Abstract :
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+
