Information properties in spectral analysis of stationary time series

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.