Detrending Bootstrap Unit Root Tests

The role of detrending in bootstrap unit root tests is investigated. When bootstrapping, detrending must not only be done for the construction of the test statistic, but also in the first step of the bootstrap algorithm. It is argued that the two issues should be treated separately. Asymptotic validity of sieve bootstrap augmented Dickey.Fuller (ADF) unit root tests is shown for test statistics based on full sample and recursive ordinary least squares (OLS) and generalized least squares (GLS) detrending. It is also shown that the detrending method in the first step of the bootstrap may differ from the one used in the construction of the test statistic. A simulation study is conducted to analyze the effects of detrending on finite sample performance of the bootstrap test. It is found that full sample OLS detrending should be preferred based on power in the first step of the bootstrap algorithm, and that the decision about the detrending method used to obtain the test statistic should be based on the power properties of the corresponding asymptotic tests.