A Continuous Time Approximation to the Stationary First-Order Autoregressive Model
研究了平稳一阶自回归模型中最小二乘估计量的连续时间渐近分布，推导了矩生成函数以计算百分位数和矩，发现自回归参数接近1时近似效果极佳，并揭示了检验功效函数的非单调性质。
We consider the least-squares estimator in a strictly stationary first-order autoregression without an estimated intercept. We study its continuous time asymptotic distribution based on an asymptotic framework where the sampling interval converges to zero as the sample size increases. We derive a momentgenerating function which permits the calculation of percentage points and moments of this asymptotic distribution and assess the adequacy of the approximation to the finite sample distribution. In general, the approximation is excellent for values of the autoregressive parameter near one. We also consider the behavior of the power function of tests based on the normalized leastsquares estimator. Interesting nonmonotonic properties are uncovered. This analysis extends the study of Perron [15] and helps to provide explanations for the finite sample results established by Nankervis and Savin [13].