Can you do the wrong thing and still be right? Hypothesis Testing in I(2) and near-I(2) cointegrated VARs

We review the I(2) model with a focus on its application to near-I(2) data, i.e. I(1) data with a second root very close to unity, and report the results of some Monte Carlo experiments. We show that with I(2) data tests on the long-run coefficients in the I(2) model have small sample properties consistent with asymptotic results. More importantly, we show also that with near-I(2) data the properties of the tests are (i) similar to those found with genuine I(2) data, (ii) systematically superior to those of the analogous tests constructed in the I(1) model, even if the latter is in principle correctly specified and the former is not. Our results thus provide strong support to the suggestion to model near-I(2) data using the I(2) model.