Bayesian mixture modeling for spectral density estimation

Abstract

We develop a Bayesian modeling approach for spectral densities built from a local Gaussian mixture approximation to the Whittle log-likelihood. The implied model for the log-spectral density is a mixture of linear functions with frequency-dependent logistic weights, which allows for general shapes for smooth spectral densities. The proposed approach facilitates efficient posterior simulation as it casts the spectral density estimation problem in a mixture modeling framework for density estimation. The methodology is illustrated with synthetic and real data sets.