A geometric minification integer-valued autoregressive model

Abstract

In this manuscript we introduce a new minification integer-valued autoregressive model of the first-order motivated to solve the problem which can arise when the binomial thinning or the negative binomial thinning operator are used. Namely, if one of these thinning operators is used in construction of the minification model, then it is possible that the model becomes zero constantly over time. As a solution for this problem, we construct a minification model by using a modification of the negative binomial thinning operator. Many important properties of the introduced model are derived and these properties are applied for the estimation of the unknown parameters and used to show the applicability and adequacy of the model. Three estimation methods are considered and the performances of the obtained estimates by these methods are checked through some simulations for different true values of the parameters. The performances of one-step-ahead predictions based on our model and four competitive models are checked through Monte-Carlo simulations. We have shown that our model with geometric marginal distributions can provide better fit in comparison with these competitive models applied to the well-known polio real data set. Finally, the adequacy of the model on this real data set is proved by using the parametric bootstrap approach.