A robust approach for outlier imputation: Singular spectrum decomposition

Abstract

Singular spectrum analysis (SSA) is a nonparametric method for separating time series data into a sum of small numbers of interpretable components (signal + noise). One of the steps of the SSA method, which is referenced to Embedding, is extremely sensitive to contamination of outliers which are often founded in time series analysis. To reduce the effect of outliers, SSA based on Singular Spectrum Decomposition (SSD) method is proposed. In this article, the ability of SSA based on SSD and basic SSA are compared in time series reconstruction in the presence of outliers. It is noteworthy that the matrix norm used in Basic SSA is the Frobenius norm or L 2-norm. There is a newer version of SSA that is based on L 1-norm and called L 1-SSA. It was confirmed that L 1-SSA is robust against outliers. In this regard, this research is also introduced a new version of SSD based on L 1-norm which is called L 1-SSD. A wide empirical study on both simulated and real data verifies the efficiency of basic SSA based on SSD and L 1-norm in reconstructing the time series where polluted by outliers.