A Continuous Time Approximation to the Unstable First-Order Autoregressive Process: The Case Without an Intercept
研究无截距项的一阶自回归过程，证明当采样间隔趋近于零时，归一化最小二乘估计的渐近分布与Ornstein-Uhlenbeck过程的连续时间估计精确分布相同，并推导矩母函数以列表展示极限分布、密度函数、矩和势函数，该逼近在自回归参数接近1时效果极佳。
We consider a first-order autoregression with i.i.d. errors and a fixed initial condition. The asymptotic distribution of the normalized least-squares estimator as the sampling interval converges to zero is shown to be the same as the exact distribution of the continuous-time estimator in an Ornstein-Uhlenbeck process. This asymptotic distribution permits explicit consideration of the effect of the initial condition. The appropriate moment-generating function is derived and used to tabulate the limiting distribution and probability density functions, the moments and some power functions. The adequacy of this asymptotic approximation is found to be excellent for values of the autoregressive parameter near one and any fixed initial condition. Copyright 1991 by The Econometric Society.