Statistica Sinica 10(2000), 191-201

INFORMATION PROPERTIES IN SPECTRAL ANALYSIS

OF STATIONARY TIME SERIES

Wei Jiang$^*$, Shaochuan Cheng$^{\dagger}$, Youmin Xi$^{\dagger}$ and Shouyang Wang $^{\dagger\dagger}$

$^*$Hong Kong University of Science and Technology, $^{\dagger}$Xi'an Jiaotong University

and $^{\dagger\dagger}$Chinese Academy of Sciences

Abstract: In this paper, we investigate some information properties of parameter estimation in spectral analysis of stationary time series based on a geometrical framework. Stationary ARMA models are studied as a submanifold in the exponential family and the so-called Whittle estimator is analyzed in association with the embedded curvatures. Asymptotic behaviors such as information loss and bias of the estimator are shown to be dependent on the curvatures of this manifold. Simulation studies are performed to compare the estimation error in AR(1) models with the corresponding results in the time domain.

Key words and phrases: ARMA model, differential geometry, Fisher information, information loss, Whittle estimator.