Time series of counts arise when the interest lies on the number of certain events occur- ring during a specified time interval. Many of these data sets are characterized by low counts, asymmetric distributions, excess zeros, over dispersion, etc, ruling out normal approximations. Thus, during the last decades there has been considerable interest in models for integer-valued time series and a large volume of work is now available in specialized monographs. Among the most successful models for integer-valued time series are the Integer valued AutoRegressive Moving Average, INARMA, models based on the thinning operation. These models are attractive since they are linear-like models for discrete time series which exhibit recognizable correlation structures. Furthermore, in many situations the collected time series are multi- variate in the sense that there are counts of several events observed over time and the counts at each time point are correlated. The talk introduces univariate and multivariate models for time series of counts based on the thinning operator, discusses their statistical and probabilistic properties and addresses estimation and diagnostic issues, illustrating the inference procedures with simulated and observed data.
 Maria Eduarda Silva. Modelling time series of counts: An inar approach. Textos de Matemtica, Departamento de Matemtica da Universidade de Coimbra, 47:107–122, 2015.