Title: Model Selection for Explosive Models,
Abstract: This paper examines the limit properties of information criteria (such as
AIC, BIC, HQIC) for distinguishing between the unit root model and the various
kinds of explosive models. The explosive models include the local-to-unit-root
model, the mildly explosive model and the regular explosive model. Initial
conditions with different order of magnitude are considered. Both the OLS
estimator and the indirect inference estimator are studied. It is found that
BIC and HQIC, but not AIC, consistently select the unit root model when data
come from the unit root model. When data come from the local-to-unit-root
model, both BIC and HQIC select the wrong model with probability approaching 1
while AIC has a positive probability of selecting the right model in the limit.
When data come from the regular explosive model or from the mildly explosive
model in the form of $1+n^{\alpha }/n$ with $\alpha \in (0,1)$, all three
information criteria consistently select the true model. Indirect inference
estimation can increase or decrease the probability for information criteria to
select the right model asymptotically relative to OLS, depending on the
information criteria and the true model. Simulation results confirm our
asymptotic results in finite sample.