Treffer: Approximate Projectors in Singular Spectrum Analysis: Approximate projectors in singular spectrum analysis

The authors present an approach to the singular spectrum analysis (SSA) using an effective and numerically stable high-degree polynomial approximation of a spectral projector, which also provides a means of time-series forecasting. The method of computing \(X_I =\sum_{i\in I} X_i\) (where \(I\) is a set of indices for which the singular-value decomposition elements \(X_i\) are defined) without performing the spectral decomposition of the lag-covariance matrix. For large time series and correspondingly large matrices, as the authors mention, their method offers a faster alternative and open way for noise-reduction applications of the SSA method. Further, the authors present a geometric forecasting algorithm based on the approximate spectral projector and demonstrate the practical applicability of their methods.