EXSSA: SSA-based reconstruction of time series via exponential smoothing of covariance eigenvalues

A critical aspect of singular spectrum analysis (SSA) is the reconstruction of the original time series under various assumptions about its underlying structure. This reconstruction depends on the choice of the components from the covariance decomposition of the trajectory matrix. In most applications, this selection is based on the prior knowledge and experience of the researcher and a variety of practical rules. This paper suggests an alternative “fully automated” approach where all components of the covariance decomposition are used via exponential smoothing of the covariance eigenvalues. We illustrate the validity of the proposed approximation via simulations on different data generating processes. A second contribution of the paper is the proposal of a “forecast revision” algorithm which combines SSA with a benchmark. An empirical exercise using four key macroeconomic variables shows how this method can be used to improve the out-of-sample forecasts of any given benchmark model. Our results suggest that the proposed method has the potential to partly automate the use of SSA.