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On the choice of parameters in singular spectrum analysis and related subspace-based methods. (English) Zbl 1245.62108

Summary: We investigate methods related to both the Singular Spectrum Analysis (SSA) and subspace-based 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.

MSC:

62M15 Inference from stochastic processes and spectral analysis
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
65C60 Computational problems in statistics (MSC2010)
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