Imputation-based semiparametric estimation for INAR(1) processes with missing data

In applied problems parameter estimation with missing data has risen as a hot topic. Imputation for ignorable incomplete data is one of the most popular methods in integer-valued time series. For data missing not at random insert ignore into journalissuearticles values(MNAR);, estimators directly derived by imputation will lead results that is sensitive to the failure of the effectiveness. In view of the first-order integer-valued autoregressive insert ignore into journalissuearticles values(INARinsert ignore into journalissuearticles values(1);); processes with MNAR response mechanism, we consider an imputation based semiparametric method, which recommends the complete auxiliary variable of Yule-Walker equation. Asymptotic properties of relevant estimators are also derived. Some simulation studies are conducted to verify the effectiveness of our estimators, and a real example is also presented as an illustration.