An overview of ARMA-like models for count and binary data

A comprehensive overview of the literature on models for discrete valued time series is provided, with a special focus on count and binary data. ARMAlike models such as the BARMA, GARMA, M-GARMA, GLARMA and log-linear Poisson are illustrated in detail and critically compared. Methods for deriving the stochastic properties of specific models are delineated and likelihood-based inference is discussed. The review is concluded with two empirical applications. The first regards the analysis of the daily number of deaths from COVID-19 in Italy, under the assumption both of a Poisson and a negative binomial distribution for the data generating process. The second illustration analyses the binary series of signs of log-returns for the weekly closing prices of Johnson & Johnson with BARMA and Bernoulli GARMA and GLARMA models.