Hidden Markov models for time series : an introduction using R

Author(s)

• Zucchini, W.
• MacDonald, Iain L.
• Langrock, Roland

Bibliographic Information

Hidden Markov models for time series : an introduction using R

Walter Zucchini, Iain L. MacDonald, Roland Langrock

（Monographs on statistics and applied probability, 150）

CRC Press, c2016

2nd ed

Note

References: p. 345-357

Includes indexes

Description and Table of Contents

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

Table of Contents

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

by "Nielsen BookData"

Details

• NCID: BB21551477
• ISBN:
  • 9781482253832
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Boca Raton
• Pages/Volumes: xxviii, 370 p.
• Size: 25 cm
• Classification:
  • LCC : QA280
  • DC22 : 519.5/5
• Subject Headings:
  • LCSH : Time-series analysis
  • LCSH : Markov processes
  • LCSH : R (Computer program language)
• Parent Bibliography ID:
  • BA00231539