Further Models for Count Time Series
Christian H. Weiß · 2018
The INARMA and INGARCH approaches became very popular during the last years if being concerned with the modeling of stationary and ARMA-like count processes. But also beyond these models, a large number of further models for count time series have been proposed in the literature. Three of these alternatives are presented in the sequel: regression models, Hidden-Markov models and NDARMA models. The main advantage of regression models is their ability to incorporate covariate information. We discuss common types of generalized linear models, where the conditional mean is “linked” to a linear expression of the available information (past obervations plus covariates). Often a log link is used in practice, whereas the INGARCH models discussed in Chapter 4 might be understood as regression models using the identity link. Hidden-Markov models are a type of parameter-driven model for count processes, where the hidden state process constitutes a finite Markov chain. The NDARMA models generate an ARMA-like dependence structure through some kind of random mixture. These three classes of models are of relevance also in Chapter 7 about the modeling of categorical time series, because they are easily modified to handle such kind of data.