Hidden Markov Models for Time Series An Introduction Using R, Second Edition

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

Model structure, properties and methodsPreliminaries: mixtures and Markov chainsIntroductionIndependent mixture modelsMarkov chainsExercises Hidden Markov models: definition and propertiesA simple hidden Markov modelThe basicsThe likelihoodExercises Direct maximization of the likelihoodIntroductionScaling the likelihood computationMaximization subject to constraintsOther problemsExample: earthquakesStandard errors and confidence intervalsExample: parametric bootstrapExercises Estimation by the EM algorithmForward and backward probabilitiesThe EM algorithmExamples of EM applied to Poisson-HMMsDiscussionExercises Forecasting, decoding and state predictionConditional distributionsForecast distributionsDecodingState predictionHMMs for classificationExercises Model selection and checkingModel selection by AIC and BICModel checking with pseudo-residualsExamplesDiscussionExercises Bayesian inference for Poisson-HMMsApplying the Gibbs sampler to Poisson-HMMsBayesian estimation of the number of statesExample: earthquakesDiscussionExercises R packagesThe package depmixS4The package HiddenMarkovThe package msmThe package R20penBUGSDiscussion ExtensionsGeneral state-dependent distributionsIntroductionUnivariate state-dependent distributionMultinomial and categorical HMMsMultivariate state-dependent distributionExercises Covariates and other extra dependenciesIntroductionHMMs with covariatesHMMs based on a second-order Markox chainHMMs with other additional dependenciesExercises Continuous-valued state processesIntroductionModels with continous-valued state processFitting an SSM to the earthquake dataDiscussion Hidden semi-Markov models as HMMsIntroductionSemi-Markov processes, hidden semi-Markov models and approximating HMMsExamples of HSMMs as HMMsGeneral HSMMR codeSome examples of dwell-time distributionsFitting HSMMs via the HMM representationExample: earthquakesDiscussionExercises HMMs for longitudinal dataIntroductionSome parameters constant across componentsModels with random effectsDiscussionExercises ApplicationsIntroduction to applications Epileptic seizuresIntroductionModels fittedModel checking by pseudo-residualsExercises Daily rainfall occurrenceIntroductionModels fitted Eruptions of the Old Faithful geyserIntroductionThe dataBinary time series of short and long eruptionsNormal-HMMs for durations and waiting timesBivariate model for durations and waiting timesExercises HMMs for animal movementIntroductionDirectional dataHMMs for movement dataBasic HMM for Drosophila movementHMMs and HSMMs for bison movementMixed HMMs for woodpecker movementExercises Wind direction at KoebergIntroductionWind direction classified into 16 categoriesWind direction as a circular variableExercises Models for financial seriesMultivariate HMM for returns on four sharesStochastic volatility modelsExercises Births at Edendale HospitalIntroductionModels for the proportion CaesareanModels for the total number of deliveriesConclusion Homicides and suicides in Cape TownIntroductionFirearm homicides as a proportion of all homicides, suicides and legal intervention homicidesThe number of firearm homicidesFirearm homicide and suicide proportionsProportion in each of the five categories Animal behaviour model with feedbackIntroductionThe modelLikelihood evaluationParameter estimation by maximum likelihoodModel checkingInferring the underlying stateModels for a heterogeneous group of subjectsOther modifications or extensionsApplication to caterpillar feeding behaviourDiscussion Survival rates of Soay sheepIntroductionMRR data without use of covariatesMRR data involving covariate informationApplication to Soay sheep dataConclusion Examples of R codeThe functionsExamples of code using the above functions Some proofsFactorization needed for forward probabilitiesTwo results for backward probabilitiesConditional independence of Xt1 and XTt+1 References Author index Subject index

Walter Zucchini, Iain K. MacDonald, Roland Langrock