Abstract:
Various nonparametric approaches for Bayesian spectral density estimation of
stationary time series have been suggested in the literature, mostly based on
the Whittle likelihood approximation. A generalization of this approximation
has been proposed in Kirch et al. who prove posterior consistency for spectral
density estimation in combination with the Bernstein-Dirichlet process prior
for Gaussian time series. In this paper, we will extend the posterior
consistency result to non-Gaussian time series by employing a general
consistency theorem of Shalizi for dependent data and misspecified models. As a
special case, posterior consistency for the spectral density under the Whittle
likelihood as proposed by Choudhuri, Ghosal and Roy is also extended to
non-Gaussian time series. Small sample properties of this approach are
illustrated with several examples of non-Gaussian time series.
