Dynamic functional principal components
成果类型：
Article
署名作者：
Hormann, Siegfried; Kidzinski, Lukasz; Hallin, Marc
署名单位：
Universite Libre de Bruxelles; Princeton University
刊物名称：
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
ISSN/ISSBN：
1369-7412
DOI：
10.1111/rssb.12076
发表日期：
2015
页码：
319-348
关键词：
摘要：
We address the problem of dimension reduction for time series of functional data (Xt:tZ). Such functional time series frequently arise, for example, when a continuous time process is segmented into some smaller natural units, such as days. Then each X-t represents one intraday curve. We argue that functional principal component analysis, though a key technique in the field and a benchmark for any competitor, does not provide an adequate dimension reduction in a time series setting. Functional principal component analysis indeed is a static procedure which ignores the essential information that is provided by the serial dependence structure of the functional data under study. Therefore, inspired by Brillinger's theory of dynamic principal components, we propose a dynamic version of functional principal component analysis which is based on a frequency domain approach. By means of a simulation study and an empirical illustration, we show the considerable improvement that the dynamic approach entails when compared with the usual static procedure.