A simple INAR(1) model for analyzing count time series with multiple features

Count time series frequently exhibit multiple features such as zero inflation, zero deflation, overdispersion, and underdispersion. In practice, heavy-tailedness and zero truncation are also suffered but are less investigated. To better handle count time series with the above statistical characteristics, we introduce a simple INAR(1) process with zero-distorted generalized geometric innovations, which has the advantage of being capable of capturing all the above features. Probabilistic and statistical properties of the process are explored and estimators of the model parameters are derived by the Yule-Walker, conditional least squares, conditional maximum likelihood, and Bayesian methods. Finally, the new model is also employed to analyze the following three real data examples. Firstly, we consider the website traffic counts, which implies that the new model can take into account count time series with overdispersion, zero inflation, and heavy-tailedness. Secondly, we demonstrate the usefulness of the new model in describing underdispersed and zero-deflated count time series via an application to the number of examination room of the emergency department of a children’s hospital. Thirdly, we employ the new model to the monthly shifted counts of robbery, which indicates the new model can better handle zero-truncated count times series.