Two-stage Procedure in P-Order Autoregressive Process

In this paper, the two-stage procedure is considered for autoregressive parameters estimation in the p-order autoregressive model ( AR(p)). The point estimation and fixed-size confidence ellipsoids construction are investigated which are based on least-squares estimators. Performance criteria are shown including asymptotically risk efficient, asymptotically efficient, and asymptotically consistent. Monte Carlo simulation studies are conducted to investigate the performance of the two-stage procedure. Finally, real-time-series data is provided to investigate to the applicability of the two-stage procedure.