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On Singular Spectrum Analysis And Stepwise Time Series Reconstruction
Author(s) -
Poskitt Donald S.
Publication year - 2020
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12479
Subject(s) - mathematics , singular spectrum analysis , series (stratigraphy) , time series , spectral analysis , population , statistics , sample (material) , statistical physics , algorithm , singular value decomposition , demography , chemistry , chromatography , spectroscopy , sociology , paleontology , physics , quantum mechanics , biology
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.