On strongly dependent zero-inflated INAR(1) processes

We consider INAR(1) processes modulated by an unobserved strongly dependent 0-1process. The observed process exhibits zero inflation and long memory. A simple method is proposed for estimating the INAR-parameters without modelling the unobserved modulating process. Asymptotic results for the estimators are derived, and a zero-inflation test is introduced. Asymptotic rejection regions and asymptotic power under long-memory alternatives are derived. A small simulation study illustrates the asymptotic results.