Stationary count time series models

During the last 20–30 years, there was a remarkable growth in interest on approaches for stationary count time series. We consider popular classes of models for such time series, including thinning‐based models, conditional regression models, and Hidden‐Markov models. We review and compare important members of these model families, having regard to stochastic properties such as the dispersion and autocorrelation structure. Our survey covers univariate and multivariate count data, as well as unbounded and bounded counts. We also discuss an illustrative data example. Besides this critical presentation of the current state‐of‐the‐art, some existing challenges and opportunities for future research are identified. This article is categorized under: Statistical Models > Time Series Models Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms We review and compare popular models for stationary count time series, covering univariate and multivariate, as well as (un)bounded count data.