Statistics and Its Interface
Volume 12 (2019)
Comparison between Basic and Toeplitiz SSA applied to non-stationary time-series
Pages: 527 – 536
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.
singular spectrum analysis (SSA), non-stationary signals, Basic SSA, Toeplitz SSA
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