Posterior consistency for the spectral density of non‐Gaussian stationary time series
将高斯时间序列谱密度估计的后验一致性结果推广到非高斯情形，并证明Whittle似然下谱密度后验一致性对非高斯序列也成立，通过实例展示小样本性质。
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 involving a nonparametric correction of a parametric likelihood has been proposed in the literature with a proof of posterior consistency for spectral density estimation in combination with the Bernstein–Dirichlet process prior for Gaussian time series. In this article, we will extend the posterior consistency result to non‐Gaussian time series by employing a general consistency theorem for dependent data and misspecified models. As a special case, posterior consistency for the spectral density under the Whittle likelihood is also extended to non‐Gaussian time series. Small sample properties of this approach are illustrated with several examples of non‐Gaussian time series.