Approximating Estimators of the First-Order Autoregression

Several approximations to the distribution of estimators in the first-order autoregression are derived and evaluated. The approximations to the least squares estimator are reasonably accurate except when the parameter of the model is close to one. Angular transformations are used to improve the accuracy of the approximations. These work quite well for most cases, especially when they are used with an Edgeworth expansion. An alternative to the least squares estimator developed by Daniels is also considered. Because of its restriction to the unit interval, this estimator is generally better approximated by the approximations derived here.