This article improves on existing Bayesian methods to estimate the spectral density of stationary and nonstationary time series assuming a Gaussian process prior. By optimising an appropriate eigendecomposition using a smoothing spline covariance structure, our method more appropriately models data with both simple and complex periodic structure. We further justify the utility of this optimal eigendecomposition by investigating the performance of alternative covariance functions other than smoothing splines. We show that the optimal eigendecomposition provides a material improvement, while the other covariance functions under examination do not, all performing comparatively well as the smoothing spline. During our computational investigation, we introduce new validation metrics for the spectral density estimate, inspired from the physical sciences. We validate our models in an extensive simulation study and demonstrate superior performance with real data.

本文改进了现有的贝叶斯方法，以在假设高斯过程先验的情况下估计平稳和非平稳时间序列的谱密度。通过使用平滑样条协方差结构优化适当的特征分解，我们的方法更适合对具有简单和复杂周期结构的数据进行建模。我们通过研究除平滑样条曲线之外的替代协方差函数的性能，进一步证明了这种最佳特征分解的效用。我们表明，最佳特征分解提供了实质性的改进，而正在检查的其他协方差函数没有，所有这些都与平滑样条曲线相比表现得更好。在我们的计算研究中，我们为光谱密度估计引入了新的验证指标，其灵感来自物理科学。