"Simulating properties of the likelihood ratio test for a unit root
in an explosive second order autoregression"
Bent Nielsen and James Reade
Department of Economics, University of Oxford
Abstract:
This paper provides a means of accurately simulating explosive
autoregressive processes, and uses this method to analyse the
distribution of the likelihood ratio test statistic for an explosive
second order autoregressive process. Nielsen (2001) has shown that
for the asymptotic distribution of the likelihood ratio unit root
test statistic in a higher order autoregressive model, the
assumption that the remaining roots are stationary is unnecessary,
and as such the approximating asymptotic distribution for the test
in the difference stationary region is valid in the explosive region
also. However, simulations of statistics in the explosive region are
beset by the magnitude of the numbers involved, which cause numerical
inaccuracies, and this has previously constituted a bar on supporting
asymptotic results by means of simulation, and analysing the finite
sample properties of tests in the explosive region.
Keywords: Envelope power function, maximal invariant parameter,
maximal invariant statistic, most stringent test, unit root tests.