This article proposes a Bayesian approach to estimating the spectral density of a stationary time series using a prior based on a mixture of P-spline distributions. Our proposal is motivated by the B-spline Dirichlet process prior of Edwards et al. (Stat Comput 29(1):67–78, 2019. https://doi.org/10.1007/s11222-017-9796-9) in combination with Whittle’s likelihood and aims at reducing the high computational complexity of its posterior computations. The strength of the B-spline Dirichlet process prior over the Bernstein–Dirichlet process prior of Choudhuri et al. (J Am Stat Assoc 99(468):1050–1059, 2004. https://doi.org/10.1198/016214504000000557) lies in its ability to estimate spectral densities with sharp peaks and abrupt changes due to the flexibility of B-splines with variable number and location of knots. Here, we suggest to use P-splines of Eilers and Marx (Stat Sci 11(2):89–121, 1996. https://doi.org/10.1214/ss/1038425655) that combine a B-spline basis with a discrete penalty on the basis coefficients. In addition to equidistant knots, a novel strategy for a more expedient placement of knots is proposed that makes use of the information provided by the periodogram about the steepness of the spectral power distribution. We demonstrate in a simulation study and two real case studies that this approach retains the flexibility of the B-splines, achieves similar ability to accurately estimate peaks due to the new data-driven knot allocation scheme but significantly reduces the computational costs.

本文提出了一种贝叶斯方法，该方法使用基于P样条分布混合的先验估计固定时间序列的频谱密度。我们的建议是由Edwards等人的B样条Dirichlet过程激发的。（Stat Comput 29（1）：67–78，2019. https://doi.org/10.1007/s11222-017-9796-9）结合Whittle的可能性，旨在降低其后验计算的高计算复杂性。B样条Dirichlet过程的强度要比Choudhuri等人先于Bernstein-Dirichlet过程的强度高。（J Am Stat Assoc 99（468）：1050-1059，2004. https://doi.org/10.1198/016214504000000557）在于能够估计具有尖峰和由于B样条的灵活性而突然改变的光谱密度的能力结的数量和位置可变。这里，我们建议使用Eilers和Marx的P样条曲线（Stat Sci 11（2）：89–121，1996. https://doi.org/10.1214/ss/1038425655），将B样条曲线基础与离散惩罚相结合根据系数。除了等距结以外，还提出了一种新的策略来更方便地放置结，该策略利用了周期图提供的有关频谱功率分布陡度的信息。我们在模拟研究和两个实际案例研究中证明，这种方法保留了B样条曲线的灵活性，由于新的数据驱动的结分配方案而获得了类似的准确估计峰的能力，但显着降低了计算成本。除了等距结以外，还提出了一种新的策略来更方便地放置结，该策略利用了周期图提供的有关频谱功率分布陡度的信息。我们在模拟研究和两个实际案例研究中证明，这种方法保留了B样条曲线的灵活性，由于新的数据驱动的结分配方案而获得了类似的准确估计峰的能力，但显着降低了计算成本。除了等距结以外，还提出了一种新的策略来更方便地放置结，该策略利用了周期图提供的有关频谱功率分布陡度的信息。我们在模拟研究和两个实际案例研究中证明，这种方法保留了B样条曲线的灵活性，由于新的数据驱动的结分配方案而获得了类似的准确估计峰的能力，但显着降低了计算成本。