A Preliminary Investigation into the Effect of Outlier(s) on Singular Spectrum Analysis

Abstract

The aim of this paper is to study the effect of outliers on different parts of singular spectrum analysis (SSA) from both theoretical and practical points of view. The rank of the trajectory matrix, the magnitude of eigenvalues, reconstruction, and forecasting results are evaluated using simulated and real data sets. The performance of both recurrent and vector forecasting procedures are assessed in the presence of outliers. We find that the existence of outliers affect the rank of the matrix and increases the linear recurrent dimensions whilst also having a significant impact on SSA reconstruction and forecasting processes. There is also evidence to suggest that in the presence of outliers, the vector SSA forecasts are more robust in comparison to the recurrent SSA forecasts. These results indicate that the identification and removal of the outliers are mandatory to achieve optimal SSA decomposition and forecasting results.