Hidden Markov and Other Models for Discretevalued Time Serie

Abstract

Survey of Models A Survey of Models for Discrete-Valued Time Series Introduction: The Need for Discrete-Valued Time Series Models Markov Chains Higher-Order Markov Chains The DARMA models of Jacobs and Lewis Models Based on Thinning The Bivariate Geometric Models of Block, Langberg, and Stoffer Markov Regression Models Parameter-Driven Models State-Spaced Models Miscellaneous Models Discussion Hidden Markov Models The Basic Models Introduction Some Theoretical Aspects of Hidden Markov Models in Speech Processing Hidden Markov Time Series Models: Definition and Notation Correlation Properties Evaluation of the Likelihood Function Distributional Properties Parameter Estimation Identification of Outliers Reversibility Discussion Extensions and Modifications Introduction Models Based on a Second-Order Markov Chain Multinomial-Hidden Markov Models Multivariate Models Models with State-Dependent Probabilities Depending on Covariates Models in Which th e Markov Chain Is Homogeneous but Not Assumed Stationary Models in Which the Markov Chain Is Nonhomogeneous Joint Models for the Numbers of Trials and the Numbers of Successes in Those Trials Discussion Applications Introduction The Durations of Successive Eruptions of the Old Faithful Geyser Epileptic Seizure Counts Births at Edendale Hospital Locomotory Behaviour of Locusta migratoria Wind Direction at Koeberg Evapotranspiration Thinly Traded Shares on the Johannesburt Stock Exchange Daily Rainfall at Durban Homicides and Suicides, Cape Town, 1986-1991 Conclusion Appendices A : Proofs of Results Used in the Derivation of the Baum-Welch Algorithm B: Data