On the choice of parameters in Singular Spectrum Analysis and related subspace-based methods

TL;DR

This paper analyzes parameter selection in Singular Spectrum Analysis and related subspace methods, providing guidelines for minimizing errors based on problem type and residual characteristics through theoretical insights and simulations.

Contribution

It offers new recommendations for choosing parameters in SSA and subspace methods tailored to specific problem types and residual structures.

Findings

Optimal parameters depend on the problem and residual type.

Error behavior varies with deterministic or stochastic residuals.

Convergence rates are characterized for different residual structures.

Abstract

In the present paper 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.