Abstract :
This paper considers the information available to invariant unit root tests at and
near the unit root+ Because all invariant tests will be functions of the maximal
invariant, the Fisher information in this statistic will be the available information+
The main finding of the paper is that the available information for all tests invariant
to a linear trend is zero at the unit root+ This result applies for any sample
size, over a variety of distributions and correlation structures, and is robust to the
inclusion of any other deterministic component+ In addition, an explicit upper bound
upon the power of all invariant unit root tests is shown to depend solely upon the
information+ This bound is illustrated via a brief simulation study that also examines
the impact that different invariance requirements have on power+
