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

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. (AU)