Functional Singular Spectrum Analysis

Abstract

In this paper, we introduce a new extension of the Singular Spectrum Analysis (SSA) called functional SSA to analyze functional time series. The new methodology is developed by integrating ideas from functional data analysis and univariate SSA. We explore the advantages of the functional SSA in terms of simulation results and with an application to a call center data. We compare the proposed approach with Multivariate SSA (MSSA) and Functional Principal Component Analysis (FPCA). The results suggest that further improvement to MSSA is possible and the new method provides an attractive alternative to the novel extensions of the FPCA for correlated functions. We have also developed an efficient and user-friendly R package and a shiny web application to allow interactive exploration of the results.