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On signal and extraneous roots in Singular Spectrum Analysis

On signal and extraneous roots in Singular Spectrum Analysis
On signal and extraneous roots in Singular Spectrum Analysis
In the present paper we study properties of roots of characteristic polynomials for the linear recurrent formulae (LRF) that govern time series. We also investigate how the values of these roots affect Singular Spectrum Analysis implications, in what concerns separation of components, SSA forecasting and related signal parameter estimation methods. The roots of the characteristic polynomial for an LRF comprise the signal roots, which determine the structure of the time series, and extraneous roots. We show how the separability of two time series can be characterized in terms of their signal roots. All possible cases of exact separability are enumerated. We also examine properties of extraneous roots of the LRF used in SSA forecasting algorithms, which is equivalent to the Min-Norm vector in subspace-based estimation methods. We apply recent theoretical results for orthogonal polynomials on the unit circle, which enable us to precisely describe the asymptotic distribution of extraneous roots relative to the position of the signal roots.
281-295
Usevich, Konstantin
1ab9effb-9945-40b6-94d7-f94dd0339110
Usevich, Konstantin
1ab9effb-9945-40b6-94d7-f94dd0339110

Usevich, Konstantin (2010) On signal and extraneous roots in Singular Spectrum Analysis. Statistics and Its Interface, 3 (3), 281-295.

Record type: Article

Abstract

In the present paper we study properties of roots of characteristic polynomials for the linear recurrent formulae (LRF) that govern time series. We also investigate how the values of these roots affect Singular Spectrum Analysis implications, in what concerns separation of components, SSA forecasting and related signal parameter estimation methods. The roots of the characteristic polynomial for an LRF comprise the signal roots, which determine the structure of the time series, and extraneous roots. We show how the separability of two time series can be characterized in terms of their signal roots. All possible cases of exact separability are enumerated. We also examine properties of extraneous roots of the LRF used in SSA forecasting algorithms, which is equivalent to the Min-Norm vector in subspace-based estimation methods. We apply recent theoretical results for orthogonal polynomials on the unit circle, which enable us to precisely describe the asymptotic distribution of extraneous roots relative to the position of the signal roots.

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1006.3436v1 - Author's Original
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Published date: 2010
Organisations: Southampton Wireless Group

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Local EPrints ID: 272928
URI: http://eprints.soton.ac.uk/id/eprint/272928
PURE UUID: a4c6f3ba-7e23-4d1d-950d-f69bd59274da

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Date deposited: 14 Oct 2011 15:56
Last modified: 14 Mar 2024 10:12

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Author: Konstantin Usevich

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