O'Reilly logo

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

An Introduction to Discrete-Valued Time Series

Book Description

A much-needed introduction to the field of discrete-valued time series, with a focus on count-data time series

Time series analysis is an essential tool in a wide array of fields, including business, economics, computer science, epidemiology, finance, manufacturing and meteorology, to name just a few. Despite growing interest in discrete-valued time series—especially those arising from counting specific objects or events at specified times—most books on time series give short shrift to that increasingly important subject area. This book seeks to rectify that state of affairs by providing a much needed introduction to discrete-valued time series, with particular focus on count-data time series.

The main focus of this book is on modeling. Throughout numerous examples are provided illustrating models currently used in discrete-valued time series applications. Statistical process control, including various control charts (such as cumulative sum control charts), and performance evaluation are treated at length. Classic approaches like ARMA models and the Box-Jenkins program are also featured with the basics of these approaches summarized in an Appendix. In addition, data examples, with all relevant R code, are available on a companion website.

  • Provides a balanced presentation of theory and practice, exploring both categorical and integer-valued series
  • Covers common models for time series of counts as well as for categorical time series,
  • and works out their most important stochastic properties
  • Addresses statistical approaches for analyzing discrete-valued time series and illustrates their implementation with numerous data examples
  • Covers classical approaches such as ARMA models, Box-Jenkins program and how to generate functions
  • Includes dataset examples with all necessary R code provided on a companion website

An Introduction to Discrete-Valued Time Series is a valuable working resource for researchers and practitioners in a broad range of fields, including statistics, data science, machine learning, and engineering. It will also be of interest to postgraduate students in statistics, mathematics and economics.

Table of Contents

  1. Cover
  2. Title Page
    1. Copyright
    2. Dedication
  3. Preface
  4. About the Companion Website
    1. Chapter 1: Introduction
  5. Part I: Count Time Series
    1. Chapter 2: A First Approach for Modeling Time Series of Counts: The Thinning-based INAR(1) Model
      1. 2.0 Preliminaries: Notation and Characteristics of Count Distributions
      2. 2.1 The INAR(1) Model for Time-dependent Counts
      3. 2.2 Approaches for Parameter Estimation
      4. 2.3 Model Identification
      5. 2.4 Checking for Model Adequacy
      6. 2.5 A Real-data Example
      7. 2.6 Forecasting of INAR(1) Processes
    2. Chapter 3: Further Thinning-based Models for Count Time Series
      1. 3.1 Higher-order INARMA Models
      2. 3.2 Alternative Thinning Concepts
      3. 3.3 The Binomial AR Model
      4. 3.4 Multivariate INARMA Models
    3. Chapter 4: INGARCH Models for Count Time Series
      1. 4.1 Poisson Autoregression
      2. 4.2 Further Types of INGARCH Models
      3. 4.3 Multivariate INGARCH Models
    4. Chapter 5: Further Models for Count Time Series
      1. 5.1 Regression Models
      2. 5.2 Hidden-Markov Models
      3. 5.3 Discrete ARMA Models
  6. Part II: Categorical Time Series
    1. Chapter 6: Analyzing Categorical Time Series
      1. 6.1 Introduction to Categorical Time Series Analysis
      2. 6.2 Marginal Properties of Categorical Time Series
      3. 6.3 Serial Dependence of Categorical Time Series
    2. Chapter 7: Models for Categorical Time Series
      1. 7.1 Parsimoniously Parametrized Markov Models
      2. 7.2 Discrete ARMA Models
      3. 7.3 Hidden-Markov Models
      4. 7.4 Regression Models
  7. Part III: Monitoring Discrete-Valued Processes
    1. Chapter 8: Control Charts for Count Processes
      1. 8.1 Introduction to Statistical Process Control
      2. 8.2 Shewhart Charts for Count Processes
      3. 8.3 Advanced Control Charts for Count Processes
    2. Chapter 9: Control Charts for Categorical Processes
      1. 9.1 Sample-based Monitoring of Categorical Processes
      2. 9.2 Continuously Monitoring Categorical Processes
  8. Part IV: Appendices
  9. Appendix A: Examples of Count Distributions
    1. A.1 Count Models for an Infinite Range
    2. A.2 Count Models for a Finite Range
    3. A.3 Multivariate Count Models
  10. Appendix B: Basics about Stochastic Processes and Time Series
    1. B.1 Stochastic Processes: Basic Terms and Concepts
    2. B.2 Discrete-Valued Markov Chains
    3. B.3 ARMA Models: Definition and Properties
    4. B.4 Further Selected Models for Continuous-valued Time Series
  11. Appendix C: Computational Aspects
    1. C.1 Some Comments about the Use of R
    2. C.2 List of R Codes
    3. C.3 List of Datasets
  12. References
  13. List of Acronyms
  14. List of Notations
    1. Index
  15. End User License Agreement