Exact and bootstrap distributions of a unit root test

Using Imhof's method, the exact distribution of a unit root test is evaluated and detailed critical values are given of the unit root test when the sample size is small and moderate. Then, the bootstrap critical values are generated by Monte Carlo experiments, and compared with the exact ones. The Monte Carlo results show that the bootstrap critical values are reasonably precise. It is also shown that the parametric bootstrap tends to yield more precise estimates of the percentiles than the nonparametric bootstrap.