Generalized dynamic principal components Articles uri icon

publication date

  • January 2016

start page

  • 1121

end page

  • 1131

issue

  • 515

volume

  • 111

international standard serial number (ISSN)

  • 0162-1459

electronic international standard serial number (EISSN)

  • 1537-274X

abstract

  • 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.

keywords

  • Dimensionality reduction;
    Reconstruction of data;
    Vector time series