Fixed Accuracy Estimation of an Autoregressive Parameter

For a first order non-explosive autoregressive process with unknown parameter -1, 1, it is shown that if data are collected according to a particular stopping rule, the least squares estimator of is asymptotically normally distributed uniformly in. 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 || = 1.