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Keywords:

  • dimension;
  • embedding;
  • forecasting;
  • mean squared error;
  • signal–noise separation;
  • time series reconstruction;
  • window length

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.