Generalized Dynamic Principal Components
提出一种全新的经验性动态主成分方法，不要求主成分是观测的线性组合，可基于多种损失函数（包括稳健损失），能更好适应非平稳序列和异常值污染，并给出适用于高维数据的迭代算法。
Brillinger defined dynamic principal components (DPC) for time series based on a reconstruction criterion. He gave a very elegant theoretical solution and proposed an estimator which is consistent under stationarity. Here, we propose a new enterally empirical approach to DPC. The main differences with the existing methods—mainly Brillinger procedure—are (1) the DPC we propose need not be a linear combination of the observations and (2) it can be based on a variety of loss functions including robust ones. Unlike Brillinger, we do not establish any consistency results; however, contrary to Brillinger’s, which has a very strong stationarity flavor, our concept aims at a better adaptation to possible nonstationary features of the series. We also present a robust version of our procedure that allows to estimate the DPC when the series have outlier contamination. We give iterative algorithms to compute the proposed procedures that can be used with a large number of variables. Our nonrobust and robust procedures are illustrated with real datasets. Supplementary materials for this article are available online.