Further Thinning‐based Models for Count Time Series
Christian H. Weiß · 2018
After having introduced important tasks and approaches for analyzing count time series in the previous chapter, we shall now return to the question of how to model the underlying process. The main characteristic of the INAR(1) model discussed before is to use the binomial thinning operator as a substitute of the multiplication for being able to transfer the AR(1) recursion to the count data case. In this chapter, we shall see that this approach can also be used to define higher-order ARMA-like models, referred to as the INARMA models. Furthermore, also different types of thinning operation have been developed for such models, to allow for different stochastic properties and alternative interpretation schemes. Finally, various thinning-based models to deal with count time series having a finite range as well as multivariate count time series are meanwhile available in the literature.