We examine some of the consequences on commonly used unit root tests when the underlying series is integrated of order two. It turns out that standard augmented Dickey-Fuller type of tests for a single unit root have excessive density in the explosive region of the distribution. The lower (stationary) tail, however, will be virtually unaffected in the presence of double unit roots. On the other hand, the Phillips-Perron test is shown to diverge to plus infinity asymptotically and thus will favor the explosive alternative. Numerical simulations are used to demonstrate the analytical results and some of the implications in finite samples.

当基本级数是二阶积分时，我们检查一些常用的单位根检验的结果。结果表明，对于单个单位根的标准扩增Dickey-Fuller类型的测试在爆炸区域的分布密度过高。较低的(静止的)尾，然而，将几乎不受影响的存在双单位根。另一方面，Phillips-Perron检验渐近发散到正无穷，因此倾向于爆炸替代。数值模拟结果表明，分析结果和一些影响有限样本。