An Imputation Method Based on the Varimax Variant of Multivariate Singular Spectrum Analysis

Abstract

Singular Spectrum Analysis (SSA) and its Multivariate extension (mSSA) are powerful tools for decomposing time series into ‘skeleton’ signals and residual noise. To address the issue of eigenvector mixing, Groth and Ghil (2011) introduced the varimax mSSA algorithm. Despite its widespread use, the detailed capabilities of varimax mSSA for handling noisy and incomplete time series have not been fully explored. In this study, we present a simple, yet effective imputation algorithm based on varimax mSSA, and conduct a comprehensive evaluation of its ability to extract dynamic signals with clearly physical interpretations from data with varying Noise levels and missing rates. Our findings show that varimax mSSA significantly reduces eigenvector mixing and improves the interpretability of reconstructed components. Analysis of both simulated and real-world GNSS time series demonstrates that varimax mSSA can accurately reconstruct the skeleton signal. Impressively, even under challenging conditions of 30% Noise and 50% data missing, the ‘skeleton’ signal extracted exhibits remarkable accuracy and consistency, achieving a normalized root-mean-square-error of 0.0884 and a correlation coefficient of 0.9883. This evidence highlights varimax mSSA’s effectiveness as a robust method for imputation and signal extraction in multivariate time series analysis.

Keywords

• Denoising
• imputation
• multivariate singular spectrum analysis
• time series
• varimax rotation