论文标题
使用多元时间序列的频率分量的主成分分析
Principal Component Analysis using Frequency Components of Multivariate Time Series
论文作者
论文摘要
多变量时间序列的尺寸还原技术将观察到的系列分解为一些有用的独立/正交单变量组件。我们开发了一种用于多元二阶固定时间序列的光谱域方法，该方法将观察到的序列线性地转换为几组较低维度的多元下属。这些多元子研究在组中的组件之间具有非零的光谱相干性，但是组件之间组件之间的光谱相干性为零。观察到的序列表示为频率成分的总和，其方差与各个频率下的光谱矩阵成正比。然后，使用对这些频率分量的方差矩阵总和及其渐近特性的特征分类来估算解散矩阵。最后，对成对成分的跨光谱进行一致的测试用于找到所需的分割到较低维度的子层中。通过仿真示例说明了所提出方法的数值性能，并提出了建模和预测风数据的应用。
Dimension reduction techniques for multivariate time series decompose the observed series into a few useful independent/orthogonal univariate components. We develop a spectral domain method 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.
