Modified fast double sieve bootstraps for ADF tests

This paper studies the finite sample performance of the sieve bootstrap augmented Dickey-Fuller (ADF) unit root test. It is well known that this test’s accuracy in terms of rejection probability under the null depends greatly on the underlying DGP. Through extensive simulations, we find that it also depends on the numbers of lags employed in the bootstrap DGP and in the bootstrap ADF regression. Based on this finding and using some well established theoretical results, we propose a simple modification that significantly improves the test’s accuracy. We also introduce different versions of the fast double bootstrap, each modified according to the same theoretical basis. According to our simulations, these new testing procedures have lower error in rejection probability under the null while retaining good power.