Fixed Accuracy Estimation of an Autoregressive Parameter

Abstract

For a first order non-explosive autoregressive process with unknown parameter \beta \in [-1, 1], it is shown that if data are collected according to a particular stopping rule, the least squares estimator of ,B is asymptotically normally distributed uniformly in /8. 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 unconditional limiting distribution when I\betaI = 1.