"Power of tests for unit roots in the presence of a linear trend"
Bent Nielsen
Nuffield College, University of Oxford
Abstract:
Dickey and Fuller (1981) suggested unit root tests for an
autoregressive model with a linear trend and a fixed initial value.
This model has nuisance parameters so later authors have often
worked with a slightly different model with a random initial value
in which nuisance parameters can be eliminated by an invariant
reduction of the model. This facilitates computation of envelope
power functions and comparison of the relative performance of
different unit root tests. It is shown here that invariance
arguments also can be used when comparing power within the model
with fixed initial value. Despite the apparently small difference
between the two models the relative performance of unit root tests
turns out to be very different.
Keywords: Envelope power function, maximal invariant parameter,
maximal invariant statistic, most stringent test, unit root tests.