Semi-nonparametric singular spectrum analysis with projection

TL;DR

This paper introduces a semi-nonparametric extension of singular spectrum analysis that incorporates prior structural information via projections, significantly improving polynomial trend extraction, especially for linear trends, over traditional SSA.

Contribution

The paper proposes SSA with projection, a novel semi-nonparametric method that enhances trend extraction by incorporating prior structural information through projections.

Findings

SSA with projection outperforms Basic SSA in extracting polynomial trends.

The method effectively extracts linear trends compared to least-squares regression.

Numerical examples demonstrate improved accuracy in trend detection.

Abstract

Singular spectrum analysis (SSA) is considered for decomposition of time series into identifiable components. The Basic SSA method is nonparametric and constructs an adaptive expansion based on singular value decomposition. The investigated modification is able to take into consideration a structure given in advance and therefore can be called semi-nonparametric. The approach called SSA with projection includes preliminary projections of rows and columns of the series trajectory matrix to given subspaces. One application of SSA with projection is the extraction of polynomial trends, e.g., a linear trend. It is shown that SSA with projection can extract polynomial trends much better than Basic SSA, especially for linear trends. Numerical examples including comparison with the least-square approach to polynomial regression are presented.