On Estimation of the Spectral Density Based on the Whittle likelihood for Linear Short Memory Gaussian Process

• Activity Number: 238
• Type: Invited
• Date/Time: Tuesday, August 13, 2002 : 2:00 PM to 3:50 PM
• Sponsor: Business & Economics Statistics Section*
• Author(s): Anindya Roy*+
• Affiliation(s): University of Maryland, Baltimore County
• Keywords: nonparametric Bayes ; Bernstein polynomial ; posterior consistency

Abstract

Many estimators of the spectral density of a linear process are derived using the Whittle likelihood. Proof of consistency under the Whittle measure is not enough to show consistency of the estimators under the original likelihood. We show that for a linear Gaussian process the probability measure induced by the exact likelihood and the Whittle likelihood are contiguous. Thus, it is sufficient to show consistency under the Whittle likelihood. In the second part of the talk we propose a non-parametric Bayesian estimator for the spectral density of a linear short memory Gaussian process using Bernstein polynomial priors. We show that the posterior distribution and the posterior expectation as a point estimate are consistent.