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On Singular Spectrum Analysis And Stepwise Time Series Reconstruction

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  • Donald S. Poskitt

Abstract

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.

Suggested Citation

  • Donald S. Poskitt, 2020. "On Singular Spectrum Analysis And Stepwise Time Series Reconstruction," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(1), pages 67-94, January.
    • Handle: RePEc:bla:jtsera:v:41:y:2020:i:1:p:67-94
    DOI: 10.1111/jtsa.12479
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