Bayesian Nonparametric Spectral Density Estimation

• Activity Number: 433
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Ori Rosen*+ and Sally Wood and Robert Kohn
• Companies: Univ of Texas at El Paso and Melbourne Business School and University of New South Wales
• Keywords: MCMC ; Spectral Density ; Whittle's Likelihood

Abstract

The Whittle approximation was originally devised for approximating the likelihood of a stationary Gaussian process based on the asymptotic properties of the periodogram. Subsequent results have shown that estimation based on Whittle's approximation and that based on the exact Gaussian likelihood are asymptotically equivalent. Results have also been obtained in cases where the underlying distribution is not Gaussian. Whittle's approximation is a function of the periodogram and of the unknown spectral density, which makes it useful for spectral density estimation. A common method for nonparametric estimation of the spectral density is based on a log-linear model in which the log periodogram is expressed as a sum of the log spectral density and an error term which follows a log chi-squared distribution. In this paper we propose to replace the log chi-squared distribution with a mixture of normal densities in order to improve the approximation in non-Gaussian settings. The model is formulated in a Bayesian framework and inference is performed via Markov chain Monte Carlo methods. We explore the resulting estimates by applying the method to real data, as well as to simulated data.