Jackknifed Whittle Estimators

The Whittle estimator is widely used in time series analysis. Althoughit is asymptotically Gaussian and efficient, this estimator suffers from large bias,especially when the underlying process has nearly unit roots. In this paper, weapply the jackknife technique to the Whittle likelihood in the frequency domain,and we derive the asymptotic properties of the jackknifed Whittle estimator. Inparticular, the second-order bias of the jackknifed estimator is shown to vanish fornon-Gaussian stationary processes when the unknown parameter is innovation-free.The effectiveness of the jackknife technique for reducing the bias of the Whittleestimator is demonstrated in numerical studies. Since the Whittle estimator isapplicable in many fields, including the natural sciences, signal processing, andeconometrics, the bias-reduced jackknifed Whittle estimator can have widespreaduse.