Dimension reduction techniques for multivariate time series decompose the observed series into a few useful independent/orthogonal univariate components. A spectral domain method is developed for multivariate second-order stationary time series that linearly transforms the observed series into several groups of lower-dimensional multivariate subseries. These multivariate subseries have non-zero spectral coherence among components within a group but have zero spectral coherence among components across groups. The observed series is expressed as a sum of frequency components whose variances are proportional to the spectral matrices at the respective frequencies. The demixing matrix is then estimated using an eigendecomposition on the sum of the variance matrices of these frequency components and its asymptotic properties are derived. Finally, a consistent test on the cross-spectrum of pairs of components is used to find the desired segmentation into the lower-dimensional subseries. The numerical performance of the proposed method is illustrated through simulation examples and an application to modeling and forecasting wind data is presented.

多元时间序列的降维技术将观察到的序列分解为几个有用的独立/正交单变量分量。针对多元二阶平稳时间序列开发了一种谱域方法，该方法将观察到的序列线性转换为几组低维多元子序列。这些多元子系列在一个组中的各个分量之间具有非零的光谱相干性，但是在组中的各个分量之间具有零的光谱相干性。观察到的序列表示为频率分量之和，其方差与相应频率处的频谱矩阵成比例。然后，使用特征分解对这些频率分量的方差矩阵之和进行估计，并推导出其渐近性质。最后，对成对的组件的跨谱进行一致性测试，以找到所需的细分为低维子系列。通过仿真实例说明了该方法的数值性能，并提出了在风数据建模和预报中的应用。