Statistical inference for the binomial Ar(1) model with missing data

In recent years, the binomial AR(1) model has been widely used in modeling time series of counts with finite range, such as rainfall prediction, process quality control, research of financial data, disease prevention and control, etc. However, in real-life applications, time series data often exhibit incompleteness missing samples, due to some sensor malfunctions or human errors, such as data input error, measurement error, experimental error or intentional abnormal value etc. In this article, we consider the statistical inference for the binomial AR(1) model with missing data. We first use the conditional least squares and conditional maximum likelihood methods with no imputation (NI) based on incomplete data. Then, we consider the imputation methods. We use the mean imputation, the bridge imputation, and the imputation based on likelihood, of which the last two methods are based on iterative schemes. The performance of the algorithm is shown in the simulation study. Finally, we illustrate our method by presenting a real-data example.