A robust approach for outlier imputation: Singular spectrum decomposition

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 L2-norm. There is a newer version of SSA that is based on L1-norm and called L1-SSA. It was confirmed that L1-SSA is robust against outliers. In this regard, this research is also introduced a new version of SSD based on L1-norm which is called L1-SSD. A wide empirical study on both simulated and real data verifies the efficiency of basic SSA based on SSD and L1-norm in reconstructing the time series where polluted by outliers.