CAUCHY ESTIMATORS FOR AUTOREGRESSIVE PROCESSES WITH APPLICATIONS TO UNIT ROOT TESTS AND CONFIDENCE INTERVALS
针对自回归过程提出新估计量，其枢轴统计量在所有参数范围内均服从标准正态分布，用于单位根检验和构造置信区间，蒙特卡洛模拟显示其局部检验功效优于普通最小二乘法。
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.