Dealing with uncertainty has been, and continues to be, an important problem to be taken into account in day-to-day activities of companies and governments. The uncertainty about some future values, whether it is the price of energy, the evolution of an epidemic, the intensity of rainfall, etc., poses difficulties for making adequate decisions. Therefore, the development of accurate forecasting models is of great importance. On many occasions, the uncertainty is about future observations that take non-negative integer (counts) values. For the treatment of the corresponding count time series, although the use of traditional models is possible, dedicated models that assume non-negative integer observations present numerous advantages, e.g. point forecasts that are easier to interpret and prediction intervals that will not include unfeasible values. The purpose of this industrial PhD thesis, is to contribute to the state of the art in the context of time series modeling with count data…