Fixed Accuracy Estimation of an Autoregressive Parameter

Abstract : For a first order non-explosive autoregressive process with unknown parameter beta epsilon (1,1), it is shown that if data are collected according to a particular stopping rule, the least squares estimator of beta is asymptotically normally distributed uniformly in beta. In the case of normal residuals, the stopping rule may be interpreted as sampling until the observed Fisher information reaches a preassigned level. The situation is contrasted with the fixed sample size case, where the estimator has a non-normal limiting distribution when (beta) = 1. (Author)