In this paper, a modified two-stage procedure in the Autoregressive model AR(1) is considered, which investigates the point and the interval estimation of the mean based on the least-squares estimator. The modified two-stage procedure is as effective as the best fixed-sample size procedure. In this regard, the significant properties of the procedure, including asymptotic risk efficiency, first-order efficiency, consistent, and asymptotic distribution of the mean, are established. Then, a Monte Carlo simulation study is deduced to investigate the modified two-stage procedure. The performance of estimators and confidence intervals are evaluated utilizing a simulation study. Finally, real-time series data is considered to illustrate the applicability of the modified two-stage procedure.
Mahmoudi E, Sajjadipanah S, Zamani M S. Modified Two-Stage Sampling Around the Mean of the First-Order Autoregressive Model. JSS 2022; 16 (1) :127-148 URL: http://jss.irstat.ir/article-1-783-en.html