Abstract: We considered an  independent replicatedly observed model of  INAR(1) (PLINAR(1)) process with Poisson-Lindley marginal distribution for overdispersed replicatedly observed time series data. Firstly, by using conditional least squares estimation, Yule-Walker estimation, quasi-likelihood estimation, and conditional maximum likelihood estimation methods to estimate the parameters of the model, we discussed the asymptotic properties of the estimators and gave predictions for the model. Secondly, through numerical simulations, the performance of different estimation methods and the impact of replicated observations were compared. Finally, a data set of the number of sunspot groups per week from replicated observations was fitted to this model, the fitting results validated the effectiveness of the model.

Key words: replicated observation, PLINAR(1) model, integer-valued time series, overdispersion