Statistica Sinica 22 (2012), 1287-1304

JACKKNIFED WHITTLE ESTIMATORS

Masanobu Taniguchi$^{1}$, Kenichiro Tamaki$^{1}$,

Thomas J. DiCiccio$^{2}$ and Anna Clara Monti$^{3}$

$^{1}$Waseda University, $^{2}$Cornell University and $^{3}$University of Sannio

Abstract: The Whittle estimator (Whittle (1962)) is widely used in time series analysis. Although it is asymptotically Gaussian and efficient, this estimator suffers from large bias, especially when the underlying process has nearly unit roots. In this paper, we apply the jackknife technique to the Whittle likelihood in the frequency domain, and we derive the asymptotic properties of the jackknifed Whittle estimator. In particular, the second-order bias of the jackknifed estimator is shown to vanish for non-Gaussian stationary processes when the unknown parameter is innovation-free. The effectiveness of the jackknife technique for reducing the bias of the Whittle estimator is demonstrated in numerical studies. Since the Whittle estimator is applicable in many fields, including the natural sciences, signal processing, and econometrics, the bias-reduced jackknifed Whittle estimator can have widespread use.

Key words and phrases: Asymptotic efficiency, innovation-free, jackknife, second-order bias, spectral density, stationary process, Whittle estimator.