Multivariate Singular Spectrum Analysis by Robust Diagonalwise Low-Rank Approximation

TL;DR

This paper introduces RODESSA, a robust multivariate singular spectrum analysis method that effectively handles outliers in complex time series data, improving accuracy over traditional MSSA methods.

Contribution

The paper proposes a novel robust low-rank approximation technique for MSSA, enhancing outlier resistance and providing a new visualization tool, with proven convergence and practical validation.

Findings

RODESSA outperforms existing methods in simulations.

It effectively detects and visualizes outliers.

Application to temperature data demonstrates practical utility.

Abstract

Multivariate Singular Spectrum Analysis (MSSA) is a powerful and widely used nonparametric method for multivariate time series, which allows the analysis of complex temporal data from diverse fields such as finance, healthcare, ecology, and engineering. However, MSSA lacks robustness against outliers because it relies on the singular value decomposition, which is very sensitive to the presence of anomalous values. MSSA can then give biased results and lead to erroneous conclusions. In this paper a new MSSA method is proposed, named RObust Diagonalwise Estimation of SSA (RODESSA), which is robust against the presence of cellwise and casewise outliers. In particular, the decomposition step of MSSA is replaced by a new robust low-rank approximation of the trajectory matrix that takes its special structure into account. A fast algorithm is constructed, and it is proved that each iteration step decreases the objective function. In order to visualize different types of outliers, a new graphical display is introduced, called an enhanced time series plot. An extensive Monte Carlo simulation study is performed to compare RODESSA with competing approaches in the literature. A real data example about temperature analysis in passenger railway vehicles demonstrates the practical utility of the proposed approach.