A robust approach to singular spectrum analysis

Abstract

Singular spectrum analysis (SSA) is a nonparametric method for time series analysis and forecasting that incorporates elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems, and signal processing. Although this technique has shown to be advantageous over traditional model‐based methods, in particular, one of the steps of the SSA algorithm, which refers to the singular value decomposition (SVD) of the trajectory matrix, is highly sensitive to data contamination. Specifically, and because SVD decomposition is least squares based, the presence of a single outlier, if extreme, may be enough to draw the leading principal component towards itself resulting in possible misinterpretations, which may subsequently, in particular and in the case of time series analysis, lead to reduced quality of model fit and forecast accuracy. In order to alleviate this problem, a robust SSA algorithm is proposed, where a robust SVD procedure replaces the least squares based one in the original SSA procedure. The SSA and the robust SSA approaches are compared in terms of model fit quality via Monte Carlo simulations that contemplate both clean and noisy/contaminated time series. The adequacy and value of the proposed approach is then compared with the standard SSA using real data about the industrial production index.

The Decomposition and Forecasting of Mutual Investment Funds Using Singular Spectrum Analysis

“…Very few studies were made in order to access effects of outliers in SSA and to generalize this methodology [ 21 , 22 ]. A first attempt to robustify the SSA by considering an SVD based on a robust norm [ 24 ] instead of the norm used in the classical algorithm, was proposed by [ 23 ]. That robust generalization was compared with the classical SSA algorithm for model fit by these authors.…”

“…That robust generalization was compared with the classical SSA algorithm for model fit by these authors. In this subsection we review that robust SSA algorithm proposed by [ 23 ] and propose a new robust algorithm for SSA that considers the SVD based on the Huber function [ 25 ] and also propose an algorithm for robust SSA model forecasting. While the robust algorithms based on the norm are very popular, they have difficulties in handling heavy tail outliers.…”

“…The robust SSA algorithm proposed by [ 23 ] replaces the classical SVD based on the least squares norm, by the robust SVD algorithm based on the norm [ 24 ]. This robust SVD is performed iteratively, starting with an initial estimate of the first left singular vector and leading to an outlier-resistant approach that also allows for missing data.…”

“…Very few attempts have been made in order to access the effect of the presence of outliers in the data while conducting a SSA. One study [ 21 , 22 ] presented some preliminary results on the effect of outliers in singular spectrum analysis, and [ 23 ] made a first attempt to robustify the SSA by considering an SVD based on a robust norm [ 24 ] instead of the norm used in the classical algorithm, which they used for model fit.…”

“…In this paper we go one step further than [ 23 ] and propose a new robust algorithm for SSA that considers the SVD based on the Huber function [ 25 ]. Moreover, we propose two robust SSA forecasting algorithms, one based on the the norm and another based on the Huber function.…”