Fast Bayesian inference on spectral analysis of multivariate stationary time series
Fast Bayesian inference on spectral analysis of multivariate stationary time series
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DOI：
10.1016/j.csda.2022.107596
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发表时间：
2022-08
期刊：
影响因子：
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通讯作者：
Zhixiong Hu;R. Prado
中科院分区：
文献类型：
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作者：
Zhixiong Hu;R. Prado
频谱分析通过在频域中表示时间序列的特征来发现趋势、周期和其他特征。然而，当考虑多元时间序列时，随着分量数量的增加，谱密度矩阵的大小呈二次增长，使得估计和推理变得相当困难。提出的新贝叶斯框架考虑了基于Whittle似然的光谱建模方法，并对定义逆谱密度矩阵的Cholesky分解的每个分量的样条表示的系数施加了折扣正则马蹄先验。与目前可用的替代方法相比，提出的先验结构导致模型提供更高的后验精度。为了利用现代硬件（如GPU）的强大功能实现快速推理，提出了一种随机梯度变分贝叶斯方法，用于高度并行化的后验推理，为高维时间序列建模提供了计算灵活性。通过广泛的模拟研究和对两个数据集的分析，证明了所提出方法的准确经验性能：来自加利福尼亚州6个地点的风速数据，以及在特定实验条件下记录的两个对比受试者的61通道脑电图数据。
Spectral analysis discovers trends, periodic and other characteristics of a time series by representing these features in the frequency domain. However, when multivariate time series are considered, and the number of components increases, the size of the spectral density matrix grows quadratically, making estimation and inference rather challenging. The proposed novel Bayesian framework considers a Whittle likelihood-based spectral modeling approach and imposes a discounted regularized horseshoe prior on the coefficients that define a spline representation of each of the components of a Cholesky factorization of the inverse spectral density matrix. The proposed prior structure leads to a model that provides higher posterior accuracy when compared to alternative currently available approaches. To achieve fast inference that takes advantage of the massive power of modern hardware (e.g., GPU), a stochastic gradient variational Bayes approach is proposed for the highly parallelizable posterior inference that provides computational flexibility for modeling high-dimensional time series. The accurate empirical performance of the proposed method is illustrated via extensive simulation studies and the analysis of two datasets: a wind speed data from 6 locations in California, and a 61-channel electroencephalogram data recorded on two contrasting subjects under specific experimental conditions.