Generalized Dynamic Principal Components

• 成果类型: Article
• 署名作者: Pena, Daniel; Yohai, Victor J.
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2015.1072542
• 发表日期: 2016
• 页码: 1121-1131
• 关键词: MULTIPLE TIME-SERIES; factor models; number; identification

摘要

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 tocompute 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.