Optimal jackknife for unit root models

A new jackknife method is introduced to remove the first order bias in unit root models. It is optimal in the sense that it minimizes the variance among all the jackknife estimators of the form considered in Phillips and Yu (2005) and Chambers and Kyriacou (2013) after the number of subsamples is selected. Simulations show that the new jackknife reduces the variance of that of Chambers and Kyriacou by about 10% for any selected number of subsamples without compromising bias reduction. The results continue to hold true in near unit root models.