Chapter 5Further Models for Count Time Series
The INARMA and INGARCH approaches described above have become very popular in recent years for the modeling of stationary and ARMA-like count processes. But a large number of other count time series models has also been proposed in the literature. Three of these alternatives are presented in this chapter: regression models in Section 5.1, hidden-Markov models in Section 5.2, and NDARMA models in Section 5.3.
5.1 Regression Models
A traditional approach for modeling count data (not just time series data) are regression models. The main advantage of regression models is their ability to incorporate covariate information (although also extensions of, for example, the INARMA models have been developed that include covariate information; see Remark 3.1.7). Here, we will review some of these regression models for count time series. Among others, we consider the observation-driven Markov models proposed by Zeger & Qaqish (1988) in Example 5.1.3, which had a groundbreaking effect for research on count time series similar to the work of McKenzie (1985) and Al-Osh & Alzaid (1987) on the thinning-based INAR(1) model (Section 2.2). It will become clear that the INGARCH model discussed in Chapter 4.1 can be understood as an instance of the family of count regression models. A much more detailed discussion of regression models for count time series can be found in Chapter 4 of the book by Kedem & Fokianos (2002); further recent references on ...
Get An Introduction to Discrete-Valued Time Series now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.