Three Essays In Nonstationary Time Series

Maximum likelihood estimation of the persistence parameter in the discrete time unit root model is known for suffering from a downward bias. The bias is more pronounced in the continuous time unit root model. Recently Chambers and Kyriacou (2010) introduced a new jackknife method to remove the first order bias in the estimator of the persistence parameter in a discrete time unit root model. This paper proposes an improved jackknife estimator of the persistence parameter that works for both the discrete time unit root model and the continuous time unit root model. The proposed jackknife estimator is optimal in the sense that it minimizes the variance. Simulations highlight the performance of the proposed method in both contexts. They show that our optimal jackknife reduces the variance of the jackknife method of Chambers and Kyriacou by around 10% in both cases and the results continue to hold in near unit root cases.