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

Chapter 7Models for Categorical Time Series

As in Part I, Markov models are very attractive for categorical processes, because of the ease of interpreting the model, making likelihood inferences (see Remark B.2.1.2 in the appendix) and making forecasts. However, without further restrictions concerning the conditional distributions, the number of model parameters becomes quite large. Therefore, Section 7.1 presents approaches for defining parsimoniously parametrized Markov models. One of these approaches is linked to a family of discrete ARMA models, which exhibit an ARMA-like serial dependence structure and allow also for non-Markovian forms of dependence; see Section 7.2. Note that the count data version of this model was discussed in Section 5.3. Two other approaches from Chapter 5, namely hidden-Markov models and regression models, can also be adapted to the categorical case, as described in Sections 7.3 and 7.4, respectively.

7.1 Parsimoniously Parametrized Markov Models

Perhaps the most obvious approach to model a categorical process $c07-math-001$ with state space $c07-math-002$ is to use a (homogeneous) pth-order Markov model; see (B.1) for the definition: