Automatic Grouping in Singular Spectrum Analysis

Abstract

Singular spectrum analysis (SSA) is a non-parametric forecasting and filtering method that has many applications in a variety of fields such as signal processing, economics and time series analysis. One of the four steps of the SSA, which is called the grouping step, plays a pivotal role in the SSA because reconstruction and forecasting of results are directly affected by the outputs of this step. Usually, the grouping step of SSA is time consuming as the interpretable components are manually selected. An alternative more optimized approach is to apply automatic grouping methods. In this paper, a new dissimilarity measure between two components of a time series that is based on various matrix norms is first proposed. Then, using the new dissimilarity matrices, the capabilities of different hierarchical clustering linkages are compared to identify appropriate groups in the SSA grouping step. The performance of the proposed approach is assessed using the corrected Rand index as validation criterion and utilizing various real-world and simulated time series.