Part I: Univariate and multivariate models based on thinning

Part II: Modelling and forecasting time series of counts

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, 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 multivariate in the sense that there are counts of several events observed over time and the counts at each time point are correlated. The first talk introduces univariate and multivariate models for time series of counts based on the thinning operator and discusses their statistical and probabilistic properties. The second talk addresses estimation and diagnostic issues and illustrates the inference procedures with simulated and observed data.