Cauchy estimators for autoregressive processes with applications to unit root tests and confidence intervals

For autoregressive processes, we propose new estimators whose pivotal stati stics 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 t ests that have limiting normal distribution regardless of period of the sea sonality. Using the estimators, confidence intervals of the autoregressive parameters are constructed. A Monte-Carlo simulation for first-order autore gressions shows that the proposed tests for unit roots are locally more pow erful than the tests based on the ordinary least squares estimators. It als o shows that the proposed confidence intervals have shorter average lengths than those of Andrews (1993, Econometrica 61, 139-165) based on the ordina ry least squares estimators when the autoregressive coefficient is close to one.