Difference-based Methods for Truncating the Singular Value Decomposition. Issue 3 (15th March 2016)

• Record Type: Journal Article
• Authors: Evans, Dafydd; Gillard, Jonathan
• Is Part Of: Communications in statistics. Volume 45:Issue 3(2016)
• Page Start: 863
• Page End: 879
• Publication Date: 2016-03-15
• Subjects: Difference-based methods -- Singular value decomposition -- Time series analysis; Primary 62M10 -- Secondary 15A18; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2013.875572
• Languages: English
• ISSNs: 0361-0918

Abstract

Abstract : Given a noisy time series (or signal), one may wish to remove the noise from the observed series. Assuming that the noise-free series lies in some low-dimensional subspace of rank r, a common approach is to embed the noisy time series into a Hankel trajectory matrix. The singular value decomposition is then used to deconstruct the Hankel matrix into a sum of rank-one components. We wish to demonstrate that there may be some potential in using difference-based methods of the observed series in order to provide guidance regarding the separation of the noise from the signal, and to estimate the rank of the low-dimensional subspace in which the true signal is assumed to lie.