An Introduction to Discrete-Valued Time Series

Chapter 2A First Approach for Modeling Time Series of Counts: The Thinning-based INAR(1) Model

As a first step towards the analysis and modeling of count time series, we consider an integer-valued counterpart to the conventional first-order autoregressive model, the INAR(1) model of McKenzie (1985). This constitutes a rather simple and easily interpretable Markov model for stationary count processes, but it is also quite powerful due to its flexibility and expandability. In particular, it allows us to introduce some basic approaches for parameter estimation, model diagnostics and statistical inference. These are used in an analogous way also for the more advanced models discussed in Chapters 3–5. The presented models and methods are illustrated with a data example in Section 2.5.

To prepare for our discussion about count time series, however, we start in Section 2.1 with a brief introduction to the notation used in this book, and with some remarks regarding characteristic features of count distributions in general (without a time aspect).

2.0 Preliminaries: Notation and Characteristics of Count Distributions

In contrast to the subsequent sections, here we remove any time aspects and look solely at separate random variables and their distributions. The first aim of this preliminary section is to acquaint the reader with the basic notation used in this book. The second one is to briefly highlight characteristic features of count distributions, which will be useful in identifying ...