Jianxin Wei: Bootstrap unit root test and cointegration rank test

The bad small sample performance of unit root tests is well known and depends partly on the existence of nuisance parameters. To deal with this Johansen (2004) presents a small sample correction of the Dickey-Fuller test. The correction factor depends on biased parameter estimates. The purpose of this study is to, through simulation, compare the small sample correction with a bootstrap approach as well as to analyze the effect of bias adjusting both the small sample correction and the bootstrap. The bootstrap works considerably better than the bias adjusted small sample correction when considering size but not for power.

Further, the bootstrap method, if used correctly gives asymptotic refinement. To be specific, in the unit root test, Park (2003) shows that the error of rejection probability by using bootstrap critical value is of order o(T^-1/2) whereas the error by using asymptotic critical value is of order O(T^-1/2).