Hidden Markov Models for Time Series: An Introduction Using R, Second Edition, 2nd Edition (Hardback) book cover

Hidden Markov Models for Time Series

An Introduction Using R, Second Edition, 2nd Edition

By Walter Zucchini, Iain L. MacDonald, Roland Langrock

Chapman and Hall/CRC

370 pages | 80 B/W Illus.

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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.


  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


"This book is an excellent resource for researchers of all levels, from undergraduate students to researchers already working with hidden Markov models. The book initially provides the mathematical theory and underlying intuition of hidden Markov models in a clear and concise manner before describing more advanced, recently developed techniques and a wide range of applications using real data. One focus of the book is the practical application of hidden Markov models. R code is usefully provided throughout the text (and combined within the appendix) aiding researchers in applying the techniques to their own problems, in addition to the description of some specific R packages. Thus the book is a valuable resource for both researchers new to hidden Markov models and as a reference for individuals already familiar with the models and concepts. In particular, the inclusion of the new Part II ("Extensions") for the second edition relating to the recent advanced techniques is an excellent addition, providing a clear description of state-of-the-art hidden Markov-type models and associated issues. Overall, the book is exceptionally well written and will be a well thumbed book in my collection."

Ruth King, Thomas Bayes' Chair of Statistics, University of Edinburgh

"…this is far and away the most accessible, up-to-date, and comprehensive introductory text on HMMs that there is, for students, applied statisticians, and indeed any quantitatively able researcher. It doubles as an excellent reference text for researchers who use HMMs. The addition of new R code and illustration of the use of HMM packages in R makes the text all the more useful, and the new chapters on applications in ecology and the environment will extend the appeal of the book into an area in which the huge potential of HMMs has only recently become apparent. If you want to find out about and use HMMs, ranging from the simplest to those at the cutting-edge research, this is the book for you!"

David Borchers, Professor of Statistics, University of St Andrews

"The authoritative text on HMMs has become even better. This second edition is welcome and timely, filled with many examples of HMMs in the real world, and very useful snippets of code to help us get going. The authors have once again hit the jackpot."

Trevor Hastie, Statistics Department, Stanford University

"The first edition of ‘Hidden Markov Models for Time Series: An Introduction using R’ was the clearest and most comprehensive description of the theory and applications of HMMs in print. This new second edition from Zucchini et al contains a highly useful update to the already impressive body of material covered in the first edition. New additions include chapters on Hidden Semi-Markov Models, continuous-valued state processes, and new application sections detailing the use of HMMs for animal movement and survival estimation. The R code provided outlines key computational procedures and provides a workable foundation upon which researchers can build their own bespoke implementations of HMMs and understand the working of other software packages, which are now considered in detail. This book is structured in an accessible, yet thorough, manner which will be appreciated by statistically literate researchers and students from a variety of disciplines. This book is highly recommended for anyone wishing to understand or use Hidden Markov models."

Dr. Toby Patterson, Senior Research Scientist, CSIRO Oceans and Atmosphere

"The first edition profoundly influenced my research and this new edition adds substantial material on R packages, hidden semi-Markov models and more. The book is a must have for any applied statistician interested in modeling incomplete encounter history or movement data for animals. The simplicity and generality of hidden Markov models make them an elegant solution for many applications and an essential method to have in an applied statistician's toolbox."

Prof. Jeff Laake, Marine Mammal Laboratory, Alaska Fisheries Science Center, Seattle

"This book is an essential for all researchers in the area of hidden Markov models and indeed, more generally, in the broad arena of statistical modelling. The theory underpinning hidden Markov models (HMMs) is meticulously delineated and perfectly complemented by a broad range of applications chosen from real-world settings in, for example, finance, zoology and the health sciences.

This second edition of the book now includes particularly valuable chapters on recent extensions to HMMs and intriguing new applications in ecology and the environment. Fragments of R code are provided throughout the text and in the Appendix and serve to fix ideas relating to both theory and practice. In summary, the book is a most welcome addition to the statistician's armoury and can be used both as a comprehensive reference work and as a well-crafted textbook."

Linda Haines, Emeritus Professor, Department of Statistical Sciences, University of Cape Town.

Table of Contents

Model structure, properties and methods

Preliminaries: mixtures and Markov chains


Independent mixture models

Markov chains


Hidden Markov models: definition and properties

A simple hidden Markov model

The basics

The likelihood


Direct maximization of the likelihood


Scaling the likelihood computation

Maximization subject to constraints

Other problems

Example: earthquakes

Standard errors and confidence intervals

Example: parametric bootstrap


Estimation by the EM algorithm

Forward and backward probabilities

The EM algorithm

Examples of EM applied to Poisson-HMMs



Forecasting, decoding and state prediction

Conditional distributions

Forecast distributions


State prediction

HMMs for classification


Model selection and checking

Model selection by AIC and BIC

Model checking with pseudo-residuals




Bayesian inference for Poisson-HMMs

Applying the Gibbs sampler to Poisson-HMMs

Bayesian estimation of the number of states

Example: earthquakes



R packages

The package depmixS4

The package HiddenMarkov

The package msm

The package R20penBUGS



General state-dependent distributions


Univariate state-dependent distribution

Multinomial and categorical HMMs

Multivariate state-dependent distribution


Covariates and other extra dependencies


HMMs with covariates

HMMs based on a second-order Markox chain

HMMs with other additional dependencies


Continuous-valued state processes


Models with continous-valued state process

Fitting an SSM to the earthquake data


Hidden semi-Markov models as HMMs


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



HMMs for longitudinal data


Some parameters constant across components

Models with random effects




Introduction to applications

Epileptic seizures


Models fitted

Model checking by pseudo-residuals


Daily rainfall occurrence


Models fitted

Eruptions of the Old Faithful geyser


The data

Binary time series of short and long eruptions

Normal-HMMs for durations and waiting times

Bivariate model for durations and waiting times


HMMs for animal movement


Directional data

HMMs for movement data

Basic HMM for Drosophila movement

HMMs and HSMMs for bison movement

Mixed HMMs for woodpecker movement


Wind direction at Koeberg


Wind direction classified into 16 categories

Wind direction as a circular variable


Models for financial series

Multivariate HMM for returns on four shares

Stochastic volatility models


Births at Edendale Hospital


Models for the proportion Caesarean

Models for the total number of deliveries


Homicides and suicides in Cape Town


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 feedback


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


Survival rates of Soay sheep


MRR data without use of covariates

MRR data involving covariate information

Application to Soay sheep data


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


Author index

Subject index

About the Series

Chapman & Hall/CRC Monographs on Statistics and Applied Probability

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General