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 (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 (INAR(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.