A new INAR(1) process with bounded support for counts showing equidispersion, underdispersion and overdispersion

The present work introduces a mixture INAR(1) model based on the mixing Pegram and binomial thinning operators with a finite range {0,1, horizontal ellipsis ,n} The new model can be used to handle equidispersion, underdispersion, overdispersion, zero-inflation and multimodality. Several probabilistic and statistical properties are explored. Estimators of the model parameters are derived by the conditional maximum likelihood method. The asymptotic properties and numerical results of the estimators are also studied. In addition, the forecasting problem is addressed. Applications to real data sets are given to show the application of the new model.

Automated summary

This paper introduces a new mixture INAR(1) model, which can handle various situations. Estimators of the model parameters are derived by the conditional maximum likelihood method, and the asymptotic properties of the estimators are studied. Applications to real data sets demonstrate the usefulness of the new model.