Based on a novel dynamic Whittle likelihood approximation for locally stationary processes, a Bayesian nonparametric approach to estimating the time-varying spectral density is proposed. This dynamic frequency-domain based likelihood approximation is able to depict the time-frequency evolution of the process by utilizing the moving periodogram previously introduced in the bootstrap literature. The posterior distribution is obtained by updating a bivariate extension of the Bernstein-Dirichlet process prior with the dynamic Whittle likelihood. Asymptotic properties such as sup-norm posterior consistency and L2-norm posterior contraction rates are presented. Additionally, this methodology enables model selection between stationarity and non-stationarity based on the Bayes factor. The finite-sample performance of the method is investigated in simulation studies and applications to real-life data-sets are presented.

翻译：基于针对局部平稳过程提出的新型动态Whittle似然近似方法，本文提出了一种估计时变谱密度的贝叶斯非参数方法。这种基于动态频域的似然近似能够通过利用先前在Bootstrap文献中引入的移动周期图来刻画过程的时频演化。通过用动态Whittle似然更新Bernstein-Dirichlet过程先验的二元扩展形式，得到后验分布。本文给出了上确界范数后验一致性和L2范数后验收缩率等渐近性质。此外，该方法基于贝叶斯因子实现了平稳性与非平稳性之间的模型选择。通过模拟研究考察了方法的有限样本性能，并展示了其在真实数据集上的应用。