Model Selection for Explosive Models

This chapter examines the limit properties of information criteria (such as AIC, BIC, and HQIC) for distinguishing between the unit-root (UR) model and the various kinds of explosive models. The explosive models include the local-to-unit-root model from the explosive side the mildly explosive (ME) model, and the regular explosive model. Initial conditions with different orders 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 UR model when data come from the UR model. When data come from the local-to-unit-root model from the explosive side, 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 ME model in the form of 1 +nα/nwithα∈ (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.