Premium
A Note on Window Length Selection in Singular Spectrum Analysis
Author(s) -
Atikur Rahman Khan M.,
Poskitt D. S.
Publication year - 2013
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/anzs.12027
Subject(s) - mathematics , singular spectrum analysis , window (computing) , spectrum (functional analysis) , mean squared error , singular value , algorithm , series (stratigraphy) , selection (genetic algorithm) , statistics , mathematical optimization , eigenvalues and eigenvectors , singular value decomposition , computer science , artificial intelligence , paleontology , physics , quantum mechanics , biology , operating system
Summary In singular spectrum analysis (SSA) window length is a critical tuning parameter that must be assigned by the practitioner. This paper provides a theoretical analysis of signal–noise separation and time series reconstruction in SSA that can serve as a guide to optimal window choice. We establish numerical bounds on the mean squared reconstruction error and present their almost sure limits under very general regularity conditions on the underlying data generating mechanism. We also provide asymptotic bounds for the mean squared separation error. Evidence obtained using simulation experiments and real data sets indicates that the theoretical properties are reflected in observed behaviour, even in relatively small samples, and the results indicate how, in practice, an optimal assignment for the window length can be made.