THE IMPOSSIBILITY OF CONSISTENT DISCRIMINATION BETWEEN I(0) AND I(1) PROCESSES

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+