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.
CITATION STYLE
Lai, T. L., & Siegmund, D. (2007). Fixed Accuracy Estimation of an Autoregressive Parameter. The Annals of Statistics, 11(2). https://doi.org/10.1214/aos/1176346154
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