Statistics and Its Interface

Volume 12 (2019)

Number 4

Comparison between Basic and Toeplitiz SSA applied to non-stationary time-series

Pages: 527 – 536

DOI: https://dx.doi.org/10.4310/SII.2019.v12.n4.a3

Authors

Michel C. R. Leles (Department of Technology, Universidade Federal de São João del-Rei, Ouro Branco, MG, Brazil)

Mariana G. Moreira (Department of Technology, Universidade Federal de São João del-Rei, Ouro Branco, MG, Brazil)

Adriano S. Vale-Cardoso (Department of Technology, Universidade Federal de São João del-Rei, Ouro Branco, MG, Brazil)

Cairo L. Nascimento, Jr. (Electronics Engineering Division, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, Brazil)

Elton F. Sbruzzi (Division of Computer Science, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, Brazil)

Homero N. Guimarães (Department of Electrical Engineering, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil)

Abstract

A comparison between two approaches of Singular Spectrum Analysis (SSA) methodology is presented: the Basic and the Toeplitz SSA. These approaches differ in assumptions about some SSA properties. Toeplitz SSA assumes time-series stationarity, which means that the process needs to be mean-reverting. However, such assumption is not a necessary condition for the Basic SSA. Therefore, the applicability of the Toeplitz SSA to non-stationary signals is still an under discussion subject. In this paper both approaches are applied to this kind of signal. Similarities and differences between these techniques are addressed. The frequency domain interpretation of eigenvectors as well as forecasting performance are presented for both methodologies. Several computer simulations involving both synthetic and actual data time-series, using the same parameters, were executed in order to compare the studied SSA approaches. The obtained results suggest the Toeplitz SSA should not be used for non-stationary time-series before removing their trend component.

Keywords

singular spectrum analysis (SSA), non-stationary signals, Basic SSA, Toeplitz SSA

Full Text (PDF format)

Cairo L. Nascimento Jr. and Michel C. R. Leles gratefully acknowledge the support from FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo) under grants 2016/04992-6 and 2017/20248-8, respectively.

Received 27 June 2018

Accepted 26 March 2019

Published 18 July 2019