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.
翻译:文献中提出了关于巴耶斯光谱光谱密度估计固定时间序列的各种非参数性方法,主要依据惠特尔概率近似值;Kirch等人建议对这一近似值进行概括化,Kirch等人证明光谱密度估计与Gaussian时间序列之前的Bernstein-Dirichlet进程相结合,在光谱密度估计与Gaussian时间序列之前的Bernstein-Dirichlet进程相结合,在Kirch等人中也证明了光谱密度的后方一致性;在本文中,我们将将后方一致性结果扩大到非Gausian时间序列,对依赖数据和错误描述模型采用一般一致的Shalizi理论;作为特殊情况,Choudhuri、Ghosal和Roy提出的惠特尔概率光谱密度的后方一致性也扩大到非Gausian时间序列;在非Gausisian时间序列中,以若干非Gausian时间序列的例子来说明这一方法的小型样本特性。