Introduction to Discrete-Valued Time Series

CHRISTIAN H. WEISS is a professor in the Department of Mathematics and Statistics, Helmut Schmidt University, Hamburg, Germany. His main area of research is discrete-valued time series. He has published numerous articles in this area and given lectures about time series analysis and discrete-valued time series. He has also written five lecture books in German.

• Preface xiAbout the CompanionWebsite xv1 Introduction 1Part I Count Time Series 92 A First Approach for Modeling Time Series of Counts: TheThinning-based INAR(1)Model 112.0 Preliminaries: Notation and Characteristics of Count Distributions 112.1 The INAR(1) Model for Time-dependent Counts 162.1.1 Definition and Basic Properties 172.1.2 The Poisson INAR(1) Model 202.1.3 INAR(1) Models with More General Innovations 222.2 Approaches for Parameter Estimation 262.2.1 Method of Moments 262.2.2 Maximum Likelihood Estimation 282.3 Model Identification 292.4 Checking for Model Adequacy 322.5 A Real-data Example 342.6 Forecasting of INAR(1) Processes 373 Further Thinning-based Models for Count Time Series 433.1 Higher-order INARMA Models 433.2 Alternative Thinning Concepts 543.3 The Binomial AR Model 593.4 Multivariate INARMA Models 644 INGARCH Models for Count Time Series 734.1 Poisson Autoregression 734.2 Further Types of INGARCH Models 854.3 Multivariate INGARCH Models 935 Further Models for Count Time Series 955.1 Regression Models 955.2 Hidden-Markov Models 1075.3 Discrete ARMA Models 116Part II Categorical Time Series 1196 Analyzing Categorical Time Series 1216.1 Introduction to Categorical Time Series Analysis 1226.2 Marginal Properties of Categorical Time Series 1266.3 Serial Dependence of Categorical Time Series 1287 Models for Categorical Time Series 1337.1 Parsimoniously Parametrized Markov Models 1337.2 Discrete ARMA Models 1397.3 Hidden-Markov Models 1467.4 Regression Models 151Part III Monitoring Discrete-Valued Processes 1618 Control Charts for Count Processes 1638.1 Introduction to Statistical Process Control 1638.2 Shewhart Charts for Count Processes 1658.2.1 Shewhart Charts for i.i.d. Counts 1668.2.2 Shewhart Charts for Markov-Dependent Counts 1718.3 Advanced Control Charts for Count Processes 1778.3.1 CUSUM Charts for i.i.d. Counts 1788.3.2 CUSUM Charts for Markov-dependent Counts 1828.3.3 EWMA Charts for Count Processes 1869 Control Charts for Categorical Processes 1939.1 Sample-based Monitoring of Categorical Processes 1949.1.1 Sample-based Monitoring: Binary Case 1949.1.2 Sample-based Monitoring: Categorical Case 1989.2 Continuously Monitoring Categorical Processes 2039.2.1 Continuous Monitoring: Binary Case 2039.2.2 Continuous Monitoring: Categorical Case 209Part IV Appendices 213A Examples of Count Distributions 215A.1 Count Models for an Infinite Range 215A.2 Count Models for a Finite Range 221A.3 Multivariate Count Models 223B Basics about Stochastic Processes and Time Series 229B.1 Stochastic Processes: Basic Terms and Concepts 229B.2 Discrete-Valued Markov Chains 233B.2.1 Basic Terms and Concepts 233B.2.2 Stationary Markov Chains 236B.3 ARMA Models: Definition and Properties 238B.4 Further Selected Models for Continuous-valued Time Series 243B.4.1 GARCH Models 243B.4.2 VARMA Models 245C Computational Aspects 249C.1 Some Comments about the Use of R 250C.2 List of R Codes 253C.3 List of Datasets 256References 257List of Acronyms 275List of Notations 277Index 279

Select Guide Rating