On singular spectrum analysis and stepwise time series reconstruction

This article provides a detailed statistical analysis of a new approach to singular spectrum analysis (SSA). It examines SSA constructed using re-scaled trajectories (RT-SSA) and presents a theoretical analysis of RT-SSA under very general conditions concerning the structure of the observed series. The spectral features of population ensemble models implicit in the large sample properties of RT-SSA are investigated, motivating a new time series modelling methodology based on a stepwise application of RT-SSA. The operation of the theoretical results is illustrated via numerical examples involving trend stationary and difference stationary processes, and a random walk with drift. An analysis of the S&P 500 index also serves as a vehicle to demonstrate the practical impact of the stepwise RT-SSA processing methodology.