For autoregressive processes, we propose new estimators
whose pivotal statistics have the standard normal limiting
distribution for all ranges of the autoregressive parameters.
The proposed estimators are approximately median unbiased.
For seasonal time series, the new estimators give us unit
root tests that have limiting normal distribution regardless
of period of the seasonality. Using the estimators, confidence
intervals of the autoregressive parameters are constructed.
A Monte-Carlo simulation for first-order autoregressions
shows that the proposed tests for unit roots are locally
more powerful than the tests based on the ordinary least
squares estimators. It also shows that the proposed confidence
intervals have shorter average lengths than those of Andrews
(1993, Econometrica 61, 139–165) based on
the ordinary least squares estimators when the autoregressive
coefficient is close to one.