This paper presents a novel approach to Bayesian nonparametric spectral analysis of stationary multivariate time series. Starting with a parametric vector-autoregressive model, the parametric likelihood is nonparametrically adjusted in the frequency domain to account for potential deviations from parametric assumptions. We show mutual contiguity of the nonparametrically corrected likelihood, the multivariate Whittle likelihood approximation and the exact likelihood for Gaussian time series. A multivariate extension of the nonparametric Bernstein-Dirichlet process prior for univariate spectral densities to the space of Hermitian positive definite spectral density matrices is specified directly on the correction matrices. An infinite series representation of this prior is then used to develop a Markov chain Monte Carlo algorithm to sample from the posterior distribution. The code is made publicly available for ease of use and reproducibility. With this novel approach we provide a generalization of the multivariate Whittle-likelihood-based method of Meier et al. (2020) as well as an extension of the nonparametrically corrected likelihood for univariate stationary time series of Kirch et al. (2019) to the multivariate case. We demonstrate that the nonparametrically corrected likelihood combines the efficiencies of a parametric with the robustness of a nonparametric model. Its numerical accuracy is illustrated in a comprehensive simulation study. We illustrate its practical advantages by a spectral analysis of two environmental time series data sets: a bivariate time series of the Southern Oscillation Index and fish recruitment and time series of windspeed data at six locations in California.

翻译：本文提出一种新颖的贝叶斯非参数谱分析方法，用于平稳多元时间序列。该方法以参数向量自回归模型为起点，在频域中对参数似然进行非参数化调整，以应对参数假设可能存在的偏差。我们证明了修正后的非参数似然、多元Whittle似然近似以及高斯时间序列精确似然之间的相互邻接性。将针对单变量谱密度的非参数Bernstein-Dirichlet过程先验进行多元扩展，直接定义于厄米特正定谱密度矩阵的修正矩阵空间上。利用该先验的无穷级数表示，我们开发了一种马尔可夫链蒙特卡洛算法，用于从后验分布中采样。为便于使用和结果复现，相关代码已公开发布。通过这一新方法，我们不仅推广了Meier等（2020）基于多元Whittle似然的方法，还将Kirch等（2019）针对单变量平稳时间序列的修正非参数似然扩展至多元情形。研究表明，修正后的非参数似然有效融合了参数模型的高效性与非参数模型的稳健性。通过综合模拟研究验证了其数值精度，并通过两个环境时间序列数据集的谱分析展示了其实用优势：包括南方涛动指数与鱼类补充量的双变量时间序列，以及加利福尼亚州六个测风站的风速时间序列。