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:基于动态 Whittle 似然逼近局部平稳过程的时间变化谱密度,提出了贝叶斯非参数方法估计时间变化谱密度。该动态频域似然逼近能够利用引入自 bootstrap 文献中的移动周期图来描述过程的时频演变。通过使用动态 Whittle 似然度量更新 Bernstein-Dirichlet 过程先验的二元扩展,获得后验分布。文中还提出了极限性质,例如超级范数后验一致性和 L2-范数后验收缩率。此外,这种方法还能基于贝叶斯因子在平稳性和非平稳性之间进行模型选择。通过模拟研究探究了该方法的有限样本性能,并给出了对真实数据集的实际应用。