Optimal dimension reduction for high-dimensional and functional time series

Marc Hallin, Siegfried Hörmann and Marco Lippi
Additional contact information
Siegfried Hörmann: Université libre de Bruxelles

Statistical Inference for Stochastic Processes, 2018, vol. 21, issue 2, No 8, 385-398

Abstract: Abstract Dimension reduction techniques are at the core of the statistical analysis of high-dimensional and functional observations. Whether the data are vector- or function-valued, principal component techniques, in this context, play a central role. The success of principal components in the dimension reduction problem is explained by the fact that, for any $$K\le p$$ K ≤ p , the K first coefficients in the expansion of a p-dimensional random vector $$\mathbf{X}$$ X in terms of its principal components is providing the best linear K-dimensional summary of $$\mathbf X$$ X in the mean square sense. The same property holds true for a random function and its functional principal component expansion. This optimality feature, however, no longer holds true in a time series context: principal components and functional principal components, when the observations are serially dependent, are losing their optimal dimension reduction property to the so-called dynamic principal components introduced by Brillinger in 1981 in the vector case and, in the functional case, their functional extension proposed by Hörmann, Kidziński and Hallin in 2015.

Keywords: Dimension reduction; Time series; Principal components; Functional principal components; Dynamic principal components; Karhunen–Loève expansion (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s11203-018-9172-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
Working Paper: Optimal Dimension Reduction for High-dimensional and Functional Time Series (2017)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sistpr:v:21:y:2018:i:2:d:10.1007_s11203-018-9172-1

Ordering information: This journal article can be ordered from
http://www.springer. ... ty/journal/11203/PS2

DOI: 10.1007/s11203-018-9172-1

Access Statistics for this article

Statistical Inference for Stochastic Processes is currently edited by Denis Bosq, Yury A. Kutoyants and Marc Hallin

More articles in Statistical Inference for Stochastic Processes from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().