book

An Introduction to Discrete-Valued Time Series

by Christian H. Weiss

February 2018

Intermediate to advanced

304 pages

9h 55m

English

Wiley

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2.0 Preliminaries: Notation and Characteristics of Count Distributions2.1 The INAR(1) Model for Time-dependent Counts2.2 Approaches for Parameter Estimation2.3 Model Identification2.4 Checking for Model Adequacy2.5 A Real-data Example2.6 Forecasting of INAR(1) Processes
3.1 Higher-order INARMA Models3.2 Alternative Thinning Concepts3.3 The Binomial AR Model3.4 Multivariate INARMA Models

4.1 Poisson Autoregression4.2 Further Types of INGARCH Models4.3 Multivariate INGARCH Models
5.1 Regression Models5.2 Hidden-Markov Models5.3 Discrete ARMA Models
6.1 Introduction to Categorical Time Series Analysis6.2 Marginal Properties of Categorical Time Series6.3 Serial Dependence of Categorical Time Series
7.1 Parsimoniously Parametrized Markov Models7.2 Discrete ARMA Models7.3 Hidden-Markov Models7.4 Regression Models
8.1 Introduction to Statistical Process Control8.2 Shewhart Charts for Count Processes8.3 Advanced Control Charts for Count Processes
9.1 Sample-based Monitoring of Categorical Processes9.2 Continuously Monitoring Categorical Processes
A.1 Count Models for an Infinite RangeA.2 Count Models for a Finite RangeA.3 Multivariate Count Models
B.1 Stochastic Processes: Basic Terms and ConceptsB.2 Discrete-Valued Markov ChainsB.3 ARMA Models: Definition and PropertiesB.4 Further Selected Models for Continuous-valued Time Series
C.1 Some Comments about the Use of RC.2 List of R CodesC.3 List of Datasets

Content preview from An Introduction to Discrete-Valued Time Series

Appendix B

Basics about Stochastic Processes and Time Series

This Appendix Aims to provide a brief survey of some relevant terms and concepts from a basic course about stochastic processes and (continuous-valued) time series analysis. Many more details can be found in introductory textbooks such as those by Box et al. (2015), Brockwell & Davis (2016), Cryer & Chan (2008), Falk et al. (2012), Shumway & Stoffer (2011) and Wei (2006). For Section B.4.2, Lütkepohl (2005) is also recommended as a comprehensive textbook about multivariate time series. For the Markov chains discussed in Section B.2, the book by Seneta (1983) offers a lot of further detail.

B.1 Stochastic Processes: Basic Terms and Concepts

A (discrete-time) stochastic process (or simply process) is a sequence $c0B-math-001$ of random variables $c0B-math-002$ defined on a probability space $c0B-math-003$ and with range $c0B-math-004$ (the state space of the process), where $c0B-math-005$ is a discrete and linearly ordered set. For simplicity, we usually choose or . We distinguish between continuous-valued ...