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

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.

Keywords

singular spectrum analysis, time series analysis, subspace-based methods, signal processing, forecasting, linear recurrent formula, esprit, frequency estimation

2010 Mathematics Subject Classification

Primary 62F10, 62F12, 62M20. Secondary 60G35, 62G05, 65C20.

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Published 1 January 2010