Asymptotic Distributions of Unit-Root Tests When the Process Is Nearly Stationary
研究当移动平均多项式的根接近1时，单位根检验统计量的渐近零分布，发现不同检验统计量的渐近性质取决于该根趋近1的速度。
Several test criteria are available for testing the hypothesis that the autoregressive polynomial of an autoregressive moving average process has a single unit root. Schwert (1989), using a Monte Carlo study, investigated the performance of some of the available test criteria. He concluded that the actual levels of the test criteria considered in his study are far from the specified levels when the moving average polynomial also has a root close to 1. This article studies the asymptotic null distribution of the test statistics for testing p = 1 in the model Yt = pY t-1 + e t – 0e t-1 as 0 approaches 1. It is shown that the test statistics differ from one another in their asymptotic properties depending on the rate at which 0 converges to 1.