On singular spectrum analysis and stepwise time series reconstruction

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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.

Original languageEnglish
Pages (from-to)67-94
Number of pages28
JournalJournal of Time Series Analysis
Issue number1
Publication statusPublished - Jan 2020


  • Grenander process
  • principle components
  • re-scaled trajectory matrix
  • signal-noise reconstruction
  • singular value decomposition
  • unobserved components
  • Wold decomposition

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