Intelligent Identification of Trend Components in Singular Spectrum Analysis

Abstract

Singular spectrum analysis (SSA) is a non-parametric adaptive technique used for time series analysis. It allows solving various problems related to time series without the need to define a model. In this study, we focus on the problem of trend extraction. To extract trends using SSA, a grouping of elementary components is required. However, automating this process is challenging due to the nonparametric nature of SSA. Although there are some known approaches to automated grouping in SSA, they do not work well when the signal components are mixed. In this paper, a novel approach that combines automated identification of trend components with separability improvement is proposed. We also consider a new method called EOSSA for separability improvement, along with other known methods. The automated modifications are numerically compared and applied to real-life time series. The proposed approach demonstrated its advantage in extracting trends when dealing with mixed signal components. The separability-improving method EOSSA proved to be the most accurate when the signal rank is properly detected or slightly exceeded. The automated SSA was very successfully applied to US Unemployment data to separate an annual trend from seasonal effects. The proposed approach has shown its capability to automatically extract trends without the need to determine their parametric form.

Keywords

• singular spectrum analysis
• time series decomposition
• trend extraction
• seasonality
• automated SSA