Bootstrap unit root tests : a Monte Carlo investigation

Abstract

In this study we investigate the finite-sample performance of some of the existing bootstrap unit root tests in terms of size and power by means of an extensive Monte Carlo study. Comparing the performance of these bootstrap tests to that of popular parametric unit root tests, such as the Dickey--Fuller and Elliott--Rothenberg--Stock tests, we find that the bootstrap-based unit root tests are less prone to size distortions frequently caused by autoregressive and moving average components in the innovations of the data generating process. Moreover, some of the bootstrap tests also seem to be more robust against forms of conditional heteroskedasticity in the innovations. In terms of power the performance of the bootstrap unit root tests are comparable to that of the well-established parametric tests. Furthermore, we discuss some practical considerations valuable in the implementation of these bootstrap unit root tests, such as an optimal method of selecting the lag parameter required in most unit root tests. We provide the reader with a practical field guide documenting in detail the most successful bootstrap unit root testing procedures, which are scattered across 20 years of statistical literature. In addition, we provide an informative review of the relevant statistical literature, which includes discussions on bootstrap procedures for independent and dependent data. The study is concluded with an application of the considered unit root tests to real-world data.