Hidden Markov Models for Time Series

Hidden Markov Models for Time Series : An Introduction Using R

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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.
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Product details

  • Hardback | 288 pages
  • 154.94 x 231.14 x 22.86mm | 544.31g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 64 black & white illustrations, 63 black & white tables
  • 1584885734
  • 9781584885733
  • 1,042,663

Review quote

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. -Journal 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. -Biometrics, 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. -Australian & 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. -International Statistical Review (2011), 79, 1
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About Iain L. MacDonald

University of Gottingen, Germany University of Cape Town, South Africa University College, London, UK Stanford University, California, USA Johns Hopkins Bloomberg School of Public Health, MD, USA London School of Economics, UK London School of Economics, UK University of Copenhagen, Denmark
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Table of contents

MODEL STRUCTURE, PROPERTIES, AND METHODS Mixture Distributions and Markov Chains Introduction 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 Introduction 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 Discussion Forecasting, Decoding, and State Prediction Conditional distributions Forecast distributions Decoding State prediction Model Selection and Checking Model selection by AIC and BIC Model checking with pseudo-residuals Examples Discussion Bayesian Inference for Poisson HMMs Applying the Gibbs sampler to Poisson HMMs Bayesian estimation of the number of states Example: earthquakes Discussion Extensions of the Basic Hidden Markov Model Introduction 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 APPLICATIONS Epileptic Seizures Introduction Models fitted Model checking by pseudo-residuals Eruptions of the Old Faithful Geyser Introduction 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 Introduction Von Mises distributions Von Mises HMMs for the two subjects Circular autocorrelation functions Bivariate model Wind Direction at Koeberg Introduction 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 Introduction Models for the proportion Caesarean Models for the total number of deliveries Conclusion Cape Town Homicides and Suicides Introduction 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 Introduction 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 Discussion 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 References Author Index Subject Index Exercises appear at the end of most chapters.
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