An Introduction to Discrete-Valued Time Series.

Cover -- Title Page -- Copyright -- Dedication -- Contents -- Preface -- About the Companion Website -- Chapter 1 Introduction -- Part I Count Time Series -- Chapter 2 A First Approach for Modeling Time Series of Counts: The Thinning‐based INAR(1) Model -- 2.0 Preliminaries: Notation and Characteristics of Count Distributions -- 2.1 The INAR(1) Model for Time‐dependent Counts -- 2.1.1 Definition and Basic Properties -- 2.1.2 The Poisson INAR(1) Model -- 2.1.3 INAR(1) Models with More General Innovations -- 2.2 Approaches for Parameter Estimation -- 2.2.1 Method of Moments -- 2.2.2 Maximum Likelihood Estimation -- 2.3 Model Identification -- 2.4 Checking for Model Adequacy -- 2.5 A Real‐data Example -- 2.6 Forecasting of INAR(1) Processes -- Chapter 3 Further Thinning‐based Models for Count Time Series -- 3.1 Higher‐order INARMA Models -- 3.2 Alternative Thinning Concepts -- 3.3 The Binomial AR Model -- 3.4 Multivariate INARMA Models -- Chapter 4 INGARCH Models for Count Time Series -- 4.1 Poisson Autoregression -- 4.2 Further Types of INGARCH Models -- 4.3 Multivariate INGARCH Models -- Chapter 5 Further Models for Count Time Series -- 5.1 Regression Models -- 5.2 Hidden‐Markov Models -- 5.3 Discrete ARMA Models -- Part II Categorical Time Series -- Chapter 6 Analyzing Categorical Time Series -- 6.1 Introduction to Categorical Time Series Analysis -- 6.2 Marginal Properties of Categorical Time Series -- 6.3 Serial Dependence of Categorical Time Series -- Chapter 7 Models for Categorical Time Series -- 7.1 Parsimoniously Parametrized Markov Models -- 7.2 Discrete ARMA Models -- 7.3 Hidden‐Markov Models -- 7.4 Regression Models -- Part III Monitoring Discrete‐Valued Processes -- Chapter 8 Control Charts for Count Processes -- 8.1 Introduction to Statistical Process Control -- 8.2 Shewhart Charts for Count Processes.

8.2.1 Shewhart Charts for i.i.d. Counts -- 8.2.2 Shewhart Charts for Markov‐Dependent Counts -- 8.3 Advanced Control Charts for Count Processes -- 8.3.1 CUSUM Charts for i.i.d. Counts -- 8.3.2 CUSUM Charts for Markov‐dependent Counts -- 8.3.3 EWMA Charts for Count Processes -- Chapter 9 Control Charts for Categorical Processes -- 9.1 Sample‐based Monitoring of Categorical Processes -- 9.1.1 Sample‐based Monitoring: Binary Case -- 9.1.2 Sample‐based Monitoring: Categorical Case -- 9.2 Continuously Monitoring Categorical Processes -- 9.2.1 Continuous Monitoring: Binary Case -- 9.2.2 Continuous Monitoring: Categorical Case -- Part IV Appendices -- Appendix A Examples of Count Distributions -- A.1 Count Models for an Infinite Range -- A.2 Count Models for a Finite Range -- A.3 Multivariate Count Models -- Appendix B Basics about Stochastic Processes and Time Series -- B.1 Stochastic Processes: Basic Terms and Concepts -- B.2 Discrete‐Valued Markov Chains -- B.2.1 Basic Terms and Concepts -- B.2.2 Stationary Markov Chains -- B.3 ARMA Models: Definition and Properties -- B.4 Further Selected Models for Continuous‐valued Time Series -- B.4.1 GARCH Models -- B.4.2 VARMA Models -- Appendix C Computational Aspects -- C.1 Some Comments about the Use of R -- Computation and Simulation for Count Models -- Stationary Marginal Distribution of Markov Chains -- Simulation of Count Processes -- Numerical Maximum Likelihood Estimation -- Categorical Random Variables -- Eigenvalues and Sparse Matrices -- C.2 List of R Codes -- C.3 List of Datasets -- References -- List of Acronyms -- List of Notations -- Index -- EULA.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.