Modelling Time Series of Counts: an Inar Approach

Abstract. Time series of counts arise when the interest lies on the number of certain events occurring during a specified time interval. Many of these data sets are characterized by low counts, asymmetric distributions, excess zeros, over dispersion, ruling out normal approximations. Several approaches and diversified models that explicitly account for the discreteness of the data have been considered in the literature, among which are the INteger-valued AutoRegressive, INAR, models. These models are based on random operations which, operating on discrete variables ensure an integer-valued result. The INAR models are attractive since they are linear-like models for discrete time series and exhibit recognizable correlation structures. This paper considers INAR models for analyzing time series of counts and discusses associated statistical inference, comprising estimation, diagnostics and model assessment.