THE IMPOSSIBILITY OF CONSISTENT DISCRIMINATION BETWEEN I(0) AND I(1) PROCESSES
证明，按照标准定义（I(0)过程满足泛函中心极限定理，I(1)过程的一阶差分为I(0)），无法一致地判断一个过程是I(0)还是I(1）；同时存在一致的单位根检验和非平凡的不一致平稳性检验。
An I(0) process is commonly defined as a process that satisfies a functional central limit theorem, i.e., whose scaled partial sums converge weakly to a Wiener process, and an I(1) process as a process whose first differences are I(0). This paper establishes that with this definition, it is impossible to consistently discriminate between I(0) and I(1) processes. At the same time, on a more constructive note, there exist consistent unit root tests and also nontrivial inconsistent stationarity tests with correct asymptotic size.