On the choice of parameters in singular spectrum analysis and related subspace-based methods

TLDR: This paper investigates methods related to both the Singular Spectrum Analysis (SSA) and subspace-based methods in signal processing and describes common and specific features of these methods and considers different kinds of problems solved by them such as signal reconstruction, forecasting and parameter estimation.

Abstract: In the present paper we investigate methods related to both the Singular Spectrum Analysis (SSA) and subspacebased methods in signal processing. We describe common and specific features of these methods and consider different kinds of problems solved by them such as signal reconstruction, forecasting and parameter estimation. General recommendations on the choice of parameters to obtain minimal errors are provided. We demonstrate that the optimal choice depends on the particular problem. For the basic model ‘signal + residual’ we show that the error behavior depends on the type of residuals, deterministic or stochastic, and whether the noise is white or red. The structure of errors and the convergence rate are also discussed. The analysis is based on known theoretical results and extensive computer simulations. AMS 2000 subject classifications: Primary 62M20, 62F10, 62F12; secondary 60G35, 65C20, 62G05.