Hidden Markov Models for Time Series: An Introduction Using R by Walter Zucchini, Iain L. MacDonald

Hidden Markov Models for Time Series: An Introduction Using R by Walter Zucchini, Iain L. MacDonald
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Hidden Markov Models for Time Series: An Introduction Using R

(Chapman & Hall/CRC Monographs on Statistics & Applied Probability)

by Walter Zucchini, Iain L. MacDonald

Published:April 28, 2009 by Chapman and Hall/CRC


Presents an accessible overview of HMMs for analyzing time series data

Covers continuous-valued, circular, and multivariate time series data

Explores a variety of applications in animal behavior, finance, epidemiology, climatology, and sociology

Shows how to apply the methods using R

Includes numerous theoretical and programming exercises at the end of most chapters

Provides all of the data sets analyzed in the text online


Reveals How HMMs Can Be Used as General-Purpose Time Series Models

Implements all methods in R

Hidden Markov Models for Time Series: An Introduction Using R applies hidden Markov models (HMMs) to a wide range of time series types, from continuous-valued, circular, and multivariate series to binary data, bounded and unbounded counts, and categorical observations. It also discusses how to employ the freely available computing environment R to carry out computations for parameter estimation, model selection and checking, decoding, and forecasting.

Illustrates the methodology in action

After presenting the simple Poisson HMM, the book covers estimation, forecasting, decoding, prediction, model selection, and Bayesian inference. Through examples and applications, the authors describe how to extend and generalize the basic model so it can be applied in a rich variety of situations. They also provide R code for some of the examples, enabling the use of the codes in similar applications.

Effectively interpret data using HMMs

This book illustrates the wonderful flexibility of HMMs as general-purpose models for time series data. It provides a broad understanding of the models and their uses.

Table of Contents


Mixture Distributions and Markov Chains


Independent mixture models

Markov chains

Hidden Markov Models: Definition and Properties

A simple hidden Markov model

The basics

The likelihood

Estimation by 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

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


Extensions of the Basic Hidden Markov Model


HMMs with general univariate state-dependent distribution

HMMs based on a second-order Markov chain

HMMs for multivariate series

Series which depend on covariates

Models with additional dependencies


Epileptic Seizures


Models fitted

Model checking by pseudo-residuals

Eruptions of the Old Faithful Geyser


Binary time series of short and long eruptions

Normal HMMs for durations and waiting times

Bivariate model for durations and waiting times

Drosophila Speed and Change of Direction


Von Mises distributions

Von Mises HMMs for the two subjects

Circular autocorrelation functions

Bivariate model

Wind Direction at Koeberg


Wind direction as classified into 16 categories

Wind direction as a circular variable

Models for Financial Series

Thinly traded shares

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


Cape Town Homicides and Suicides


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-Behavior 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 behavior


Appendix A: Examples of R code

Stationary Poisson HMM, numerical maximization

More on Poisson HMMs, including EM

Bivariate normal state-dependent distributions

Categorical HMM, constrained optimization

Appendix B: Some Proofs

Factorization needed for forward probabilities

Two results for backward probabilities

Conditional independence of Xt1 and XTt+1


Author Index

Subject Index

Exercises appear at the end of most chapters.

Editorial Reviews The book would be a good text for a seminar or a course on HMM or for self-learning the topic. ¡­ Those who have the background necessary to use the R code and to replicate the results throughout the book will find plenty of material in this book to extend what they learn to their own data. The book is written very pedagogically ¡­ all the data sets, errata sheet, R code, among other things, can be accessed at the web site. ¡ªJournal of Statistical Software, Vol. 43, October 2011

¡­ this book has a very nice mix of probability, statistics, and data analysis. It is suitable for a course in stochastic modeling using hidden Markov models, but also serves well as an introduction for nonspecialists. ¡ªBiometrics, 67, September 2011

¡­ this is an excellent book, which should be of great interest to applied statisticians looking for a clear introduction to HMMs and advice on the practical implementation of these models. It is also an ideal teaching resource. ¡ªAustralian & New Zealand Journal of Statistics, 2011

It is clear that much care has gone into this book: it has a very detailed contents list, a list of abbreviations and notations, thoughtful data analyses, many references and a detailed index. In fact, it would be difficult not to thoroughly recommend it to anyone interested in learning how to tackle these types of data. ¡ªInternational Statistical Review (2011), 79, 1