A comparison of stepwise common singular spectrum analysis and horizontal multi-channel singular spectrum analysis

The problem of forecasting a time series by using information provided by a second time series is considered. Two multivariate extensions of Singular Spectrum Analysis (SSA) are compared in terms of forecast error: Horizontal Multi-channel SSA and Stepwise Common SSA. Different signal structures, defined in terms of trend, period, amplitude and phase, are investigated. In broad terms we find that neither Horizontal Multichannel SSA nor Stepwise Common SSA is best in all cases. Horizontal MSSA is outperformed particularly in cases where different trends are considered.