On L2 convergence of the maximum weighted pairwise likelihood estimators in the AR(1) models

Recently, the strong consistency and asymptotic distribution for the maximum consecutive pairwise likelihood estimators (MCPLE) have been established in the linear time series models. In this paper, the weak convergence of the maximum weighted pairwise likelihood estimator (MWPLE) of the parameters of the AR(1) models is established by using the concept of ???? convergence (convergence in mean square).