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.
Highlights
Singular spectrum analysis (SSA) is a non-parametric technique that is increasingly becoming a standard tool in the field of time series analysis
In order to enable a better comparison based on the corrected Rand (CR) index, a dashed horizontal line y = 1 is added to all figures of the CR index
We have proposed a novel dissimilarity measure between components of a time series based on various matrix norms such as Frobenius, L1-norm, 1-norm, 2-norm and so on
Summary
Singular spectrum analysis (SSA) is a non-parametric technique that is increasingly becoming a standard tool in the field of time series analysis. While the review of theory and applications of automatic grouping via the frequency-based method is beyond the scope of this paper, the interested reader is referred to the whole and precise details on this topic that are explained in [1,3,29,31]. The elementary components are grouped automatically via distance-based clustering techniques such as hierarchical methods. It seems that this interesting approach is an straightforward process, one question that needs to be asked is which clustering method can provide an accurate and reasonable grouping.
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