra dependenciesIntroduction
HMMs with covariates
HMMs based on a second-order Markox chain
HMMs with other additional dependencies
Exercises

Continuous-valued state processesIntroduction
Models with continous-valued state process
Fitting an SSM to the earthquake data
Discussion

Hidden semi-Markov models as HMMsIntroduction
Semi-Markov processes, hidden semi-Markov models and approximating HMMs
Examples of HSMMs as HMMs
General HSMM
R code
Some examples of dwell-time distributions
Fitting HSMMs via the HMM representation
Example: earthquakes
Discussion
Exercises

HMMs for longitudinal dataIntroduction
Some parameters constant across components
Models with random effects
Discussion
Exercises

Applications
Introduction to applications

Epileptic seizuresIntroduction
Models fitted
Model checking by pseudo-residuals
Exercises

Daily rainfall occurrenceIntroduction
Models fitted

Eruptions of the Old Faithful geyserIntroduction
The data
Binary time series of short and long eruptions
Normal-HMMs for durations and waiting times
Bivariate model for durations and waiting times
Exercises

HMMs for animal movementIntroduction
Directional data
HMMs for movement data
Basic HMM for Drosophila movement
HMMs and HSMMs for bison movement
Mixed HMMs for woodpecker movement
Exercises

Wind direction at KoebergIntroduction
Wind direction classified into 16 categories
Wind direction as a circular variable
Exercises

Models for financial seriesMultivariate HMM for returns on four shares
Stochastic volatility models
Exercises

Births at Edendale HospitalIntroduction
Models for the proportion Caesarean
Models for the total number of deliveries
Conclusion

Homicides and suicides in Cape TownIntroduction
Firearm homicides as a proportion of all homicides, suicides and legal intervention homicides
The number of firearm homicides
Firearm homicide and suicide proportions
Proportion in each of the five categories

Animal behaviour model with feedbackIntroduction
The model
Likelihood evaluation
Parameter estimation by maximum likelihood
Model checking
Inferring the underlying state
Models for a heterogeneous group of subjects
Other modifications or extensions
Application to caterpillar feeding behaviour
Discussion

Survival rates of Soay sheepIntroduction
MRR data without use of covariates
MRR data involving covariate information
Application to Soay sheep data
Conclusion

Examples of R codeThe functions
Examples of code using the above functions

Some proofsFactorization needed for forward probabilities
Two results for backward probabilities
Conditional independence of Xt1 and XTt+1

References

Author index

Subject index

Walter Zucchini, Iain K. MacDonald, Roland Langrock