Weighted norms in subspace-based methods for time series analysis

Gillard, J. W. ORCID: https://orcid.org/0000-0001-9166-298X and Zhigljavsky, A. A. ORCID: https://orcid.org/0000-0003-0630-8279 2016. Weighted norms in subspace-based methods for time series analysis. Numerical Linear Algebra with Applications 23 (5) , pp. 947-967. 10.1002/nla.2062

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Abstract

Many modern approaches of time series analysis belong to the class of methods based on approximating high-dimensional spaces by low-dimensional subspaces. A typical method would embed a given time series into a structured matrix and find a low-dimensional approximation to this structured matrix. The purpose of this paper is twofold: (i) to establish a correspondence between a class of SVD-compatible matrix norms on the space of Hankel matrices and weighted vector norms (and provide methods to construct this correspondence) and (ii) to motivate the importance of this for problems in time series analysis. Examples are provided to demonstrate the merits of judiciously selecting weights on imputing missing data and forecasting in time series. Copyright © 2016 John Wiley & Sons, Ltd.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	time series analysis; low-rank approximation; missing values and forecasting
Publisher:	Wiley
ISSN:	1070-5325
Date of First Compliant Deposit:	23 August 2016
Date of Acceptance:	19 July 2016
Last Modified:	25 Nov 2024 01:30
URI:	https://orca.cardiff.ac.uk/id/eprint/93902

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